Document text
Reference
9°*eAv o*
NBS
PUBLICATIONS
NAT'L INST. OF STAND & TECH
A 1 1 1 □ b □ 3 M fl 3 7
PACKAGE CHECKING
FIELD MANUAL
U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
To Accompany
NBS Handbook 133:
CHECKING THE
NET CONTENTS
OF PACKAGED GOODS
[ -oc— ; NBSIR 85-3172
^ 100 I
.1156
85=3172
1985
£ /
(NATIONAL BUREAU
X QF STANDARDS
X library
Alg;
/?£r
PACKAGE CHECKING FIELD MANUAL
TO ACCOMPANY NBS HANDBOOK 133
"CHECKING THE NET CONTENTS OF PACKAGED GOODS"
Carroll S. Brickenkamp
Stephen Hasko
Mary G. Natrella
NATIONAL BUREAU OF STANDARDS
i
INDEX
Page
INTRODUCTION 1
SECTION 1. TEST PROCEDURE OUTLINES 3
Outline of Package Test-Core Method 5
Category A or B, Standard Pack by Weight 6
Random Pack, Category B, Dry Tare 9
Packages Labeled by Liquid Volume 11
Packages Labeled by Count 14
SECTION 2. SAMPLING PLANS 17
Table 2-5. Sampling Plans of Category B 19
Table 2-2. Sampling Plans of Category A 20
Table 2-3. Values of 0.8598/-/H for Sample
Size n 21
Table 2-4. Values of f for Percent of Lot
Sampled 21
Appendix H. Calculation of the Average
Range 22
Table 5-1. Sampling Plans for Packages
Labeled by Low Count 24
Table 5-2. Sampling Plans for Packages
Given Tolerances 25
SECTION 3.. VARIABLE TARE 27
Table 2-6. Initial Tare Sample Size for
Alternative Tare Procedure 29
Table 2-7. Total Number of Packages to be
Opened for Tare 30
Table 3-2. Test Allowances for Foam Products 32
SECTION 4. WEIGHING RULES
33
Table 3-1. Recommended Maximum Units of Measure
to be Used in Recording
Package Weights 35
Table 4-1. Weighing Devices Appropriate to Use
to Check Common Consumer Products
Labeled by Liquid Volume 36
Table 4-2. Recommended Maximum Units of Measure
to be Used for Recording the
Weights of Packaged Goods
Labeled by Liquid Volume 37
Table 4-3. Permitted Difference in Weights of Two
Equal Quantities According to the
Type of Scale Used to Weigh 38
SECTION 5. MAV's 39
Table 2-8. MAV's for an Individual Package
Labeled by Weight 41
Table 2-9. MAV's for an Individual Package
Labeled by Volume 43
Table 2-10. MAV's for an Individual Package
Labeled by Count 45
Table 2-11. MAV's for an Individual Package
Labeled by Length, Width,
or Area 46
Table 2-12. USDA Lower Limits for Individual
Packages 47
SECTION 6. REPORT FORMS AND WORKSHEETS 49
Table 2-1. Guide to Locations on the Report
Form 51
Standard Pack Report Form 53
Standard Pack Report Form-Weight Only 55
Random Pack Report Form 57
Worksheet for Packages Labeled by Liquid
Volume 59
Worksheet for Packages Labeled by Count 61
m
Worksheet for Checking Paint 63
Table 4-4. Thickness of Paint Can Walls
and Labels 64
Worksheet for Checking Polyethylene
Sheeting 65
SECTION 7. EXAMPLES 67
Category B, Standard Pack Packages Labeled by Weight
Using an Equal-Arm Package
Checking Scale 69
Category B, Standard Pack, Weight, Using an Electronic
Single Pan Balance 70
Category A, Standard Pack, Weight, Using an Equal-Arm
Package Checking Scale 71
Category B, Standard Pack, Volume 72
Category B, Random Pack, Weight 75
Category B, Standard Pack, Volume,
Alternative Tare 78
Category B, Standard Pack, Count 82
SECTION 8. RANDOM NUMBER TABLE
85
1
INTRODUCTION
The Second Edition of NBS Handbook 133, "Checking the Net Contents of
Packaged Goods" (1984) was written to meet several needs of weights and
measures regulatory programs (package testing procedural guide, textbook
for new inspectors, and reference book for unusual types of packages).
This field manual is intended to be an adjunct to Handbook 133 (H-133),
not a substitute for it. It may serve well as a checklist and quick
reference guide, but H-133 remains the source of detailed explanations
and procedures.
This manual has been assembled by extracting tables and report forms
from H-133, rearranging the material, and adding tabbed dividers for
convenient reference. Test procedure outlines and examples of completed
report forms and worksheets have been added. A variation on the
"Standard Pack Report Form" for packages labeled by weight only has also
been included.
Page numbers for the field manual are printed at the top of each page.
Page numbers from H-133 are printed at the bottom of each applicable
table or chart for ease of reference back to the handbook.
The field manual is comprised of eight sections: Test Procedure Outlines,
Sampling Plans, Variable Tare, Weighing Rules, MAV's, Report Forms and
Worksheets, Examples, and a Random Number Table. A description of
each section appears on the first page after each tab divider.
3
SECTION 1. TEST PROCEDURE OUTLINES
Each outline describes the steps that are necessary to determine whether
or not packages are in compliance and where to record information on the
report form or worksheet. The outlines do not describe how to carry out
each step; for this information, the inspector will have to consult H-133.
The outlines for packages labeled by volume and count are abbreviated in
their descriptions of how to determine lot conformance after an average
net contents for the sample has been obtained. These latter outlines
assume the inspector is familiar with these procedures. If necessary, the
inspector should study the outline for standard pack packages labeled by
weight.
The outlines are presented in the following order:
o
Outline of Package Test — Core Method
o
o
o
o
Category A or B, Standard Pack by Weight
Random Pack, Category B, Dry Tare
Packages Labeled by Liquid Volume
Packages Labeled by Count (can by used as a model
for packages labeled by length, area, and dry volume)
.
5
FIGURE 3-4.
OUTLINE OF PACKAGE TEST
Standard Pack Packages Labeled by Weight
1. Fill in pertinent data on report form: what is being tested, UNIT OF MEASURE,
MAV, INSPECTION LOT SIZE, SAMPLING PLAN information.
2. Select RANDOM SAMPLE and RANDOM TARE SAMPLE
3. Determine AVERAGE TARE WEIGHT
4. Determine NOMINAL GROSS WEIGHT (labeled weight + average tare weight)
i
5. Determine PACKAGE ERRORS by comparing sample packages with nominal
gross weight
6. Determine UNREASONABLE ERRORS by comparing minus package
errors with MAV
If number of unreasonable errors is greater than allowed by sampling plan,
inspection lot fails test. No further testing is necessary.
7. Determine AVERAGE PACKAGE ERROR.
If average package error is zero or plus, inspection lot passes test.
No further testing is necessary.
If CATEGORY B plan is being used, and average package error is a
minus value, inspection lot fails test. No further testing is necessary.
8. If a CATEGORY A plan is being used and average package error is minus,
determine T.
If average minus package error is larger in magnitude (disregarding the sign)
than T, inspection lot fails test. If average error is smaller, inspection lot passes.
3-8
6
CATEGORY A OR B, STANDARD PACK BY WEIGHT
PROCEDURE
LOCATION
ON THE
REPORT FORM
Fill out report form heading, including PRODUCT IDENTITY, BRAND,
LOT CODE. CONTAINER DESCRIPTION.
LABELED CONTENTS
□
UNIT OF MEASURE
0
Look up MAV in Table 2-8 (poge 41)
0
Convert MAV to DIMENSIONLESS UNITS by dividing 3 * 2
0
Determine inspection LOT SIZE (N)
0
Look, up sampling plan from Category A or B (page 20 or IQ)
Check whether A or B
6
Record SAMPLE SIZE (n)
0
Record TARE SAMPLE SIZE
0
Record ALLOWED NUMBER OF UNREASONABLE ERRORS
0
■n
If DRY TARE, select random sample from inspection lot and random
tare sample from unused tare stock.
Weigh tare units, record tare weights
0
If WET TARE, select random sample from inspection lot, and select
random tare sample from the random sample.
Gross weigh individual packages in tare sample, record
0
Empty tare sample packages, determine tare weights, record
0
If ALTERNATIVE TARE procedure is followed, check "alternative"
0
Look Up INITIAL TARE SAMPLE SIZE In Table 2-6 (p. 29), record
11
3
7
CATEGORY A OR B, STANDARD PACK BY WEIGHT
PROCEDURE
LOCATION
ON THE
REPORT FORH
Select initial tare sample from sample, determine gross weights
0
Determine tare weights
0
Calculate net weights tor initial, tare sample
0
Determine range of net weights (Rc)
0
Determine range of tare weights (Rt)
10
Determine Rc t Rt by dividing 9 t 10
11
Look up how many packages must be opened tor average tare (nt)
in Table 2-7. Record
Open additional packages for tare if necessary
12
Average tare weights and record
13
If moisture allowance is to be applied,
ur if foam aerosol or vacuum pack coffee being checked,
record TARE CORRECTION
0
Compute NOMINAL GROSS WEIGHT by adding: [T] + [13] - 13a
Record.
14
Compute PACKAGE ERRORS for packages opened for tare by subtracting:
| a ] - 14 Record
0
Compute PACKAGE ERRORS in DIMENSIONLESS UNITS by dividing:
0 ' 0 Kecord
0
Enter these package errors in cross hatched area of form
1
0
Compare unopened packages in sample with NOMINAL GROSS WEIGHT to
determine remaining package errors; record in cross hatched area
\
^
Count number of minus package errors larger than MAV in
4 [Record.
1G
8
CATEGORY A OR B, STANDARD PACK BY WEIGHT
PROCEDURE
LOCATION
ON THE
REPORT FORM
If the number in
check YES: LOT FA
16 is larger than number in 8
ILS . No further testing is necessary.
17
If number in 16
check NO— CONTINL
is equal or less than number in 8
E.
17
Sum package errors, record TOTAL ERROR
15
Average package errors, record AVERAGE ERROR
18
Convert AVERAGE ERROR in D
by multiplying: 18 x
IMENSIONLESS UNITS to units of weight
2
19
If
10
is zero or plus, check YES GO TO
20 No further testing.
20
If
18
is minus: check NO
20
If CATEGORY B, check "Cat. B, Lot Fails". No further testing.
20
If CATEGORY A, check "Cat A, go
". Determine RANGES
Lo 21
RANGES
Calculate AVERAGE RANGE, record
21
Use
6
to look up value in Table 2-3, column 2, (p. ZO), record
22
Calculate d by multiplying:
21
X
22
23
Calc
6
Ulc
te (n/N x 100) by dividing and multiplying:
5 x 100
24
Use
2‘
4 to look up f in Table 2-4 (page 21).
25
Calculate T by multiplying:
23
X
25
26
If 1
8 i
s larger than
26
check YES LOT FAILS
27
If
18
is smaller than
26
check NO LOT PASSES
27
Record DISPOSITION OF LOT,
Check APPROVED only if [17
APPROVED or
] is NO AND
RE Jf
20
ICTED
is YES
28
9
RANDOM PACK, CATEGORY B, DRY T ARE
PROCEDURE
LOCATION
ON THE
REPORT FORM
Fill out report form heading, including:
LOT SIZE
E
From LOT SIZE, look up in Table 2-5 (p. 19) :
SAMPLE SIZE (n) and record
2
check CATEGORY B
E
l|
Look up in Table 2-5 the TARE SAMPLE SIZE and record
E
Look up in Table 2-5 the ALLOWED NUMBER OF UNREASONABLE ERRORS
B
Record UNIT OF MEASURE and check whether "lb" or "oz"
E
Check DRY TARE on right hand side of form
TARE
□
DRY
Select RANDOM SATPLE from INSPECTION LOT.
Rearrange packages from lightest to heaviest.
Select RANDOM TARE SAMPLE from unused tare stock. Have at
least two complete tare units (boat, soaker, label, shrink wrap)
prepared for each boat size.
Compare two tare units to determine whether tare weights vary.
If tare weiqhts vary, record each tare weiaht on riaht hand
side of form
PACKAGE 1
TARE 1
Average tare weights
1
B
If tare weiqhts do not vary, record "actual dry unit used"
TARE
0
DRY
actual dry unit tart
Record PRODUCT DESCRIPTION, LOT CODE, UNIT PRICE
1
E
Record LABELED WEIGHT for each package arranged from
lightest to heaviest
1
0
If tare weiqht.s do not vary, compare each unoDenod packaae with:
Actual dry tare unit + weights equal to LABELED WEIGHT of each
package.
Record package errors for each package
1
0
10
RANDOM PACK, CAT EGORY B, DRY TARE
PROCEDURE
LOCATION
ON THE
REPORT FORM
If dry tare weiahts vary, compare each unopened packaqe with:
Weights equal to: AVERAGE TARE + LABELED WEIGHT; by adding
6 ♦ [¥]
Record package errors for each package
9
Look up MAV in Table 2-8 (p. 41) for lightest package; record
10
Convert MAV to DIMENSIONLESS UNITS by dividing:
10
,0
11
If any minus package errors are larger than MAV in [77]
look up MAV's for those package labeled weights. Record
10
&
11
Circle minus package errors in
9 that are larger than MAV in
11
Count circled package errors and record how many
0
If the number recorded in 13
check YES LOT FAILS
is more than zero
14
If the number recorded in
13
is zero, check NO CONTINUE
14
Sum the package errors. Record TOTAL ERROR
12
Calculate AVERAGE ERROR by dividing: 12 * 2
0
Convert AVERAGE ERROR in
by multiplying: IS x
DIM!
5
ENSIONLESS UNITS to units of weight
16
If AVERAGE ERROR in
16
is zero or plus , check YES GO TO 18
17
If AVERAGE ERROR in
16
is minus , check NO LOT FAILS
17
Record DISPOSITION OF LOT, APPROVED or REJECTED
Check APPROVED if [u]is NO and 17 is YES ; REJECTED if 14 is
YES or 17 is NO.
18
11
PACKAGES LABELED BY LIQUID VOLUME
LOCATION
LOCATION
PROCEDURE
ON TIE
ON THE
S1EP NUMBERS REFER TO WORKSHEET; BOXES TO REPORT FORM
WORKSHEET
REPORT FORM
Fil] out report form heading, including
PRODUCT IDENTITY, BRAND, LOT CODE,
CONIAINER DESCRIPTION, and
LABELED CONTENTS
m
UNIT OF MEASURE
a
Determine inspection LOT SIZE (N), Record
E
Look up sampling plan Category A or B, Table
2-?(p,19) or Table 2-5(p.20); check A or B
B
Record SAMPLE SIZE (n)
E
Record TARE SAMPLE SIZE
□
Record ALLOWED NUMBER OF UNREASONABLE ERRORS
B
Select sample and from it, tare sample.
Cross weigh first package in tare sample
1. Gross Weight
Select appropriate flask, wet it down. Record
6. Volune of Flask
Weigh empty flask; record weight
4. Flask Weight(empty)
Open first package, pour liquid into flask
Set liquid level to mark on flask neck
Weigh flask and liquid
3. Flask Weight(full)
Take liquid's temperature; record
7. Temp of Liquid
Empty remaining liquid from package, clean
container, weigh tare; record tare weight
2. Tare Weight
12
PACKAGES LABELED BY LIQUID VOLUME
PROCEDURE
LOCATION
ON THE
WORKSHEET
LOCATION
ON THE
RETORT FORM
Subtract empty flask weight from full flask
weight (Step 3 - Step 4 on worksheet)
5. Weight of Liquid
Repeat procedure from measuring the gross
weight through finding the weight of the
liquid for second package selected for
tare; record all measurements.
Steps 1. through 7.
marked "(2nd Pkg)"
If the weights recorded in Step 5 do not vary
frcm each other, check NO
Step 8.
If the weights recorded in Step 5 DO vary
frcm each other, look up how much they are
allowed to vary in Table 4-3 (page 38).
If weights vary by more than Table 4-3,
check YES : ALL PACKAGES I1UST BE OPENED
Step 8.
If weights vary by less than Table 4-3,
check NO and continue
Step 8.
Average weights recorded in Step 5
Step 9.
Coirpute AVERAGE WEIGHT OF LABELED V0LUI1E
by the following arithtnetic:
[7] x Step 9 -r Step 6
Step 10.
Determine AVERAGE TARE by averaging weights
recorded in Step 2
Step 12.
13
Determine NOMINAL GROSS WEIGHT by adding:
Step 12 + Step 10
Record
Step 13.
14
Determine PACKAGE ERRORS for packages opened
for tare by subtracting:
Step 1 - Step 13
Step 14.
13
PACKAGES LABELED BY LIQUID VOLUME
PROCEDURE
LOCATION
ON THE
WORKSHEET
LOCATION
ON THE
REPORT FORM
Determine PACKAGE ERRORS for these
packages in D HENS IONLESS UNITS by dividing
Step 14 t 2
Record on worksheet and in crosshatched area
of report form.
Step 15
\
Look up NAV in Table 2-9 (page 43).
Step 16
3
Convert NAV in volume units to weight
by the following arithmetic:
Step 16 x Step 10 t j~~1~|
Step 17
Convert MAV to DIMENSIONLESS UNITS dividing
Step 17 t 2
Step 18
□
Coirpare unopened packages in sample with
NOMINAL GROSS WEIGHT, record PACKAGE ERRORS
in crosshatched area of report form
\
Count number
than MAV in
of minus package errors larger
4
16
Continue filling out report form
17 and
18
Convert AVER^
by the follou
@ * 2
>100 ERROR to units of volume
jing arithmetic:
x | 1 | t Item 10
Step 19
19
ConpLete report form to indicate
DISPOSITION OR LOT as APPROVED or REJECTED
20 through [?8|
as applicable
14
PACKAGES LABELED BY COUNT
PROCEDURE
STEP NUMBERS REFER TO WORKSHEET; BOXES TO REPORT FORM
LOCATION
ON THE
WORKSHEET
LOCATION
ON THE
REPORT FORM
Fill out report form heading, including
PRODUCT IDENTITY, BRAND, LOT CODE,
CONTAINER DESCRIPTION, and
LABELED CONTENTS
0
UNIT OF MEASURE
E
Determine inspection LOT SIZE (N), Record
5
Look up sampling plan Category A or B Table
2-2 (p. 20) or Table 2-5 (p. 19); check A or B
6
Record SAMPLE SIZE (n)
E
Record TARE SAMPLE SIZE
E
Record ALLOWED NUI BER OF UNREASONABLE ERRORS
E
Select sample and from it, tare sample
Gross weight first package in tare sample
1. Gross Weight
Weigh empty container and record tare weight
2. Tare Weight
Open first package and count items in package
3. Count in Package
Weigh counted items in first package
4. Weight of Counted
Items
Calculate weight of labeled count by
the following arithmetic:
| 1 | x step 4 t step 3
5. Weight of Labeled
Count
Repeat procedure, from measuring the gross
weight through calculating the weight of
the labeled count, for second package
selected for tare; record
Steps 1. through 5.
15
PACKAGES LABELED BY COUNT
PROCEDURE
STEP NUMBERS REFER TO WORKSHEET; BOXES TO REPORT FORM
LOCATION
ON THE
WORKSHEET
LOCATION
ON THE
REPORT FORM
Look up MAV in Table 2-10 (p. 45); record
Step 6.
3
Calculate MAV/6 by the following arithmetic
Step 6 x Step 4 -f 6 * Step 3
Step 7.
If the value in Step 7 is smaller than the
scale division, ALL PACKAGES MUST BE OPENED;
deck NO
Step 8.
If the value in Step 7 is equal to or larger
than the scale division, check YES
Step 8.
If the weights recorded in Step 5 do not vary
from each other, check NO; record weight from
Step 5
Step 9.
If the weights recorded in Step 5 DO vary
from each other, look up how much they are
allowed to vary in Table 4-3 (p. 38).
Step 9.
If weights. in Step 5 vary by more than Table
4-3, check YES; ALL PACKAGES MUST BE OPENED
If weights in Step 5 vary less than Table
4-3, check NO and average weights in Step 5.
Step 9.
Determine AVERAGE TARE by averaging weights
recorded in Step 2
Step 10.
13
Determine NOMINAL GROSS WEIGHT by adding:
Step 10 + Step 9; record
Step 11.
14
Determine PACKAGE ERRORS for packages opened
for tare by subtracting:
Step 1 - Step 1 1
Step 12.
16
PACKAGES LABELED BY COUNT
PROCEDURE
SfEP NUMBERS REFER TO WORKSHEET; BOXES TO REPORT FORM
LOCATION
ON TI E
WORKSHEET
LOCATION
ON THE
REPORT FORM
Determine Pi0
in DIMENSION
Step 12 -r
CKP
LES
2
GE ERRORS for these packages
S UNITS by dividing:
Step 12.
Record on worksheet and in crosshatched area
of report form.
Step 13.
\
Convert MAV in count to units of weight by
the following arithmetic:
Step 6 x Step 9 t | 1 [
Step 14.
Convert MA
Step 14 -r
/ t
2
o DIMENSIONLESS UNITS dividing:
Step 15.
0
Coinpare unopened packages in sample with
NOMINAL GROSS WEIGHT record PACKAGE ERRORS
in crosshatched area of report form
0
Count number
than MAV in
of
0
minus package errors larger
0
Continue filling out report form
fl7] and [Ts]
Convert AV
following
H ><
ERA!
ari
2
3E ERROR back to count by the
Ihmetic:
x [T] t Step 9
Step 16.
19
Complete report form to indicate
DISPOSITION OF LOT as APPROVED or REJECTED
20 through 28
as applicable
17
SECTION 2. SAMPLING PLANS
In this section tables from H-133 describe the various types of sampling
plans and associated look-up values. The tables are in the most likely
order of use:
o Sampling plans of Category B (Table 2-5)
o Sampling plans of Category A (Table 2-2)
o Values of 0.8598/Vn for sample size n (Table 2-3)
o Values of f for percent of lot sampled (Table 2-4)
o Calculation of the average range (Appendix H)
o Sampling plans for packages labeled by low count
(Table 5-1)
o Sampling plans for packages given tolerances (Table
5-2)
.
19
Table 2-5. Sampling plans of Category B.
1
Lot size
2
Sample size
3
Tare sample sizea
4
(number of packages
in lot)
(number of packages
in sample)
(number of packages
chosen for
tare determination)
Number of minus
package errors
allowed to ex-
ceed the MAVb
N
n
nt
Up to and
including 250
10
2
0
251 and greater
30
2
0
aSpecial rules for tare sampling apply when Section 2.11.4. is used (glass or
aerosol packages).
bSee Tables 2-8 through 2-11 (pages B~9 to B-14), Sections 2.12. and 2.13.
B-5
20
Table 2 “2. Sampling plans of Category A.
1
2
3
4
Lot size
Sample size
Tare sample sizea
Number of minus
(number of packages
(number of packages
(number of packages
package errors
in lot)
N
in sample)
n
chosen for tare
determination)
nt
allowed to exceed
the MAVb
30 or less
all
2
0
31-800
30
2
1
801-2,000
50
5
2
2,001-5,000
80
5
3
5,001-15,000
125
5
5
15,001 and greater
200
10
7
aSpecial rules for tare sampling apply when Section 2.11.4. is followed (this
is the tare procedure for variable tare and must be used for glass or
aerosol packages).
bSee Tables 2-8 through 2-11 (pages B~9 to B— 14), and Sections 2.12. and
2.13.
Table 2~3. Values of 0.8598 and 2 for sample size n.
7n 7£
1
2
3
n
0.8598
2
sample size
/n
7n
used only when R
used only when s
is calculated
is calculated
30
0.1570
0.3652
50
0.1216
0.2828
80
0.09613
0.2236
125
0.07691
0.1789
200
0.06080
0.1414
B-3
21
Table 2-M. Values of f for percent of lot sampled *
Percent of
lot sampled
f
Percent of
lot sampled
f
Percent of
lot sampled
f
1
.99
36
.80
71
.54
2
.99
37
.79
72
.53
3
.98
38
.79
73
.52
4
.98
39
.78
74
.51
5
.97
40
.77
75
.50
6
.97
41
.77
76
.49
7
.96
42
.76
77
.48
8
.96 1
43
.75
78
.47
9
.95 1
44
.75
79
.46
10
.95 ;
45
.74
80
.45
1 1
.94 |
46
.73
81
.44
12
.94
47
.73
82
.42
13
.93 ;
48
.72
83
.41
14
.93
49
.71
84
.40
15
.92
i
50
.71
85
.39
16
.92
51
.70
86
.37
17
.91
52
.69
87
.36
18
.91
53
.69
88
.35
19
.90
54
.68
89
.33
20
.89
55
.67
90
.32
21
.89
56
.66
91
.30
22
.88
57
.66
92
.28
23
.88
58
.65
93
.26
24
.87
59
.64
94
.24
25
.87
60
.63
95
.22
26
.86
61
.62
96
.20
27
.85
62
.62
97
.17
28
.85
63
.61
98
.14
29
.84
64
.60
99
.10
30
.84
65
.59
100
0
31
.83
66
.58
32
.82
67
.57
33
.82
68
.57
34
.81
69
.56
35
.81
70
.55
^Percent of lot sampled = sample size x 100 = £ x 100
lot size N
B-4
22
APPENDIX H. CALCULATION OF THE AVERAGE RANGE
To calculate the average range of package errors for groups of 5
packages:
1. Record the package errors in successive groups of five packages in
the order of weighing. (See Figure 2-5, page 2-19, and page A-l.)
For example, the following package errors were recorded on the
report form (only the first three columns are shown):
pkg.
pkg.
pkg.
pkg.
pkg.
pkg.
number
error
number
error
number
error
(1)
+2
(6)
-2
(11)
+2
(2)
+4
(7)
-4
(12)
-4
(3)
+5
(8)
-5
(13)
+5
(4)
+10
(9)
-10
(14)
+10
(5)
+3
(10)
-3
(15)
-3
Calculate the range (R)
of package
errors for
each group
of five.
R does not
have a sign.
The range is obtained as
follows:
o If there are only plus errors in a group of five, subtract the
smallest plus error from the largest plus error. This is the range
(R) for the group.
For example for the first group of five packages:
+2
+4
+5
+ 10
+3
R = +10 - (+2) = 8
o If there are only minus errors in the group, subtract the largest
number with a minus sign from the smallest number with a minus
sign. This is the range (R) for the group.
For example for the second group of five packages:
-2
-4
-5
-10
-3
R = -2 - (-10) = 8
H-l
23
o If there are both plus and minus errors in the group of five, add
the largest error which has a plus sign to the largest error which
has a minus sign (but ignore the minus sign). This is the range
(R) of the group.
For example for the third group of five packages:
+2
-4
+5
+10
-3
R = +10 + 4 = 14
3. Calculate the sum of all R and note the number of groups. For
example, let us consider the previous three examples as one set of
sample data. For these examples the sum of R = 8 + 8 + 14 = 30
and the number of groups is 3.
4. Calculate the average R, called R, as follows:
r = sum of all R (step 3)
number of groups
In the example above, R = 3£ = 10
3
When calculating the range in net weights or range in tare weights for
the alternative tare procedure, the range is the difference between the
largest and smallest weights.
For example, the following tare weights are recorded:
0.201 lb
0.200 lb
0.204 lb
0.199 lb
0.201 lb
The range in tare weights is 0.204 lb - 0.199 lb = 0.005 lb.
H-2
24
Table 5~1 . Sampling plans for packages labeled by low count3
1
2
3
4
Lot size
(number of packages
in lot)
N
Sample size
(number of
packages in
sample)
n
Tare sample size
(number of packages
chosen for tare
determination)
nt
Number of packages
allowed to contain
fewer than the
labeled count.
Up to and includ-
ing 500
10
2
1
501-5000
30
2
2
5001 and greater
50
5
3
aLabeled count is 50 or fewer units.
B-22
25
Table 5-2. Sampling plans for packages given tolerances.
1
2
3
4
Lot size
Sample size
Tare sample size
Number of package
N
n
nt
errors which may
exceed allowable
difference
Up to and including 500
10
2
0
501-5,000
30
2
1
5,0001 and over
50
5
2
B-23
27
SECTION 3. VARIABLE TARE
This section provides three tables needed to determine the average tare
of glass, aerosol, or other variable tare packages. (This procedure is
called the "Alternative Tare Method" in H-133.) The tables:
o Specify the number of packages to open initially as a
function of the sampling plan category (A or B) and
lot size (Table 2-6. Initial tare sample size for
alternative procedure.)
o Specify the total number of packages for which tare
weights must be determined (to obtain an average
tare) as a function of the sample size and the value
of the ratio Rc/Rt (Table 2-7. Total number of
packages (nt) to be opened for tare determination.)
o Correct the tare weights of foam aerosol products
(Table 3-2. Test allowances for foam products.)
29
Table 2-6. Initial tare sample size for alternative tare
procedures.
Sampling plan Category
Lot size
Initial tare sample size
A
all
5 packages
B
equal to or less
than 250 packages
2 packages
greater than 250
5 packages
packages
B-6
Table 2~7- Total number of packages (n^) to be opened for tare determination.
30
o
o
C\J
II
c
in
c\j
ii
c
o
CO
II
c
o mo
C o Ol co c— m
W ^ f f- i-l
4->
C
in «- n co o
(M cm «— o o
-U O 0 31
C OO S- C— VO iO
co in cm «“ o
.sr m c\j «— o
*** *-** c—
N a- MJN m
OMD f-iO iO
cr* -a- o\ in o
inmir?-?
«— oo in co cm
O' CO S- VO lO
c — cm c — on oi
in in -=r -=r on
s m o co in
on co m cm c\j
S- (\J co =r o
in in -=r =r zr
co w o co in
on on on c\j cm
mr-cccovo
CM CM »—»—»—
c— in cm o co
on on on on cm
m in on cm o
CM CM CM CM CM
4- cm o oico t'-ioin-=ron
CM CM CM » — t- r-
in
on cm cm
O O CMD
a
E
cO
CO
CO
o
CO
CO
oc.
o
CO
Q.
o
0.
CD
n
E
3
c
o
in
ii
c
4J
c
O CUC3- O
in -=r -=r -=r .=r
s- -=r co in
on on on cm cm
on <- oc s co
CM CM r- t- «-
in co cm >- o o o'Coco n c- sco co in
o
on
ii
c
J->
c
O CJC CO co -=r
on Oil CM CM Oil
on o'
CM CM «-
■=r on cm «— o
O' CO CO SCO
m io in in in
=r m
4->
c
0000100 cossmin
in in =r
on on on on cm
CM CM CM CM CM
CM CM CM CM CM
O O O O O
CM O' cO CO O
O 4->
•H CC
4-> \
03 O
CC CC
o o o o
W 3" CO CO O
CO
W O O O «- CM
J
o o o o o
CM 3 cO CO O
O O O o o
cm 3 m co o
o o o o o
CM 3 CO CO O
o o o o o
CM 3 lO CO o
CC I I I I
o
CM CM 3 CO CO
o o o o o
I I I I I
cm cm cm cm on
I I I I I
onononon-=r
i i i i i
O CM 3 CO CO O CM 3 lO CO
CM CM CM CM CM
O CM 3 co GO
on on on on on
3 3 3 3 in
I I I I I
r- r- CM r-
O CM 3 lO CO
in in in in co
i i i i i
3 3 3 3
O CM 3 VO CO
in in in in in
*
B-7
Including those already opened for initial tare determination.
Table 2~7 (continued). Total number of packages (nt) to be opened for tare determination.
31
o
o
CM
II
c
UN
CM
o
co
II
c
tp
rH
Q.
e
cO
<n
c
■H
o
cn
UN
<1)
II
CO
c
o
m
Q.
tin
O
i.
0)
JO
o
e
CNN
3
II
c
c
4->
c
4->
c
4->
c
ON On C — VO vO
on on N
Nf-<-00
o o o o o
o o o o o
CM CM
O O
ON ON On OO CO
OO 0 — O'— C — NO
vo no vo in un
UN IA UN UN IA
LfN
co co n o- t~ vovovomin un un un un ia un un un urn un un un ixn un un
UN
4->
C
UN UN UN UN UN
UN UN UN UN UN
UN UN UN UN UN
UN UN UN UN UN
UN UN UN UN UN
UN
4->
C
4->
c
moncnmon on on (M cm oo cmcmcmcmcm cm cm (m cm cm cm cm cm cm cm
CM
CM CM CM CM CM
CM CM CM CM CM
CM CM CM CM CM
CM CM CM CM CM
CM CM CM CM CM
O O O O O
cm 43- vo oo o
O O O O O
CM =T VO oo O
O O O O O
CM 4T VO OO O
O O O O O
CM 43- VO CO O
O O O O O
CM =r vO CO O
O
CM
O 4_>
-r-t CC
4-> \
to o
CC CC
VO vO VO vO C~- C- C~- C— CO oo to oo CO O' O' O' O' O' c o o o o •—
I I I I I I I I I I I I I I I 1 I I I I I I I I I
O CM 43- vo 00
vo vO vO vO vO
O CM =r vo 00
c— c— c— c— C~-
O CM 43- vo CO
OO OO CO OO CO
O CM 43- vo OO
ON O' ON O' ON
O CM 3 VO CO O
o o o o o —
B-8
Including those already opened for initial tare determination.
32
Table 3-2. Test allowances for foam aerosol products
Avoirdupois:
Labeled
weight of package
Test allowance
Ounce Pound
0 to less than
1
1/2 oz
0
0
1 1/2 oz to
less than
5
oz
1/16
0.004
5 oz to
less than
8
oz
1/8
0.008
8 oz to
less than
1 1
oz
3/16
0.012
11 oz to
less than
14
oz
1/4
0.016
14 oz to
less than 1
lb 1
oz
5/16
0.020
1 lb 1 oz or
more
3/8
0.023
Metric:
Test allowance
Labeled
weight of package
Grams
0 to less
than 50 g
0
50 g to less
than 100 g
1
100 g to less
than 200 g
3
200 g to less
than 300 g
5
300 g to less
than 400 g
7
400 g to less
than 500 g
9
Over 500 g
10
B-17
33
SECTION 4. WEIGHING RULES
This section contains reference tables for:
o Determining the maximum size of the unit of
measure to record package errors for packages
labeled by weight. This table also guides the
inspector in the selection of appropriate weighing
equipment. (Table 3-1.)
o Selecting the capacity of scale to be used when
weighing liquids (Table 4-1.)
o Determining the maximum size of the unit of
measure used to record package errors when weighing
packages labeled by liquid volume (Table 4-2.)
o Determining whether the variation in the weights of
equal amounts of product from two different
packages not labeled by weight is too large to permit
package error determination by weighing. (Table
4-3.)
Table 3-1. Recommended maximum size of scale division on the scale used in
checking package weights.
35
>>
L.
O
bO
CD
.P
03
O
s:
-P
CO
CD
bO
03
O
03
Q.
bO
C
•iH
s:
bO
CD
2
S-
o
>»
t-
03
CO
CO
CD
o
CD
c
CD
X)
CD
O
c
03
H
03
JD
>»
O
03
t-
D
O
O
03
SI
tc
t-
CD
SI
03
O
.P
>»
H
03
C
03
C
<
03
B-l 6
The equal-arm package scale must be used as null-indicator for packages labeled from 1.92 to 5.4H
or 82 to 250 g to eliminate effects of possible tower errors.
36
Table 4-1 . Weighing devices appropriate to use to check common
consumer products labeled by liquid volume.
Labeled volume
( inch-pound)
Device
Labeled volume
(metric)
Up to and including
4.25 fl oz
analytical or other
high accuracy balance
Up to and including
126 mL
Greater than 4.25 fl oz
to and including 32 fl oz
small capacity
equal-arm scale
or equivalent
Greater than 126 mL
to and including 1 L
Greater than 32 fl oz
to and including 3 gal
large capacity
equal -arm scale
or equivalent
Greater than 1 L
to and including 12 L
Greater than 3 gal
commercial scale and
substitution weighing
Greater than 12 L
B-18
37
Table *1-2. Recommended maximum size of scale division on the scale
to be used in checking weights of packaged goods labeled
by liquid volume.
Inch-Pound
Metric
Labeled volume
Scale division
Labeled volume
Scale
division
(oz avoir)
(lb)
(g)
Up to and including 4.25 fl oz
a
a
Up to and including 3 mL
o
o
Greater than 3 mL
to and including 126 mL
0.1a
Greater than 4.25 fl oz
to and including 17.00 fl oz
1/32b
0.002b
Greater than 1 26 mL
to and including 503 mL
1 .0b
Greater than 17.00 fl oz
to and including 55.00 fl oz
1/16
0.004
Greater than 503 mL
i to and including 2.041 L
2.0
Greater than 55.00 fl oz
to and including 1.25 gal
1/8
0.01
Greater than 2.041 L
j to and including 5.489 L
5.0
Greater than 1.25 gal
to and including 1.875 gal
1/4
0.02
Greater than 5.489 L
to and including 37.5 L
10.0
Greater than 1 .875 gal
to and including 4.375 gal
1/2
Greater than 4.375 gal
to and including 9 gal
1
0.05
Greater than 9 gal
to and including 18 gal
2
0.1
aUse analytical or other high accuracy balance.
bUse package checking scale as null indicator.
B-19
38
Table 4-3. Maximum permitted difference In weights of two equal
quantities according to the type of scale used to weigh.
Type of Scale
Pounds
Grams
Analytical or other high accuracy balance
0.0001
0.05
Small capacity equal-arm scale
or equivalent
0.002
1 .0
Large capacity equal-arm scale
or equivalent
0.004
2.0
Commercial scale up to and including
30 lb (14 kg)
0.01
5.0
Commercial scale above 30 lb (14 kg)
up to and including 100 lb
0.02
9.0
B-20
SECTION 5. MAY’S
In this section, tables list the limits of unreasonable minus package errors
(MAV's) for application to individual packages according to their labeled
net quantity statements:
o Weight (Table 2-8.)
o Volume (Table 2-9.)
o Count (Table 2-10.)
o Length or Area (Table 2-11.)
U.S.D.A. Lower Limits for Individual Packages
o
41
Table 2-8. MAV’s for an individual package labeled by weight3.
Avoirdupois units
Metric units
Labeled weight
MAV
Labeled weight
MAV
Pounds or ounces
Decimal
pounds
Fractional
ounces
Grams
Grams
up to and including
0.08 lb
up to and including
1 .28 oz
10% of
labeled weight
up to and including
36
10% of
labeled
weight
0.08+b toc 0.12 lb
1 .28+ to 1 .92 oz
0.008
1/8
36+ to 54
4
0.12+ to 0.18 lb
1 .92+ to 2.88 oz
0.012
3/16
54+ to 82
5
0.18+ to 0.26 lb
2.88+ to 4.16 oz
0.016
1/4
82+ to 118
7
0.26+ to 0.34 lb
4.16+ to 5.44 oz
0.020
5/16
118+ to 154
9
0.34+ to 0.46 lb
5.44+ to 7.36 oz
0.024
3/8
154+ to 209
1 1
0.46+ to 0.58 lb
7 .36+ to 9.28 oz
0.028
7/16
209+ to 263
13
0.58+ to 0.70 lb
9.28+ to 1 1 .20 oz
0.032
1/2
263+ to 318
15
0.70+ to 0.84 lb
11.20+ to 13.44 oz
0.036
9/16
318+ to 381
16
0.84+ to 0.94 lb
13.44+ to 15.04 oz
0.040
5/8
381+ to 426
18
0.94+ to 1 .08 lb
15.04+ to 17.28 oz
0.044
11/16
426+ to 490
20
1 .08+ to 1 .26 lb
0.048
3/4
490+ to 572
22
1 .26+ to 1 .40 lb
0.052
13/16
572+ to 635
24
1 .40+ to 1 .54 lb
0.056
7/8
635+ to 698
25
1 .54+ to 1 .70 lb
0.060
15/16
698+ to 771
27
aApplies only to shortages in package weight (that is, the MAV is
compared with minus package errors only)
b0.08+ means "greater than 0.08"
c"to" means "to and including"
B-9
42
Table 2-8. (continued) MAY * s fop an Individual package labeled by weight*
Avoirdupois units
Metric units
Labeled weight
MAY
Labeled welcht.
MAV
Decimal
Fractional
Grams or
Pounds
pounds
ounces
kilograms
Grams
1 .70+ to 1 .88
0.064
1
771+ to 852
29
1 .88+ to 2.14
0.070
1 1/8
852+ to 971
32
2.14+ to 2.48
0.078
1 1/4
971+ to 1.125
35
2.48+ to 2.76
0.086
1 3/8
1 .125+ to 1 .350
40
2.76+ to 3.20
0.094
1 1/2
1 .350+ to 1 .600
45
3.20+ to 3.90
0.11
1 3/4
1.600+ to 1 .800
50
3.90+ to 4.70
0.12
2
1 .800+ to 2.100
55
4.70+ to 5.80
0.14
2 1/4
2.100+ to 2.640
65
5.80+ to 6.80
0.15
2 1/2
2.640+ to 3.080
70
6.80+ to 7.90
0.17
2 3/4
3.080+ to 3-800
80
7.90+ to 9.40
0.19
3
3.800+ to 4.400
85
9.40+ to 11 .70
0.22
3 1/2
4.400+ to 5.200
100
11.70+ to 14.30
0.25
4
5.200+ to 6.800
115
14.30+ to 17.70
0.28
4 1/2
6.800+ to 8720
130
17.70+ to 23.20
0.31
5
8.20+ to 10.60
145
23.20+ to 31 .60
0.37
6
10.60+ to 14.30
170
31 .60+ to 42.40
0.44
7
14.30+ to 19.25
200
42.40+ to 54.40
0.50
8
19.25+ to 24.70
230
54.40+
2% of labeled
24.70+
2% of labeled
weight
weight
B-10
Table 2~9. MAV's for an Individual package labeled by volume - liquid or
43
%
B-ll
aApplies to shortages in package volume (that is, minus package errors).
bCo nvert to metric units and use laboratory glassware.
cUse laboratory glassware.
b0.50» means "greater than 0.50."
e"to" means "to and Including."
Table 2~9 (continued). HAV'a for an individual package labeled by volume - liquid or dry.
44
Liquid
and dry
(HAV)
(ml.)
26
a
fn
s*
xr
52
59
<bt
89
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118
133
00
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177
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237
266
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B-12.
Table 2-9. MAV’s for an individual package labeled by volume - liquid or
43
%
B-ll
aApplie3 to shortages in package volume (that is, minus package errors).
bCo nvert to metric units and use laboratory glassware.
cUse laboratory glassware.
d0.5O means "greater than 0.50."
e"to" means "to and including."
Table 2~9 (continued). MAV*3 for an Individual package labeled by volume - liquid or dry
44
Liquid
and dry
(MAV)
(ml.)
26
O
nn
37
a
•=r
52
59
a
C-
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133
s
177
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237
266
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B-1Z
45
Table 2-10. MAV*s for an individual package labeled by count3.
Labeled count
MAV
up to and including
1 7b
0
l8-50b
1
51-83
2
84-116
3
117-150
4
151-200
5
201-240
6
241-290
7
291-345
8
346-400
9
401-465
10
466-540
1 1
541-625
12
626-725
13
726-815
14
816-900
15
901-990
16 !
991-1075
17
1076-1165
18
1166-1250
19
1251-1333
20
1334 and over
1.5? of labeled count rounded off
to the nearest whole number
aApplies only to shortages in package count (that is, minus package error:;').
bSee Section 5.2. for sampling plans to be used with these package sizes.
B-13
46
CO
£-
O
L.
S-
C0
CO
bO
co
o
cG
(X
CO
3
C
P
CO
£
P
d)
i.
3
CO
CO
Cl)
E
Cl)
bo
CO
X
o
CO
a
c
•<H
CO
0)
bO
*—
CO
P
C
C-
cO
o
.c
p
CO
i .
o
CO
p
P
cO
>>
a>
rH
x
c
bO
o
CO
CO
c
CO
CO
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CO
rH
s
a
a.
+
<
r-
cO
jO
bO
C
•o
3
•o
c
(0
o
p
(0
c
CO
0)
E
s
o
p
s
o
CD
0)
CO
B-14
Section 2.13. for exceptions: textiles, polyethylene sheeting.
47
Table 2-12. U.S. Department of Agriculture, Meat and Poultry,
Groups and Lower Limits for individual packages*
Definition of
Group (numbers are
labeled weight in ounces)
Group
Name
Homogeneous,
Fluid When Filled
All Other
Products
Lower Limit for
Individual Weights
A
less than 3
10 % of labeled weight
1
3-16
7.1 g
0.25 oz
8/32 oz
4/16 oz
2/10 oz
2/8 oz
1/4 oz
2
over 16
3-7
14.2 g
0.50 oz
16/32 oz
8/ 1 6 oz
5/10 oz
4/8 oz
2/4 oz
3
-
over 7
to 48
28.3 g
1 oz
4
over 48
to 1 60
42.5 g
1.50 oz
1 16/32 oz
1 8/16 oz
1 5/10 oz
1 4/8 oz
1 2/4 oz
5
1
over 160
2 oz
1/4 lb
*See also Appendix J.
B-15
49
SECTION 6. REPORT FORMS AND WORKSHEETS
This section contains:
o A table referring to locations on the report form and
where to obtain further information in H-133.
o Standard Pack Report Form
o Standard Pack Report Form - Weight Only
o Random Pack Report Form
o Worksheet for Packages Labeled by Liquid Volume
o Worksheet for Packages Labeled by Count
o Worksheet for Checking Paint
o Table 4-4. Thickness of Paint Can Walls and labels
o Worksheet for Checking Polyethylene Sheeting
51
Table 2-1, Guide to locations on the report form for
standard pack packages on page 55
Box
Subject
Section
Handbook 133
Page
1
Labeled Contents
2.2.1 .
2-2
2
Unit of Measure
2.9.1 .
2-16
3
Maximum Allowable Variation (MAV)
2.12.
2-27 & B-9
to B-15
4
MAV (dimensionless units)
2.9.1 .
2-16
5
Lot Size (N )
2.3.3
2-8
6
Sample Size (n)
2.6., 2.7.
2-9, 2-14
7
Tare Sample Size (nt)
2.6., 2.7. , 2.11 .4.
2-9, 2-14,
2-23
8
Allowed Number of Unreasonable Errors
2.6.1 ., 2.7.1 .
2-10, 2-14
9
Range of Met Weights (Rc)
2.11.4.
2-25
10
Range of Tare Weights (Rt)
2.11.4.
2-25
1 1
Rc ■+ Rt
2.11 .4.
2-25
12
nt from Table 2-7
2.11.4.
2-25
13
Average Tare
2.11., 2.11 .3.,
2.11.4
2-20, 2-23,
2-26
13a
Tare Correction
moisture 2.14.,
foam 3.11.6.,
vacuum pack 3.15.
2- 29
3- 37
3-42
14
Nominal Gross Weight
3.5.
3"7
15
Total Package Error
2.9.3.
2-18
16
Actual Number of Unreasonable Errors
2.6.1 ., 2.7.1
2-10. 2-14
17
Decision on Unreasonables
2.6.1 . , 2.7.1 .
1
OvJ
O
1
C\J
18
Average Error (dimensionless units)
2.6.2., 2.7.2.
2-11, 2-15
19
Average Error (labeled units)
2.6.2., 2.7.2.
2-11, 2-15
20
Decision on Average
2.6.2., 2.7.2.
2-11, 2-15
21
Average Range
2.6.2., Appendix H
2-11, H-1
22
Value from Table 2-3, column 2
2.6.2.
2-12
23
d
2.6.2.
2-12
24
(n/N) x 100
2.6.2.
2-13
25
f
2.6.2.
2-13, B-4
26
T
2.6.2.
2-13
27
Decision on Average (for Cat. A only)
2.6.2.
2-1 4
28
Disposition of Lot
Summary of boxes
17, 20, 27
2-4
B-2
DATE
STANDARD PACK REPORT FORM
REPORT NUMBER
Location of TEST (Name, Address)
□ Retailer
□ Wholesaler
□ Packager
PRODUCT IDENTITY
BRAND
LOT CODE(S)
CONTAINER DESCRIPTION
jJ LABELED CONTENTS
_2j UNIT OF MEASURE
D lb.
□ oz.
3 | MAV (same
units as label)
See
Worksheet
4 | MAV (dimensionless
units)
See
Worksheet
I 6 | SAMPLE SIZE (n)
O A (p 20)
O B (p. 19)
CH
TARE SAMPLE
SIZE
□ Alternative
<P 29)
0
Allowed Number
UNREASONABLE
ERRORS
This report form is designed for standard packages not labeled by weight: for example, liquid volume,
count, area, etc.
Fill out report form heading, boxes [T] & [T], and boxes | 5 | through
8 .
Go to appropriate worksheets, follow directions on the worksheet, recording data on the report form
as directed by the worksheet.
1 9 | R^ (See Worksheet)
10 1 RT (See Worksheet)
nj Rc
+ Rr
12 | n, (Table 2-7
13 1 AVERAGE TARE
14 1 NOMINAL GROSS
Range of Net
Weights
Range of
Tare Weights
0,
0 =
p 30&31)
See
Worksheet
WEIGHT
See
Worksheet
PACKAGE ERRORS
Comments:
28 | DISPOSITION OF LOT
□ APPROVED
□ REJECTED
Acknowledged Receipt of Report
Official
55
DATE
STANDARD PACK REPORT FORM
WEIGHT ONLY
REPORT NUMBER
Location of TEST (Name, Address)
□ Retailer
□ Wholesaler
□ Packager
PRODUCT IDENTITY
BRAND
LOT CODE(S)
CONTAINER DESCRIPTION
1 I LABELED WEIGHT
jJ UNIT OF MEASURE
□ lb
O 02
3 | MAV Table 2-8
p. 41 & 42
4 | MAV (dimensionless
units)
0 + 0 =
| 5 | LOT SIZE (N)
| 6 | SAMPLE SIZE (n)
□ A (p 20)
□ B (p. 19)
bl TARE
WEIGHT
IT
GROSS
WEIGHT
NET
WEIGHT
0
TARE SAMPLE
SIZE
□ Alternative
(P 29)
d | PACKAGE
ERROR
0-0
0
8 | Allowed Number
UNREASONABLE
ERRORS
e I PACKAGE
— 1 ERROR
(dimensionless
units) ^[7]
| 9 | Rc (see (~c~| )
Range ot Net
Weights
10|rt (see [b~|)
Range of TARE
Weights
H | Rc -a. Rt =
0 + 0 =
12J n, (Table 2-7,
13 1 AVERAGE TARE
13a
TARE CORRECTION
□ dry
□ Moisture
p. 30 & 31)
□ wet
O Foam (p. 32)
□ alternative
□ Vacuum Pack
WEIGHT
□+0-
PACKAGE ERRORS
TOTALS
f-) (0 / + )
Comments:
28 1 DISPOSITION OF LOT
□ APPROVED
□ REJECTED
Acknowledged Receipt of Report
Official
57
Acknowledged Receipt of Report
Official
58
RANDOM PACK REPORT FORM
Page 2 of 2
REPORT NUMBER
ALTERNATIVE TARE CALCULATIONS:
1 3 1 GROSS WEIGHT
| b | TARE WEIGHT
6b| Rt =
| c | NET WEIGHT
6aj RC =
| d | PACKAGE ERROR
□ "@-0
6cj Rc h- Rt =
0 + 0
| e | PACKAGE ERROR
(In scale dlv)
0-0
6dj n, (Table 2-7 p. 30)
Additional
Tare weights:
GROSS WT
6eJ AVERAGE
— TARE
tare WT
0
i
i
i
GROUP I
1
2
3
4
5
6
7
8
9
10
0" AVERAGE
R
R
LOT DISPOSITION CATEGORY A
NOTE: PACKAGES SHOULD NOT BE ARRANGED FROM LIGHTEST TO HEAVIEST WHEN FOLLOWING A
ON PAGE 1,
THE NUMBER OF MINUS
PACKAGE ERRORS
EXCEEDING THE MAV
IS RECORDED IN BOX fTT|
BOX [71 CONTAINS THE
1 — 1 ALLOWED NUMBER.
IS 1 1 3 | Greater than | 4 | ?
YES-*-LOT FAILS. RECORD
DISPOSITION IN BOX Qej PAGE 1
NO -♦GO TO [20]
RANGE OF PACKAGE
ERRORS FOR EACH
GROUP OF 5 PACKAGES
SUM OF -A- NO OF GROUPS
R
" 20[
AVERAGt
ERROR
(Scale dlv)
TOTAL . NO. OF
ERROR PACKAGES
CD + CD
Til AVERAGE
ERROR
In units of weight
AVERAGE
UNIT OF
ERROR
X
MEASURE
In no. of
scale dlv.
[0
X
0
jgj IS [20]
MINUS?
IJ NO -► RECORD DISPOSITION IN BOX Qa] , PAGE 1
mrES^GOToJI^
_£5j TABLE 2-3
Col. 2 value (page 20)
££j Use[~27]to~
24 x 25
ili (n/N)x100 =
([T]-t-[T])xioo =
£9j T =
26 x 28
look up t in Table 2-4 (page 21) f »
DISREGARDING THE SIGNS,
IS [20I larger than [29] ?
I.'! YES-*- LOT FAILS
r I NO-*- RECORD DISPOSITION IN BOX [Ti] . PAGE 1
Record final lot disposition on page 1 in box 1 18 |
59
WORKSHEET FOR PACKAGES LABELED BY LIQUID VOLUME
NUMBERS WITH BOXES (eg. [3] ) REFER TO REPORT FORM (page 53)
STEP NUMBERS (e g. STEP 5) REFER TO WORKSHEET
Fill out report form up through box [IT] , skip boxes QT) and [T]
(1st Pkg) (2nd Pkg) (3rd) (4th) (5th)
8. Do the weights recorded in Step 5 differ from each other by more than the value in Table 4-3 (page 38)?
YES I I If this box is checked, open all packages in sample and determine each
package error by volume (see Section 4.6.).
NO I I If this box is checked, continue below.
9. AVERAGE WEIGHT OF LIQUID IN FLASK = AVERAGE OF STEP 5 =
10. AVERAGE WEIGHT
OF LABELED VOLUME
LABELED VOLUME
FLASK VOLUME
x AVG. WEIGHT OF l IQUID IN FLASK
box 0
Step 6
x Step 9 =
*11. (RC/RT =
(n,=.
See Table 2-7 (pages 30 8 31)
12. AVERAGE TARE = AVERAGE OF STEP 2 (or average of Step 2 and additional tares)*
Record in box [13] on report form
•Alternative Tare procedure for liquids packed in glass.
tlf additional packages are opened for tare, provision should be made for recording all pertinent data
60
13. NOMINAL GROSS WEIGHT
AVERAGE + AVERAGE WEIGHT
TARE OF LABELED VOLUME
= Step 12 + Step 10
Record in box [TT] on report form
14. For packages opened for Tare:
PACKAGE ERROR = GROSS WEIGHT - NOMINAL GROSS WEIGHT
(weight)
Step 1 - Step 13
1
2
3
4
5
15. PACKAGE ERROR = PACKAGE ERROR -i- UNIT OF MEASURE
(dimensionless units) (weight)
= Step 14 box [2]
1
2
3
4
5
Record package errors on report form in crosshatched area.
16. MAV
(volume)
from Table 2-9 =
(pages 43 & 44)
Record In box [T] on report form.
17. MAV
(weight)
MAV x AVERAGE WEIGHT OF LABELED VOLUME
<volume> LABELED VOLUME
= Step 16 x
Step 10
box [7]
18. MAV
(dimensionless
units)
MAV + UNIT OF MEASURE
(weight)
Step 17 ■+■ box QF]
Record In box [T] on report form
19. Compare unopened packages with nominal gross weight (Step 13, box [T4~| ).
Record package errors for remaining packages In sample directly on report form In crosshatched area.
Compare minus package errors with MAV (Step 18, box |~4~|).
Average package errors (box [is] ). Convert back to units of volume as given below:
AVERAGE PACKAGE ERROR _
AVG. PACKAGE ERROR x
UNIT OF
.. LABELED VOLUME
(volume)
(dimensionless units)
MEASURE
AVG. WEIGHT OF
LABELED VOLUME
=
box [Tb] x
box [T]
box (T]
Step 10
Record in box (T9] on report form
(Boxes above with "3". "4", "5" in corners are for larger tare sample sizes.)
61
WORKSHEET FOR PACKAGES LABELED BY COUNT
NUMBERS WITH BOXES (eg [3] ) REFER TO REPORT FORM (page 53)
STEP NUMBERS (eg "Step 5") REFER TO WORKSHEET
Fill out report form through box [IT] , skip boxes (jT] and [Tj
(1st Pkg)
(2nd Pkg)
(3rd)
(4th)
(5th)
1. Gross Weight
2. Tare Weight
3. Count in Each
Package
4. Weight of Counted
Items
5. Weight of Labeled
Count
Count X Step 3
6. MAV from Table 2-10 _
(count) (page 45)
7. MAV/6
(weight)
MAV/6 x
(count)
WEIGHT OF COUNTED ITEMS
COUNT IN PACKAGE
=
Step 6
6
Step 4 (for first package)
Step 3 (for first package)
Record in box [3] on the report form
8. If using an equal-arm package checking scale, is value calculated in Step 7 equal to or larger than Vi the smallest graduation?
If using an electronic package checking scale , is value calculated in Step 7 at least as large as the smallest increment?
NO □ If this box is checked, open all packages in sample and determine each
package error by actually counting the items inside the packages.
YES □ If this box is checked, continue below.
9. Do the weights recorded in Step 5 above differ from each other by more than the value in Table 4-3 (page 38)?
YES □ If this box is checked, open all packages in sample and determine each
package error by counting items inside packages.
NO □ Average Weight of Labeled Count = average of Step 5 =
10. AVERAGE TARE = AVERAGE OF STEP 2
Record In box
0
on report lorm
11. NOMINAL GROSS WEIGHT
AVERAGE
TARE
+ AVERAGE WEIGHT
OF LABELED COUNT
Step 10 + Step 9 =
Record in box [T4] on report form
62
12. For packages opened for Tare:
PACKAGE ERROR
(weight)
=
GROSS WEIGHT
Step 1
NOMINAL GROSS WEIGHT
Step 11
=
1
2
3
4
5
13. PACKAGE ERROR
PACKAGE ERROR
UNIT OF MEASURE
(dimensionless units)
(weight)
=
Step 12 -r-
box [2]
1
2
3
4
5
Record these package errors on report form in crosshatched area.
14. MAV
(weight)
MAV x AVERAGE WEIGHT OF LABELED COUNT
(count)
LABELED COUNT
Step 6 x
Step 9
box [7]
15. MAV
(dimensionless
units)
MAV -H UNIT OF MEASURE
(weight)
Step 14 -s- box[
Record in box [7] on report form
16. Compare unopened packages with nominal gross weight (Step 11 or box [14] ).
Record package errors for remaining packages in sample directly on report form in crosshatched area.
Compare minus package errors with MAV (Step 15 or box |~4~|).
Average package errors (box [18] ). Convert back to units of count as given below:
AVERAGE PACKAGE ERROR
(count)
AVG. PACKAGE ERROR x UNIT OF
(dimensionless units) MEASURE
LABELED COUNT
AVG. WEIGHT OF
LABELED COUNT
box [TT]
x box [I] x
box [7]
Step 9
Record in box [79] on report form.
(Boxes above with “3”. "4", and “5" in corners are for larger tare sample sizes)
63
WORKSHEET FOR CHECKING PAINT
Audit
©
Can Height
Can Diameter
©
Average
Liquid
Diameter
©
Average
Liquid
Level
©
Average
Container
Depth
©
Average
Liquid
Depth
©
Volume
®
Top
Middle
©
Bottom
Average
1 cu. in. » 0.004329 gal.
1 cm3 = 0.001 L
Volume (To) » 0.7854 x ©x(£)x©
If volume in
©
is less than labeled volume, use possible violation procedures
Possible Violation
Label
©
Gross
Weight
©
Lid Weight
Wet (-) Dry
©
Liquid
Level
©
Tare
©
Water
Volume
( 3©“
Net Weight
■©-CD
Weight of
Label Volume
0*0
'"Sr
©
Package Volume
f(T)
/
A- 7
64
Table 4-4. Thickness of paint can walls and labels.
Wall thickness
Inch-pound
Metric
can size
in
can size
mm
1 gal
0.010
4 L
0.25
1/2 gal
0.010
2 L
0.25
1 qt
0.009
1 L
0.23
1 pt
0.008
500 mL
0.23
250 mL
0.20
Label thickness
( paper)3
(all can sizes)
Inch-pound
Metric
0.004 in
0.10 mm
aThe thickness of labels lithographed directly onto the container may be
ignored.
B-21
65
Labeled Length
Labeled Width
Labeled Thickness [
WORKSHEET FOR CHECKING
POLYETHYLENE SHEETING
0.8 X Labeled Thickness
0.93 X Labeled Thickness
Compare with All Thickness Measurements
Compare with Average Package Thickness
Package
Length
Width
Thickness
Package
Length
Width
Thickness
Package
Average
Package
Average
’MM'
Package
Average
Package
Average
y/y/A
Package
Average
’yy/y
Semple
Average
A-ll
67
SECTION 7. EXAMPLES
This section contains worked examples of worksheets and report forms for
commonly encountered packages. (The section does not appear in H-133.)
o Category B, standard pack, labeled by weight, using
an equal-arm package checking scale.
o Category B, standard pack, labeled by weight, using
an electronic scale.
o Category A, standard pack, labeled by weight, using
an equal-arm package checking scale.
o Category B, standard pack, labeled by volume.
o Category B, random pack.
o Categoy B, standard pack, labeled by count.
69
0ATE STANDARD PACK REPORT FORM report number
8/2/85 WEIGHT ONLY | S%OS
Location of TEST (Name, Address) sTRetailer
□ Wholesaler
□ Packager
S+fOp *N ’Pop
PRODUCT IDENTITY
Sufldir frosted
BRAND
Krumbli
LOT CO DEIS) C
6l0l/62di/2<35
CONTAINER description
GoJnd beeind baX
plash’c liner
jJlabe
ISej
:LED WEIGHT
r fans lb)
_2j UNIT OF MEASURE
0.0 02- ?Ibz.
3 | MAV Table 2-8
p 41 & 42
0.0+O Ur
4j MAV (dimensionless
units)
EW3--SS &’2°
| 5 | LOT SIZE (N)
48
[ 6 | SAMPLE SIZE (n)
l/\ QA (p. 20)
1 U 88 (p, 19)
3 1 GROSS
WEIGHT
1. 1 08 Ur
M2. 4 Ur-
bl TARE
WEIGHT
0.l8*j Ur
0-18 4 Ur
cl NET
WEIGHT
(on\y USi
l6 & 1 "h
J
•md+iVe +
i re )
1 7 1 TARE SAMPLE
SIZE
| — | Alternative
/- \ — 1 (p 29)
d | PACKAGE
ERROR
E-0
-01 4
*K OQZ Ur
1 8 1 Allowed Number
UNREASONABLE
ERRORS Q
e 1 PACKAGE
— 1 ERROR
(dimensionless
units) [7]+ g]
-7
-+ 1
0 Rc (see [7] )
Range of Net
Weights
10 |RT (see [~b~[ )
Range of TARE
Weights
1 1 [ Rq -t- Rt —
0^0 =
n (Table 2-7,
p. 30 & 31)
13j AVERAGE TARE
□ dry
0-/54^'®we'
□ alternative
13a| TARE CORRECTION
□ Moisture
A\ □ Foam (p. 32)
□ Vacuum Pack
14l NOMINAL GROSS
—'weight .9375 *
0+0- @ = t,\2lUr-
PACKAGE ERRORS
Comments:
nr
DISPOSITION OF LOT
□ APPROVED
gf' REJECTED
7X'.
Acknowledged Receipt cf Report
Official
70
date STANDARD PACK REPORT FORM report number
3/15/85 WEIGHT ONLY 15 208
Location ol TEST (Name, Address) S^Retailer
Q Wholesaler
Q Packager
Joe's yMcurkct
PRODUCT IOENTITY
Spag he.'tH
BRAND
M«a
LOT CODES) C
T2T24J
CONTAINER DESCRIPTION
Cotrdboond
box
1 [ LABE
Hoff
ELED WEIGHT
!,(/&•)
2 | UNIT OF MEASURE
0.OOI erl
Q oz.
3 | MAV Table 2-8
p. 41 & 42
0.04+Ur
4j MAV (dimensionless
units)
| 5 | LOT SIZE (N)
89
| 6 | SAMPLE SIZE (n)
i n <P 20>
/ U KB (p 19)
jJ GROSS
WEIGHT
/. OS3 Ur
I.077 Ur-
bl TARE
WEIGHT
O.Obl Ur
0.06 ^Ur
cl NET
WEIGHT
(only Ui
ed -£crr c
I+QYIAO i /»ve
fasub)
| 7 1 TARE SAMPLE
SIZE
O | — | Alternative
1 — 1 (p. 29)
d | PACKAGE
ERROR
□ “0
■f .021 Ur
+. O/S* Ur
1 8 1 Allowed Number
UNREASONABLE
ERRORS Q
e 1 PACKAGE
— 1 ERROR
(dimensionless
un,,s,[7]i-[T]
+3st
+15“
LlJ Rc (see jT] )
Range ol Net
Weights
10 K (see |~b~|)
Range of TARE
Weights
11 | Rg -j. RT =
[3-0 =
]2j n, (Table 2-7, Hj AVERAGE TARE
* 30 4311 .OUUr^
Q alternative
I3ajTARE CORRECTION
□ Moisture
Q □ Foam (p. 32)
□ Vacuum Pack
14] NOMINAL GROSS .
— WEIGHT I.CCO t . O-Se 2 UOr'*
0+0- 0 = /. o^Un
Comments:
DISPOSITION OF LOT:
^APPROVED
□ REJECTED
~T~ Align,
Acknowledged Receipt ot Report
Olticial
71
Comments:
28 1 DISPOSITION OF LOT.
% APPROVED
□ REJECTED
/6fain~
Acknowledged Reofifpt of Report YJ
Q-G&aa^
OtUciafJ
~Doe^
72
DATE
2/ll 1 84
STANDARD PACK REPORT FORM
REPORT NUMBER
1+0/2.
PROOUCT IDENTITY
OrU _
brand
iVcuibJ^
LOT CODE(S)
SNfrZ. PNG 1
s libl
_tj LABELED CONTENTS
IZf/crif
2 j UNIT OF MEASURE
<5.00 1 St
3 | MAV (same
units as label)
Worksheet J!/
Location ol TEST (Name, Address) (^Retailer
□ Wholesaler
□ Packager
Cash/Cow
CONTAINER description
Ccu^
4 I MAV (dimensionless
See
Worksheet
units)
31
[ 5 | LOT SIZE (N)
96
| 6 | SAMPLE SIZE (n)
/n °/(p 20)
/U ETB (p. 19)
cn
^ I TARE SAMPLE
SIZE
□ Alternative
J. ( P ■ 29)
0
3 | Allowed Numoer
UNREASONABLE
ERRORS ^
I 9 [Rr (See Worksheet)
Range ot Net
Weights
This report form is designed for standard packages not labeled by weight: for example, liquid volume,
count, area, etc.
Fill out report form heading, boxes □ ‘HI- and boxes m through
8
Go to appropriate worksheets, follow directions on the worksheet, recording data on the report form
as directed by the worksheet.
Ill Rc - Rr
0 -0 ;
Hi AVERAGE TARE H NOMINAL GROSS
WE!GHT _ ,
See . See /■) XCt? /Jr~
Worksheet 6, 0%0w U r'Worksheet ' **
I2J Rr (See Worksheet)
Range ol
Tare Weights
52 1 n, (Table 2-7
p. 30&31 )
Comments:
28 | DISPOSITION OF LOT:
^APPROVED
□ REJECTED
7T ^Milh Q^triuA^
Acknowledged Receipt o( Report Official 71
73
WORKSHEET FOR PACKAGES LABELED BY LIQUID VOLUME
NUMBERS WITH BOXES (e g. (3] ) REFER TO REPORT FORM (page 53)
STEP NUMBERS (e.g. STEP 5) REFER TO WORKSHEET
Fill out report form up through boxjjf] , skip boxes [Tj and |~4~|.
(1st Pkg)
(2nd Pkg)
(3rd)
(4th)
(5th)
1. Gross Weight
°*9g4 IP
0. 813 (A
2. Tare Weight
*rt =
0.080 (Sr
0.081 (Sr
>
Net Weight
*Rc =
(cmbu, LbO£
. f^crr at
\J
teAMjUnjJt
'h-AJL. )
3. Flask Weight (full)
1, / 2. (£ (Jr~
1, Iz5“ Ur
4. Flask Weight (empty, wetted)
0. 5*<5V (Sr
5. Weight of Liquid (Step 3 -Step 4)
0. 5^2 Ur
0-5 '41 Ur
6. Volume of Flask
8 (lay
Sfloy
7. Temperature of Liquid
1S°P
IS °F
8. Do the weights recorded in Step 5 differ from each other by more than the value in Table 4-3 (page 38)?
YES □ If this box is checked, open all packages in sample and determine each
package error by volume (see Section 4.6.).
NO □ If this box is checked, continue below.
9. AVERAGE WEIGHT OF LIQUID IN FLASK = AVERAGE OF STEP 5 =
O.S^ISUr-
10. AVERAGE WEIGHT
OF LABELED VOLUME
LABELED VOLUME
FLASK VOLUME
• X AVG. WEIGHT OF LIQUID IN FLASK
'll. (RC/RT=.
12. AVERAGE TARE = AVERAGE OF STEP 2 (or average of Step 2 and additional tares)'
O.OSOSMr-
Record in box (TT) on report form
'Alternative Tare procedure for liquids packed in glass.
$lf additional packages are opened for tare, provision should be made for recording all pertinent data
74
13. NOMINAL GROSS WEIGHT = AVERAGE + AVERAGE WEIGHT
TARE OF LABELED VOLUME
Step 12 + Step 10
Ur-
0. OZOSitr -f l^\Record in box 0 on report form
14. For packages opened for Tare:
PACKAGE ERROR = GROSS WEIGHT - NOMINAL GROSS WEIGHT
(weight)
Sieo 13
)0.onUr
*0*00(0 Ur
3
4
5
15. PACKAGE ERROR
(dimensionless units)
PACKAGE ERROR -h UNIT OF MEASURE
(weight)
Record package errors on report form in crosshatched area.
16. MAV from Table 2-9 =
(volume) (pages 43 & 44)
0.
Record in box [T] on report form.
17. MAV
(weight)
MAV
(volume)
= Step 16 x
AVERAGE WEIGHT OF LABELED VOLUME
LABELED VOLUME
Step 10
18. MAV
(dimensionless
units)
box T~|
O.OltUr-
= wnr
(weight)
MEASURE
i4
Record in box [T] on report form
19. Compare unopened packages with nominal gross weight (Step 13, box (T4~[ ).
Record package errors for remaining packages in sample directly on report form in crosshatched area.
Compare minus package errors with MAV (Step 18, box f~4~|).
Average package errors (box [iff]). Convert back to units of volume as given below:
AVERAGE PACKAGE ERROR
(volume)
AVG. PACKAGE ERROR x UNIT OF x LABELED VOLUME
(dimensionless units)
box 1£
MEASURE
box |~2~|
AVG. WEIGHT OF
LABELED VOLUME
box [T] _
Step 10
-(s.S x O.QOlhrX ISjOcy
0, 015 7 oy
Record in box [19] on report form
(Boxes above with "3", “4”, "5” in corners are for larger tare sample sizes.)
oo
75
DATE
Y/2 0/85
RANDOM PACK REPORT FORM
(Page 1 of 2)
REPORT NUMBER
3 | TARE SAMPLE SIZE 4 | ALLOWED NUMBER OF
LOCATION OF TEST (Name, Address) ^Retailer 1 | LOT SIZE (N)
□ Wholesaler
JS. Packager
Qaalihj foods
57
UNIT OF MEASURE
(size of scale div.)
0,00 2 L-
2 | SAMPLE SIZE (n)
□ A (p. 20)
SO gB(p. 19)
I | alternative
(P- 29)
>tlb
□ oz
UJ product description, lot code
UNIT PRICE
8 1 LABELED
— WEIGHT
_9j PACKAGE ERROR
0/ +
10 1 MAV
L— J (Weight)
(p. 41 & 42)
11 j MAV (dimen-
sionless)[lO |-^-j 5
brick cheese.
0'4y
f
A
/es
oA?
2-
*1.13
<9.57
12-
O' S2-
10
O.Sft
3
O.(ol~
sz
0A3
If
0.63
\5
Ko
0. S2-
2
0.%1
L
12 1 TOTAL ERROR
-5- 0
1 3 1 NUMBER OF MINUS
' PACKAGE ERRORS
EXCEEDING MAV
m,
PACKAGE 1
TARE 1
6 | AVERAGE TARE
TARE 2
6 | AVERAGE TARE
TARE
UNREASONABLE ERRORS
o
DRY CLd-UCll -hXAd_
Q WET (page 2 for alternative)
PACKAGE 2
TARE 3
6 1 AVERAGE TARE
TARE 4
6 | AVERAGE TARE
LOT DISPOSITION
(B only; see page 2 tor A)
IS (tT|gREATER THAN ZERO?
□ Y&S
OB'nO ■
-LOT FAILS
O— ► CONTINUE
15J AVERAGE _ TOTAL
ERROR ERROR
NO. OF
PACKAGES
= 0 + 0 - s
16 AVERAGE
— 1 ERROR - ERROR In
in units of weight Scale div
AVERAGE UNIT OF
MEASURE
0 * B
= - 0.010 dr-
17 1 IS AVERAGE ERROR Of ♦?
□ YES — GO TO [7b]
*<N0— LOT FAILS
^ □ LOT ACCEPTED
B'LOT REJECTED
COMMENTS:
Setentia)t> "HriomcVvu,
Acknowledged Receipt of Report
Official
76
RANDOM PACK REPORT FORM
Page 2 of 2
REPORT NUMBER
ALTERNATIVE TARE CALCULATIONS:
1 3 j GROSS WEIGHT
| b | TARE WEIGHT
6bJ Rt =
| c | NET WEIGHT
6aj Rc =
| d | PACKAGE ERROR
0-0-0
6cJ Rc -f Rj =
@ * 0
1 e | PACKAGE ERROR
(in scale div)
0^0
6d| nt (Table 2-7 p 30)
Additional
Tare weights:
GROSS WT
6e| AVERAGE
— TARE
TARE WT
LOT DISPOSITION CATEGORY A
NOTE: PACKAGES SHOULD NOT BE ARRANGED FROM LIGHTEST TO HEAVIEST WHEN FOLLOWING A
0
ON PAGE 1,
THE NUMBER OF MINUS
PACKAGE ERRORS
EXCEEDING THE MAV
IS RECORDED IN BOX fl3~|
BOX [T] CONTAINS THE
ALLOWED NUMBER
20j
AVERAGE
ERROR
(Scale div)
TOTAL NO. OF
ERROR PACKAGES
QU GO
Til AVERAGE
ERROR
in units of weight
AVERAGE UNIT OF
ERROR * MEASURE
in no. of
scale div.
I
I
I
I
I
GROUP I
t
1
2
3
4
5
6
7
8
9
10
0" AVERAGE
R
IS 1 13 | Greater than | 4 | ?
u YES -►LOT FAILS. RECORD
DISPOSITION IN BOX QfT|. PAGE 1
NO— GO TO [20]
RANGE OF PACKAGE
ERRORS FOR EACH
GROUP OF 5 PACKAGES
SUM OF -r NO. OF GROUPS
R
R =
0 * 0
22 1 IS0MINUS? □ NO — RECORD DISPOSITION IN BOX [Te] . PAGE 1
□ YES — GO TO [23]
25[ TABLE 2-3
Col. 2 value (page 20)
ill (n/N)x 100 =
([T]^Q)xioo =
0 Use [27] to
look up 1 in Table 2-4 (page 21) f =
iil t= [0 x [is]
DISREGARDING THE SIGNS,
IS [20I larger than [29] ?
I I YES -►LOT FAILS
I I NO — RECORD DISPOSITION IN BOX [71]. PAGE 1
Record final lot disposition on page 1 in box 18
THIS PAGE TS BLANK
.
78
DATE
&/I8/85
STANDARD PACK REPORT FORM
REPORT NUMBER
ISA 9 O
PRODUCT IDENTITY
beer
BRAND
Mopptj Hour
LOT CODE(S)
22T>T*86
1 | LABELED CONTENTS
2 | UNIT OF MEASURE
0,002. ?£
3 | MAV (same
units as label)
Worksheet^# 5*
CONTAINER DESCRIPTION
0he-wo4j /rnefaJ
glass bottle/^
4 | MAV (dimensionless
units)
Location of TEST (Name, Address) & Retailer
□ Wholesaler
□ Packager
M's
[ 5 [ LOT SIZE (N)
J 7-0
I 6 | SAMPLE SIZE (n)
This report form is designed for standard packages not labeled by weight: for example, liquid volume,
count, area, etc.
10
□ A (p. 20)
B B (p. 19)
| 7 | TARE SAMPLE
SIZE
S+ 9t Alternative
/-* (P- 29)
0
8 | Allowed Numoer
UNREASONABLE
ERRORS
0
Fill out report form heading, boxes | 1 | & E and boxes £¥] through
8 .
Go to appropriate worksheets, follow directions on the worksheet, recording data on the report form
as directed by the worksheet.
| 9 | Rr (See Worksheet)
10 1 Rt (See Worksheet)
111 Rc - Rt
IlJ n, (Table 2-7
13 | AVERAGE TARE
14 | NOMINAL GROSS
S„0,N*' O.OffHtr
Range o 1 A A£)//jL
Tare Weights UiUUIUT
0^0 = 4
p. 30&31)
z
See 0 0395SIS-
Worksheet
s..waGHT /.mu-
Worksheet # 9 v ^
PACKAGE ERRORS
TOTALS
(-) (0/+)
Comments:
28 | DISPOSITION OF LOT:
APPROVED
□ REJECTED
Acknowledged Receipt ot Report
'Do-e-~
79
WORKSHEET FOR PACKAGES LABELED BY LIQUID VOLUME
NUMBERS WITH BOXES (eg. (3) ) REFER TO REPORT FORM (page 53)
STEP NUMBERS (e g. STEP 5) REFER TO WORKSHEET
Fill out report form up through boxQs] , skip boxes [T] and [T]
1. Gross Weight
(1st Pkg)
(2nd Pkg)
(3rd)
(4th)
(5th)
l.lMUr
/./? 7 Ur-
2. Tare Weight
Net Weight
*rt = o.ooi
0 . follr
O.nsUr-
'Rc = O.OO'i
o. m
3. Flask Weight (full)
)AO°l
1.10 ?
4. Flask Weight (empty, wetted)
0-SZS
O.S8£"
5. Weight of Liquid (Step 3 -Step 4)
0.5W
0. 52.5
6. Volume of Flask
2ft
7. Temperature of Liquid
lo°f
irF
8. Do the weights recorded in Step 5 differ from each other by more than the value in Table 4-3 (page 38)?
YES □ If this box is checked, open all packages in sample and determine each
package error by volume (see Section 4.6.).
NO If this box is checked, continue below.
9. AVERAGE WEIGHT OF LIQUID IN FLASK = AVERAGE OF STEP 5 =
0. SZlf JUr-
10. AVERAGE WEIGHT
OF LABELED VOLUME
LABELED VOLUME
FLASK VOLUME
x AVG. WEIGHT OF LIQUID IN FLASK
*11. (RC/RT =
12. AVERAGE TARE = AVERAGE OF STEP 2 (or average of Step 2 and additional tares)*
s Or-
Record in box 13) on report form
‘Alternative Tare procedure for liquids packed in glass.
Ilf additional packages are opened for tare, provision should be made for recording all pertinent data
80
13. NOMINAL GROSS WEIGHT = AVERAGE + AVERAGE WEIGHT
TARE OF LABELED VOLUME
Step 12
Step 10
d
.3<?S5t tr+ O.lSSZSUr
7Ur?
I. I?l Ur-
Record in box [m] on report form
14. For packages opened for Tare:
PACKAGE ERROR = GROSS WEIGHT
(weight)
Step 1
(TlSfUr- P8lUr~?
- NOMINAL GROSS WEIGHT
Step
+ .005
ttj
-hO. OObiij
.i
4
5
15. PACKAGE ERROR
(dimensionless units)
PACKAGE ERROR
(weight)
UNIT OF MEASURE
16. MAV from Table 2-9 =
(volume) (pages 43 & 44)
Q-s
Record in box QT] on report form.
17. MAV
(weight)
MAV x AVERAGE WEIGHT OF LABELED VOLUME
(volume)
= Step 16
LABELED VOLUME
Step 10
18. MAV
(dimensionless
units)
box (T|
yS.sU *• on
O.D37.7 Mr-
= MAV
(weight)
M±±£2zlL.
-r- UNIT OF MEASURE
= Step 17 -r- box (jT| =
)L
so7oi?-i
.ooi-lh- y
19. Compare unopened packages With nominalgross weight (Step 13, box [l4~] ).
Record package errors for remaining packages in sample directly on report form in crosshatched area.
Compare minus package errors with MAV (Step 18, box |~4~|).
Average package errors (box [l8]). Convert back to units of volume as given below:
AVERAGE PACKAGE ERROR _ AVG. PACKAGE ERROR x UNIT OF x LABELED VOLUME
(volume) (dimensionless units) MEASURE AVG. WEIGHT OF
LABELED VOLUME
Record in box [T] on report form
box 1£
x box [T] x
box m
+0.4*0.062- Ur* >2- ft
+o.o[z
Step 10
Record in box [l9] on report form
loesabove with "3", "4", "5" in corners are for larger tare sample sizes.)
81
THIS PAGE. IS BLANK
82
DATE
7/I/8S
STANDARD PACK REPORT FORM
REPORT NUMBER
IS 5 OS
Location of TEST (Name, Address) d Retailer
□ Wholesaler
□ Packager
Jr ■ C
PROOUCT IDENTITY
p &per clip*
BRAND
cfrp Jo'irrt
LOT CODE(S)
ncme
CONTAINER DESCRIPTION
plooKe. b
5
jJ LABELED CONTENTS
loo
2 I UNIT OF MEASURE
0.00 2. g"
3 | MAV (same
units as label)
See “>
Worksheet O
4 | MAV (dimensionless
units)
See «->
Worksheet S
fTTToTslzE*(N?
80
| 6 | SAMPLE SIZE (n)
(0
□ A (p. 20)
ja 8 <p- 19)
| 7 | TARE SAMPLE
SIZE
□ Alternative
^ (p. 29)
0
8 | Allowed Number
UNREASONABLE
ERRORS
3
0 Rc (See Worksheet)
Range of Net
Weights
This report form is designed for standard packages not labeled by weight: for example, liquid volume,
count, area, etc.
Fill out report form heading, boxes | 1 | & m. and boxes | 5 | through
8
Go to appropriate worksheets, follow directions on the worksheet, recording data on the report form
as directed by the worksheet.
1 Rt (See Worksheet)
Range of
Tare Weights
nj Rc * Rt
0^0 =
2£j n, (Table 2-7
p. 30&31 )
13] AVERAGE tase
See 0.0&2 lv~
Worksheet
^&GHT0j2^Ur-
Worksheet ^ '
Comments:
28 1 DISPOSITION OF LOT:
$ APPROVED
□ REJECTED
Mo>dfU h/h 1 m
Acknowledged Receipt ot Report ' ’ Official ^
83
WORKSHEET FOR PACKAGES LABELED BY COUNT
NUMBERS WITH BOXES (eg (T) ) REFER TO REPORT FORM (page 53)
STEP NUMBERS (eg. "Step 5") REFER TO WORKSHEET
Fill out report form through box [|] , skip boxes [T] and [T]
1. Gross Weight
2. Tare Weight
3. Count in Each
Package
4. Weight of Counted
Items
5. Weight of Labeled
Count
_ Labeled Step 4
~ Count x Step 3
(1st Pkg) (2nd Pkg) (3rd) (4th) (5th)
0.(18 (Jtr
O.noUIr
Q.oozUr
O.OOZ (Jr
lol
97
0.l33Ur
0.1 l~j Ur
o. muir
0,12-1 Ur
6. MAV from Table 2-10
(count) (page 45)
3
Record in box QT] on the report form
7. MAV/6
(weight)
MAV/6 x WEIGHT OF COUNTED ITEMS
<count> COUNT IN PACKAGE
Step 6
0.5 *
Step 4 (for first package)
Step 3 (for first package)
0.O00(o ULr -
7 o*
8. If using an equal-arm package checking scale, is value calculated in Step 7 equal to or larger than Vi the smallest graduation?
If using an electronic package checking scale, is value calculated in Step 7 at least as large as the smallest increment?
NO If this box is checked, open all packages in sample and determine each
package error by actually counting the items inside the packages.
Coit+wujlC. ClS OjjjAJJt
YES □ If this box is checked, continue bSIOW. “ ' “
9. Do the weights recorded in Step 5 above differ from each other by more than the value in Table 4-3 (page 38)7
YES □ If this box is checked, open all packages in sample and determine each
package error by counting items inside packages.
NO Averaae Weiaht of Labeled Count = averane of Sten 5 = 0-l2JS(Jlr-
10. AVERAGE TARE = AVERAGE OF STEP 2
O.OOZJUr-
Record in box 13 on report lorm
11. NOMINAL GROSS WEIGHT = AVERAGE
TARE
AVERAGE WEIGHT
OF LABELED COUNT
- Step 10 + Step 9
0. tzM- Ur-
Record in box [iT] on report form
84
12. For packages opened for Tare:
PACKAGE ERROR
(weight)
GROSS WEIGHT
NOMINAL GROSS WEIGHT
(2TT C6AW if-lMVtiXJ
+0.D>ZUr
-O.OOUbr
3
4
13. PACKAGE ERROR
(dimensionless units)
PACKAGE ERROR
(weight)
UNIT OF MEASURE
14. MAV _ MAV x AVERAGE WEIGHT OF LABELED COUNT
(weight) (count) LABELED COUNT
Step 6
Step 9
box|Tl
15. MAV
(dimensionless
units)
(37 o.
O.OOiM Ur
UNIT OF MEASURE
loo
■ vm
(weight)
= Step 14 h- boxfT]
Iff
? *
2-
o. 002-(
16. Compare unopened packages with nominal gross weight (Step 11 or box (u] ).
Record in box [T| on report form
Record package errors for remaining packages in sample directly on report form in crosshatched area.
Compare minus package errors with MAV (Step 15 or box [7]).
Average package errors (box [l8] ). Convert back to units of count as given below:
AVERAGE PACKAGE ERROR
(count)
AVG. PACKAGE ERROR x UNIT OF
(dimensionless units) MEASURE
LABELED COUNT
AVG. WEIGHT OF
LABELED COUNT
box [i7]
x box [2] x
box (T]
Step 9
(H xo.oozUrjOol
0.1215'Mr-j
clips
Record in box n9^ on report form.
(Boxes above with "3". 4 . and "5 " in corners are for larger tare sample sizes)
85
SECTION 8. RANDOM NUMBER TABLE
87
Reproduced, with permission from
A Million Random Digits, by the
Rand Corporation, Copyright, 1955, The Free press.
TABLE OF RANDOM DIGITS
31000
63837
17813
08076
19164
87014
83331
56364
32768
85680
47293
97023
35804
69886
47494
33898
89236
06100
68848
08674
26877
95856
65227
25165
01752
53984
87855
70753
80386
78600
97809
03548
00574
21143
11605
85683
79483
74858
87491
57785
07758
57784
22934
17165
37776
13995
74006
90843
85761
89037
89630
94575
64517
80897
04861
20355
08661
11092
19682
84287
13496
74367
32701
87819
29050
68419
49317
30340
62744
45214
61481
09786
08768
93715
43847
71877
53924
09630
62975
64470
99283
86530
86819
38955
91744
09047
83453
12775
32000
60098
83724
89682
53950
41500
16023
56126
46618
87708
91994
38384
13810
51503
55122
22997
82556
85630
22794
81623
10927
52252
93350
28643
39097
00914
69844
05002
71178
15414
99874
58046
70358
57182
45747
30830
70542
98169
51114
18115
40718
46082
28010
95831
94028
57041
75137
05576
47156
09300
11197
97670
80748
66311
79421
00202
68501
39746
23690
67845
83962
09451
39380
72397
88106
07851
67756
55865
70318
58189
35340
91500
34223
72744
83926
40078
80791
91332
44474
09925
41416
96671
51010
08021
53914
37499
40228
48890
58264
18790
91535
04933
24076
93198
77444
53782
48866
49408
42923
28162
09789
15155
5C307
90901
18117
36505
01598
48320
09322
13457
84931
51701
51083
00619
05548
25431
15175
43249
71593
85595
59834
01488
00370
17413
75537
79824
24428
55737
45462
12484
64858
43581
39551
38058
10445
18463
80812
02369
11289
99499
32922
88429
92788
62546
26147
83529
10012
98650
95898
74254
45173
17430
95591
85858
51058
2614 0
00995
67853
23563
410G3
63355
72454
95508
17513
29416
61238
25818
08844
59844
68794
32783
60318
94574
45842
67221
77115
43398
87786
42425
92091
86274
82166
99463
15216
28719
04716
80246
39244
76967
83263
57849
85890
30245
87395
80966
28721
11095
61270
51111
50490
40940
02832
33361
79191
97398
40881
98552
13567
4 67089
47435
75156
70217
50564
15287
94279
69154
75473
23597
48246
74325
66320
90155
90959
99765
59374
45204
87750
79826
34043
73218
72788
26143
68901
51249
35382
67776
06271
46832
40591
23477
21063
31229
89632
64623
849S6
85990
47639
98862
93422
66212
86413
82884
83862
88274
68301
99673
40945
27047
91550
18903
45535
45586
22697
54985
64852
58775
66737
27384
03122
17454
03250
23232
06450
3281S
88752
28722
94656
35461
56349
81936
14964
83638
25932
16298
23521
72454
11640
75847
15678
22842
44615
97810
55128
99785
33467
33834
04860
20064
98145
84774
07907
10992
40422
07368
26795
24353
78969
21501
75317
09049
69440
16137
58042
44218
52775
49082
54400
80940
39231
54836
18038
03557
42723
68340
47452
17443
69289
11213
60979
04130
72380
73582
92606
07225
18014
71063
50111
56656
76389
37904
98017
07663
65614
11410
90637
63675
43554
CC742
66785
79065
93573
19853
68997
96338
40823
96247
55573
14878
05422
65358
85636
31948
82428
00637
41814
68871
31683
06917
32850
80134
01832
25905
28941
58659
66731
99910
27156
06220
07507
391 19
38024
99720
51243
22351
63266
94057
06573
90484
42010
53308
33206
36137
77611
78925
06071
G63 14
35705
73882
03 111
88447
43279
35057
16881
87372
72616
18796
58537
1G0IG
72229
54720
098-16
51392
G-l
88
TABLE OF RANDOM DIGITS
32942
95416
42339
59045
26693
07410
99859
83828
21409
29094
59981
68155
45673
76210
58219
46251
25437
69654
99716
11563
65558
51904
93123
27887
53138
99187
19258
86421
16401
19397
35641
00301
16096
34775
21562
14031
00936
81518
48440
02218
60677
15076
92554
26042
23472
66314
05212
6785,9
89356
20056
20416
87410
75646
64176
82752
28701
56992
70423
62415
40807
74579
33844
33426
07570
00728
62615
52342
82968
75540
80045
93945
06293
22879
08161
01442
75689
76131
96837
67450
44511
02921
16929
35424
93209
52133
14295
34969
14216
03191
61647
05303
91109
82403
40312
62191
57071
90357
12901
08899
91039
78471
57741
13599
84390
32146
89242
79337
59293
47481
07740
14955
59592
97035
80430
87220
42446
41880
37415
47472
04513
18534
22346
54556
17558
73689
39284
33737
42512
86411
23753
33922
37329
89911
55876
28379
78355
54013
50774
30666
61205
08845
99145
94316
88974
29828
01769
71825
55957
98271
02784
17639
38284
59478
90409
21997
05851
58653
99949
63505
40409
42396
40112
11469
03476
03328
13318
14192
98167
75631
74141
60571
54786
26281
01855
30706
09531
81853
59334
70929
03544
72865
16829
86542
00396
20363
56324
31093
77924
28622
83543
78192
21626
91399
07235
07104
64666
34767
97298
92708
01994
82201
75694
02808
65983
74373
15360
73776
40914
85190
54278
68142
67957
70896
379S3
20487
19138
31200
30616
14639
44406
28155
03521
36415
78452
92359
87971
29031
51780
27376
81056
58147
68841
53625
02059
75223
18875
52809
70594
41649
32935
75109
56474
74111
31966
29969
35983
03742
76822
12073
59463
G-2
49057
87496
20624
14819
48667
65114
36701
25762
12827
45692
45738
29550
24736
09574
35036
08803
86027
51867
12116
38469
21488
09095
78777
71240
87225
83297
40111
49326
81686
40601
97983
45040
19200
16383
68739
04756
19506
60695
88494
58501
69869
62877
19584
39576
18290
30648
87349
20389
53805
85243
63606
37011
57346
69512
56464
98086
58850
28968
45297
80419
07079
19322
56325
84819
48754
53069
20665
21282
07768
60375
75071
21427
94842
26210
95002
50424
82848
41975
71663
79656
87327
95897
65171
20376
13475
30296
66667
10101
63203
75144
67023
90073
83205
71344
96216
67251
-28701
03846
94589
88403
00871
09354
22745
65806
78187
43345
25716
70020
54005
23973
06392
79028
57123
$2872
94991
49494
08860
08038
43624
46013
14894
05030
19561
56517
96479
29690
26096
81361
93099
33868
81031
2205S
21487
54613
81052
42574
47773
36027
27174
44830
97069
90327
61842
29604
47994
66731
40311
88495
18821
12463
56199
30068
82800
696S2
45133
85551
90729
64938
52403
56841
84238
26570
51790
42122
40S74
22369
36757
89117
54998
87031
66578
32019
65884
58485
10909
18510
89541
13555
21168
81318
13010
69645
49608
54738
17894
28912
15059
80192
83964
61904
73652
64425
85149
75409
67104
53188
78476
07804
62404
34828
66693
13094
74183
73020
31086
99054
62944
47351
89098
26735
95350
16371
03426
13895
42170
44236
57360
81644
94761
92813
81091
56513
88321
97910
22235
86155
55488
50590
74514
58791
16783
19272
61994
71090
784 1G
26430
82096
01605
65846
65228
70093
98901
84550
25769
82586
84420
15868
99505
11426
62723
89
TABLE OF RANDOM
12651
61646
11769
75109
86996
81769
74436
02630
72310
45049
36737
98863
77240
76251
00654
82861
54371
76610
94934
72748
21325
15732
24127
37431
09723
74146
47887
62463
23045
41490
90759
64410
54179
66075
61051
55683
98078
02238
91540
21219
79686
17969
76061
83748
55920
70333
00201
86201
69716
78185
14042
53536
07779
04157
41172
59911
08256
06596
48416
69770
62368
62623
62742
14891
39247
57529
97751
54976
48957
74599
15469
90574
78033
66885
13936
18625
23674
53850
32827
81647
74626
68394
88562
70745
23701
11119
16519
27384
90199
79210
41101
17336
48951
53674
17880
32123
91576
84221
78902
82010
26091
68409
69704
82267
14751
67680
79790
48462
59278
44185
15184
19260
14073
07026
25264
58010
45039
57181
10238
36874
56425
53996
86245
32623
78858
82630
84066
13592
60642
17904
14927
40909
23900
48761
44860
23740
22505
07489
85986
74420
32990
97446
03711
63824
07953
05310
24058
91946
78437
34365
21839
39937
27534
88913
49055
08833
42549
93981
94051
28382
58336
11139
47479
00931
91560
62032
91144
75478
47431
52726
45171
30557
53116
04118
58301
91611
62656
60128
35609
63698
55472
63819
86314
49174
93582
18573
09729
74091
53994
10970
60866
02955
90288
82136
83644
45043
55608
82767
60890
74646
17831
09737
79473
75945
28394
40137
03981
07585
18128
11178
77776
31343
14576
97706
16039
69605
44104
40103
95635
05635
19916
52934
26499
09821
87331
02606
58552
07678
56619
65325
65183
73160
87131
35530
47946
10740
98914
44916
11322
89717
98642
89822
71691
51573
83666
60139
25601
93663
25547
02654
DIGITS
97669
25757
32535
07122
76763
18029
07469
42341
98173
79260
64688
09343
70278
67331
98729
44124
05610
53750
95938
01485
63529
73977
95218
96074
42138
07954
22597
60012
98866
90959
75385
51378
08360
95946
95547
17720
87817
41705
95785
12563
83612
41540
86492
06447
60568
62154
77930
67663
29529
75116
36473
42123
43929
50533
33437
68797
56080
14223
59199
30162
52242
98832
69533
91174
57979
08759
78494
52785
68526
64618
42117
71831
22961
94225
31816
80820
00420
63555
74489
1
80141
45630
65891
58220
35442
60414
76965
99546
30323
31664
22845
45260
08575
49321
36191
17095
30847
62329
63898
23268
74283
13151
93115
01437
56945
89661
29616
76531
19589
83139
28454
08388
27182
22557
61501
67481
28546
37444
80824
63981
39942
08143
60377
42925
42815
11159
99718
63432
88642
37858
25431
92467
31742
87142
03607
32059
21744
97711
36648
35620
97949
85965
87089
11687
92414
67257
82469
12430
84754
19354
72745
19218
47712
67677
51889
70926
83725
72643
64233
97252
17133
95372
97642
33856
54825
55680
30289
42411
91886
51818
78292
24375
65609
85810
18620
49198
78356
50682
22505
01692
36291
73604
78614
78849
23096
72825
86557
65661
41854
26037
53296
94455
06560
78029
98768
71296
79485
13619
98868
40857
19415
79334
70577
38048
03607
06932
32601
27994
05641
22G00
86064
47517
43300
59080
80392
63189
81G73
CS657
09559
23510
95875
80993
61299
36979
73599
35055
30705
99582
53390
46357
13244
09854
18080
02321
05809
041
88189
30143
52687
194 20
60061
6164 2
4GGB3
33761
47542
23551
94829
48672
23736
84994
13071
G-3
90
TABLE OF RANDOM
42902
51104
38993
54071
75033
82989
95401
97093
57790
09271
13523
66327
39522
83279
50432
74785
72548
36886
97749
52364
77739
44753
03957
53267
13225
58236
98093
81969
21510
20727
94641
38922
76016
66041
92109
15317
99242
46970
58119
15178
00624
09824
83319
26428
69711
23295
02389
05795
70981
05664
70292
13217
90859
05792
09833
08550
22580
43519
51755
50308
94981
10727
29544
37001
02751
70318
46657
73496
92074
63918
27510
92421
43020
79733
81369
41289
29535
33408
05708
76999
37586
71952
19967
77327
45052
65737
05451
24726
95840
89663
87473
53058
80611
24464
50379
89920
40997
03736
00992
80443
10203
39157
90207
07120
19280
63864
57186
93586
52497
32459
45006
51623
30675
56395
67037
01839
83286
87159
72173
69624
07708
41627
62416
05579
87013
17655
18629
94121
20967
82561
96137
55079
15672
21474
22403
66495
22010
73641
70391
31391
54585
37425
12794
71143
65025
28180
01067
68577
99878
01960
44655
45433
72815
11383
27507
31321
57930
02748
46178
27490
36218
26166
64389
39466
53435
06853
28955
15516
22467
54482
45231
95235
00120
85500
41753
60484
63181
83125
42402
86905
83577
81518
87638
08719
84819
09724
39466
80440
69636
37481
58504
66886
64596
23484
25596
37033
02248
28174
29215
51118
28026
12852
46235
15058
00222
12831
55496
60299
47364
52600
14507
71736
33817
42164
89793
82424
22539
73202
32091
97375
59133
35497
25135
24968
93294
72031
14923
44610
70690
35644
65161
59905
40133
95680
78737
50062
64153
20669
81461
80140
18116
19026
22965
39908
30649
29105
00954
71562
10193
41802
DIGITS
43897
24684
62233
05749
76653
05895
27692
65558
28890
75645
88392
37826
81599
97612
34122
78430
15990
86418
53689
73170
89471
59481
53923
52588
54986
91655
23601
77178
43468
77172
76430
07105
45987
62177
37542
10125
89295
83401
28737
53214
71980
77666
57012
83722
06961
32846
99935
81786
90285
03818
49409
45496
62194
98232
59969
68330
70244
27806
33662
90457
82481
33622
89729
10488
54507
13428
13249
68163
31032
72138
11801
43094
91733
79865
67010
37772
97740
44905
16840
25538
16811
52264
09700
08766
08450
37418
31034
44631
02044
89446
93555
80327
29829
75884
69962
12071
57996
42605
92034
89189
37862
96041
66652
05173
59475
85507
19646
80758
31519
71022
33850
94000
57166
88739
92350
75457
95469
48064
31695
17608
84309
56068
84979
78592
36446
65520
87874
72484
86640
33610
74557
10290
39575
62266
10125
43927
45219
38479
80100
82717
74706
30555
42290
45357
08567
86209
95045
62490
34554
65505
80064
26860
44549
42538
48425
65081
97037
67297
54273
67483
89404
45328
34152
24787
98162
70997
37271
13166
32827
29958
36053
04285
77365
33273
97811
40988
25091
68407
18356
62600
15068
60067
48628
46522
78010
20907
90064
06280
57942
71723
43400
04787
54631
05421
50230
04863
23752
10000
33331
62358
26478
73671
81592
18436
67676
02906
93295
27011
42904
33856
67645
06609
224S3
49017
99946
11126
75877
89720
83213
65129
12442
89020
11700
42936
43010
97897
16835
41673
63777
90758
93726
95312
18215
20184
842S9
88536
24552
78781
39807
00018
91235
27259
08170
77321
12795
53790
85828
60565
09835
42761
G-4
91
TABLE OF RANDOM DIGITS
43398
79666
37687
36431
34822
78711
15270
42232
87128
31711
54489
52503
11005
00067
23146
17324
40078
14214
19160
25276
67297
25163
16386
62687
07398
56959
16184
32709
57507
92221
78207
34228
39440
67765
80627
99508
47528
01328
67220
50824
66199
99811
13887
31301
41034
91987
73491
22639
94096
01702
80125
84984
47804
90908
11106
69743
16618
59364
73 313
89143
41686
85487
91526
28593
54635
80967
75537
81999
02257
62232
24148
95247
12340
39407
71596
22989
64262
12716
32930
32303
54147
01638
95954
66666
30544
07529
10668
23743
02743
10252
36379
13588
44587
31015
34971
38653
73761
61363
95667
03372
72327
65811
53782
01608
38741
41133
06312
13340
18870
27204
15039
81095
50787
28452
61100
40499
67587
16761
25929
43836
46910
72907
18515
12710
11580
15009
81751
07942
14046
54993
10538
10295
62995
16527
55334
70204
91225
78307
55577
78715
30403
98849
55318
99947
23625
75147
49930
47054
08485
91397
20770
53498
05412
19184
25997
51096
90416
18721
42390
31517
05027
43924
37581
31418
57010
22013
11299
76690
92730
10867
50232
30821
45382
85723
15635
20724
99075
91270
13936
74962
65692
61084
48856
34766
09098
81215
08824
06387
10900
83463
86127
96878
53819
10715
67213
26483
16992
89421
15216
71632
84697
87543
67935
72389
18299
89691
53802
42595
310S9
20914
20295
92548
68410
15006
02091
98925
64297
94922
26349
58805
53560
52945
68649
31696
69387
45034
92695
98157
83536
55140
35222
86197
20082
60378
05392
08071
77462
20243
55151
02607
54802
07781
29975
44720
62534
84209
92329
32234
11385
09067
00779
38828
71137
85054
64660
77482
85873
17317
94357
78210
44973
39257
65815
13929
77081
05125
52020
97099
77116
45921
18963
60035
35598
14404
14872
82925
46064
94665
73523
23638
08869
05514
24215
65237
82139
47847
69726
75453
08780
53120
63717
10310
33607
01858
28266
48093
35976
93334
17638
65818
43995
83182
39647 ‘
41504
23286
89412
39331
84989
92091
01383
77149
59117
30291
68266
65760
00956
24954
88932
90733
35767
53961
61089
68699
38891
87153
18783
65166
56622
93342
14032
67089
04524
19251
57440
69100
47893
83969
54252
47327
31685
25146
33188
05213
17157
65663
35800
58711
15872
33342
02963
58353
51594
48982
85028
75444
83187
91970
91498
17234
52283
39538
25225
92624
18517
77361
43466
80409
95407
46777
22668
52823
95769
71506
39644
66877
68001
13782
91933
61130
61752
05736
92168
35393
01026
26984
54507
21486
26920
52995
98095
74643
85157
45893
49287
03567
25614
83669
08353
61573
49629
06100
27128
43137
77812
13101
28366
30073
89021
40881
36162
05808
75544
68156
75440
64496
12748
58655
44844
11933
16752
85910
19874
61262
74598
41321
15346
05181
52254
42138
18237
87381
29763
65051
91174
80750
19773
83029
816S9
66067
38729
53160
17249
44596
76354
33601
83429
96263
16342
15595
48978
93559
90668
86972
42G32
40502
80542
96241
14487
84488
74117
78176
67889
32552
62792
30147
55911
80640
74650
71207
14412
62573
15635
23958
75948
59083
91189
98557
21505
89477
3 3010
41064
03418
28472
39593
19710
78441
12397
76800
62801
62770
1G001 .
78043
70078
13091
09599
99793
84549
50498
13340
41986
G-5
92
TABLE OF RANDOM
07018
31172
12572
23968
55216
52444
65625
97918
46794
62370
72161
57299
87521
44351
99981
17918
75071
91057
46829
47992
13623
761G5
43195
50205
75736
27426
97534
89707
97453
90836
96039
21338
88169
69530
53300
68282
98888
25545
69406
29470
54262
21477
33097
48125
92982
66290
27544
72780
91384
47296
53348
39044
04072
62210
01209
34482
42758
40128
48436
30254
99268
98715
07545
27317
52459
95342
97178
10401
31615
95784
38556
60373
77935
64608
28949
39159
04795
51163
84475
60722
41786
18159
96649
92406
42773
95627
30768
30607
89023
60730
98738
15548
42263
79489
85118
75214
61575
27805
21930
94726
73904
89123
19271
15792
72675
33329
08896
94662
05781
59187
66364
94799
62211
37539
80172
68349
16984
86532
96136
53893
19193
99621
66899
12351
72438
49017
23489
19172
80439
76263
76941
7700S
27646
82072
28048
55430
25875
26446
25738
32962
33023
26895
65304
34978
43053
87337
74487
83196
61939
05045
81773
36773
21247
54735
68996
74279
85087
94186
67793
18178
34968
76028
54285
90845
35464
99696
78454
21700
12301
88832
55282
61051
97260
89829
69121
31337
83886
72886
42598
05464
94128
97990
58609
20002
76530
06511
48241
49521
64568
69459
69981
03469
56128
80405
97485
23701
56612
86307
02364
88677
09237
24607
12817
98120
30937
11007
45461
24725
02877
746G7
60622
78444
39582
91930
97948
79973
43668
19599
30021
68572
71080
71367
23485
82364
30321
09923
26729
74573
16583
37689
63094
72826
65558
22616
33472
19806
42212
41268
84923
21002
17295
74244
43088
27056
86338
59338
27190
99302
84020
15425
DIGITS
85366
56223
09300
94564
18712
59344
20149
17596
51669
47429
55008
93371
60620
66662
27036
26797
64423
42379
91676
75127
77473
07268
31330
07337
55901
78967
00704
85734
21776
85764
29895
71507
28517
77761
17244
46476
54562
79373
72993
98998
98382
11265
25366
06636
25349
54892
59168
83951
91075
04724
43999
54952
68699
31912
09317
50029
19016
56837
05206
33851
75366
43688
27460
65145
65429
77026
33087
65961
10056
72834
94764
45312
71171
15400
72182
35268
05044
56420
39214
89822
23672
37333
85734
S9886
81200
31519
53462
90489
81693
17849
97073
01574
57310
59375
54417
39454
19616
72239
93791
22610
62175
48746
56084
54029
22296
53284
28024
45421
37956
14252
43269
91133
05562
82385
91760
48268
82821
19526
63257
14288
99839
24228
32079
53517
18558
98918
59330
20121
89779
58862
41589
70883
72035
81800
50296
24266
26814
01194
48587
93319
2S951
22676
05303
39725
60054
20405
69324
80823
20905
68727
16937
18134
51873
10973
77090
82224
17069
S7880
54945
73489
68076
15868
70063
26794
81386
96796
59341
16136
01803
17537
86547
62195
72492
33536
60137
88071
92209
50728
67442
47529
81981
30999
50147
93941
80754
95079
42588
98590
12829
64366
88251
76708
09558
86759
15065
17192
23082
00728
78660
74196
70666
76059
44446
94188
14060
18427
45658
40044
59484
59966
13221
99234
99629
22430
49247
31816
63033
14597
28953
21162
42982
74427
25625
74309
15855
06703
21846
78329
98578
25447
67515
75585
90005
19717
08865
30588
40676
94961
31154
83133
47331
09737
83735
84058
12382
14748
42380
99376
30496
84523
6-6
93
table: or
RANDOM
29257
36060
81080
67493
23666
04426
95304
83272
18379
46498
72622
55513
82844
85553
16852
63755
08166
33097
46244
16769
23931
55916
48477
33067
76572
96443
13697
61186
63971
20547
33595
83707
92545
83866
06895
87400
72301
05172
25637
13665
10716
35521
73850
99275
97475
81465
80905
77978
42899
65518
77706
53575
16463
00350
44697
75622
35864
56564
40277
66044
18418
16826
26355
51841
01235
02205
51273
87582
80276
88583
08345
03180
15659
86285
09579
43734
89733
87697
28098
70926
89981
80872
87829
56857
78208
20660
70109
01273
42633
77445
48210
18773
36169
60470
37941
65433
21735
36444
40569
32023
09638
39323
55045
58988
30967
89418
30419
67738
14877
17948
23083
08913
59531
11403
96757
30343
01516
78510
15138
49538
18284
64484
57502
80120
95894
47943
40974
82162
34485
44930
55480
50090
91328
09979
23824
29905
4632S
06091
12419
35540
82268
73981
37205
65249
07751
42183
74789
78645
68686
12399
82178
50120
06396
62927
27126
49836
15424
10577
89926
89407
96881
32775
85851
60822
08530
20414
02812
65040
27108
34291
62174
64315
82589
31761
26476
48808
13755
89592
43057
35053
93162
69261
87781
82538
75030
81009
59154
63054
77841
35348
11796
19222
73310
68903
54526
48728
67741
07718
37592
95126
73347
09803
63349
39332
23487
34704
15020
45067
29373
24970
24147
47285
01070
86152
20380
38113
53850
17580
01850
33698
01435
59660
45587
96635
57407
76230
93764
38424
43810
11252
76698
49005
35125
73104
93675
21081
41735
47975
16487
37540
25671
3220G
93142
93930
57886
03245
76312
63143
57914
10925
G
DIGITS
22251
17616
60716
77125
18653
60045
80649
35179
03185
57068
57931
04063
57516
46529
47030
48531
56618
90035
88363
04097
84835
96208
68558
23560
89245
14846
77137
62636
88927
34322
28019
08547
04275
79277
28833
86725
45970
42670
35291
22685
11064
93492
05362
57562
99582
48688
96755
83554
76916
15224
94868
22697
33740
60701
04034
78417
52968
52982
82340
92970
15986
65898
74181
51391
11313
30633
50721
65017
48735
0,4476
07969
17850
88197
14309
25013
22790
79293
01093
72673
60257
85949
60249
30159
45499
29735
02439
03144
12100
12971
59574
68015
76627
38973
81699
34262
60078
31045
99679
76253
81056
16461 .
. 57491
58625
14327
19825
30083
54764
62024
68310
21207
23468
57382
48057
70725
59933
58588
06080
23844
44412
87882
34977
74098
73551
81743
58364
27794
66180
76055
69035
91186
71199
65640
69121
12071
46595
09817
63102
80393
76848
09779
92537
92368
09251
29892
53919
27592
36651
05904
45764.
11336
40350
87365
28918
39266
22549
37622
38430
48356
93062
86591
83330
99819
24740
34199
90176
90243
18207
85800
53786
28723
95984
54304
13061
77554
92988
53853
20086
12130
90105
26139
08496
25862
41090
06267
07824
61706
27750
03274
64051
62435
56338
54017
47320
67925
40813
68160
55907
46168
06840
96853
69045
51759
99114
86318
60963
94427
23023
88559
65920
9 <
13113
60138
69612
38184
41601
6023 9
840G5
82019
52464
11836
97292
15584
05498
54391
33149
02843
64856
71551
6618G
36921
83189
38168
69103
75653
64780
89936
16311
78716
51 188
87349
14113
18177
97474
326G9
21:
61894
91043
64156
61020
55339
7
94
TABLE OF RANDOM 08GIT5
12304
04213
03857
77012
84959
59502
54256
54169
18949
00578
52525
24721
81450
99816
07524
06066
38128
36539
68551
74800
32362
41206
88773
78930
14709
55291
39114
43274
08119
42433
51077
99516
90497
26100
79144
29369
93401
32750
04395
63773
42533
89580
38883
55304
05990
04754
07817
51857
33035
00758
32520
68082
07089
28568
15498
18689
25625
09537
43720
39550
57766
90922
46815
02604
10651
16644
40236
98798
16895
47562
54973
61336
84051
15680
61130
18843
01926
08340
63318
39291
30789
48386
59732
94241
28859
23835
05112
17169
92771
81220
99348
87514
12386
12568
79923
52403
25537
61636
84602
75830
94954
12924
25669
91119
51663
28337
02935
11644
94210
85920
02045
59831
38770
48734
87524
39668
61855
36871
50775
30592
77174
97729
23913
48357
63308
84205
12639
79348
36085
27973
31893
11224
92074
54641
53673
82986
90226
06873
21440
75593
06252
31044
12478
37622
99659
39097
59195
57175
55564
65411
54053
73645
91616
11075
80103
92640
43265
78025
73539
14621
95234
80109
27587
67228
80145
48122
50637
16690
20427
04251
89174
38509
70183
58065
65489
16862
18929
90730
35385
15679
76054
03096
10934
93242
13431
39901
38669
82462
30166
79613
39221 64403
27463
10433
07606
14704
78488
02979
52997
09079
35052
59679
46888
69929
75233
01514
33319
53638
83161
08289
59723
91330
82433
61427
17239
75249
58952
35766
31672
50082
82558
71239
10853
42581
08792
80822
66731
20341
27398
72906
41067
39859
54458
90542
77563
13008
65442
26337
66530
166S7
36084
99076
34314
23729
85264
37741
50156
28603
10708
68933
53863
21679
49848
20212
95997
72749
86070
61699
19657
21066
29159
99127
49280
66476
22569
30921
23803
32781
20508
10456
25123
82601
48698
86804
39779
53045
29083
18310
02445
83490
28324
78290
22654
79424
93171
29493
73060
05438
78848
21222
22509
58052
94655
59881
73303
84795
46887
37543
12070
01151
00217
74945
29306
71156
07467
47209
02896
40180
52349
02624
47538
30491
39659
19233
00997
30781
89366
72890
83027
49302
44605
42552
09081
57256
55053
68949
86588
81732
61205
98340
07370
25804
52349
20145
54183
68367
14568
66179
63268
15912
56581
59255
48255
03675
88717
34897
64019
80421
94358
83868
92889
25249
10664
31461
37253
78117
31536
38256
97799
78542
74387
85480
33475
43352
00890
57143
17381
68856
25853
35041
16090
51690
54607
72407
55538
65157
07456
22255
25626
57054
54421
1S130
60103
69593
49464
41373
49502
17972
82578
16364
31065
83613
69889
58S69
29571
42547
70457
03426
72937
83'792
07831
59309
13276
26710
73000
39044
47450
03197
127S7
47709
10175
12822
86687
65530
49325
64477
73709
73945
92396
68263
31833
82093
16747
10386
59293
99742
50866
78028
75573
67257
24590
02770
48582
00906
58595
47416
13389
80268
05085
96666
16285
93699
60912
94532
95632
92709
90110
47506
53693-
49892
52507
32097
37594
10067
67327
12639
08141
12640
28437
09268
89160
19666
08814
37841
12847
22795
66948
65581
84393
15S90
13257
61973
24450
52351
16602
63955
17276
10646
74692
48438
51839
52901
53355
83281
19177
35179
46560
00123
44546
79896
05575
96855
23820
11091
79821
34189
921G6
15181
66628
58599
G-8
TABLE OF RANDOM DIGITS
00958
98267
66194
28926
99547
30346
26957
78240
43195
24837
14056
57841
00833
88000
67299
96789
22551
12111
86683
61270
12633
15075
47189
99951
05755
25893
57092
76396
72486
62423
13092
50817
46409
17469
32483
72872
54109
74626
22111
87286
20724
19944
34450
81974
93723
37009
52173
36327
72135
33005
25961
70386
74185
77536
84825
73962
47022
12296
41623
62873
63164
76372
90822
60280
88925
05366
00082
72121
79152
96593
15902
61363
95268
41377
25684
53845
17851
92603
09091
75884
31694
55633
18813
90291
05275
23016
96567
38840
26903
28624
17292
18430
05959
33836
53758
75465
99837
85141
21155
99212
89013
86492
75047
59643
31074
44551
77837-
30752
95260
68032
49675
13139
22986
82575
42187
40789
73539
99439
86692
90348
64086
82765
20389
93029
11881
79143
31528
39249
05173
68256
28231
07703
96777
33605
29481
76327
50155
04860
32918
10798
05428
65225
64285
86579
77447
56800
69853
75583
38682
55733
96180
50261
88659
11717
88909
52712
95148
66393
07111
89741
76869
19027
12764
32712
60671
50472
24399
17313
79665
07409
77168
64382
26927
54318
51043
79482
10156
87785
49603
85048
97826
82559
69027
41569
05422
00872
36839
01840
14860
76529
68457
71054
94300
18582
55813
35973
75910
16921
48284
48074
32091
50229
65799
13777
93030
81440
18180
6S025
89261
65881
83893
89983
95140
400S9
21441
64000
19357
74288
60608
49826
48420
68527
2S646
44721
81925
96237
34204
08890
41795
28507
13429
41773
59936
30327
76898
20753
53940
49246
73092
81744
6375?
93547
77926
16709
05242
444)5
49199
55899
09790
70636
/
16625
45515
67953
12108
57846
32511
70880
22070
52622
61881
68215
11274
55624
32991
17436
58036
64192
90611
15145
01748
03834
43782
90599
40282
51417
27618
84184
78922
73561
52818
09083
76175
19985
26309
91536
46772
42243
68046
44250
42439
49023
58432
67083
36876
93391
28701
34710
49359
50693
89311
09934
99103
09325
67389
45869
37943
25584
09609
63360
47270
99610
42772
60561
76873
04117
90305
10189
79778
68016
13747
08151
61816
58555
54305
86189
93424
72586
88903
30061
14457
01223
79607
95426
34900
09778
67157
51986
42865
14508
49315
16562
41081
38012
41230
20528
32685
51403
31926
69813
58781
38172
03718
32119
69506
67143
62871
58781
34143
68790
69766
62295
84295
30634
66562
31442
66036
48399
73451
26698
39437
71685
65452
89047
6366S
02656
36359
20250
68686
05947
09335
20063
09398
01843
35139
61344
50492
52655
33359
94713
28393
75313
35762
45824
21535
48707
98453
35129
73541
62087
36549
87891
16709
97814
26600
79266
03758
42184
67000
66680
61277
98845
81227
38052
48243
91867
73900
66673
58861
08168
10289
03483
76777
27319
78196
16909
63090
60719
29756
10696
75713
47286
97825
15559
43482
07676
55890
12228
33910
26873
88758
26346
68685
24920
36374
87702
01401
10518
25359
52702
82966
53615
17057
07212
75930
56G04
32138
73735
78459
74164
18466
39173
46895
16136
92301
33754
78374
72191
94 337
24234
44821
48579
35499
634 75
95235
51410
83735
82390
49173
80738
89279
96866
22721
96619
20297
01714
00189
G0064
57631
77199
8 2 7 4
91269
52190
47-181
82784
612
19057
51986
69657
97293
•l 7 7 2 <J
96
TABLE OF RANDOM BOGUS
04340 19889
41110 86887
73187 80431
95568 86799
23893 19483
27266 77468
19559 64945
57245 77311
49721 89049
18624 78634
57278 28133
97953 43227
07431 45121
20930 54735
78003 86322
48541 02641
52684 87995
44032 67360
40757 07266
42290 21749
37592 08604
32583 59967
75625 48032
91808 34409
11926 91034
78782 17338
54319 43047
34359 78839
52871 79550
69226 39419
07575 58710
91682 48619
62040 64062
80099 81346
77758 41609
20009 11788
52091 84347
19569 02594
48286 19309
44400 82261
19322 99470
21704 81386
59506 33660
69876 11749
47268 55681
80651 73964
91894 81410
40239 16519
88212 51975
55103 14461
15360 93359
70678 38035
23620 33295
71594 59029
63723 62966
24852 88450
80184 48999
46973 78646
18043 96840
84956 48341
89681 97881
43702 10623
54462 31774
13231 93527
34505 46547
53542 99986
64315 84822
05891 58701
59390 38399
26756 37752
68884 04609
73502 30408
55454 08551
40787 87299
66757 59927
92577 67823
15333 05876
70625 57559
54688 70326
69027 03208
77442 46535
27681 24853
04226 93412
39931 61597
21889 89837
69919 24170
95580 75795
01629 03406
51509 19550
03354 83574
26017 84967
74950 80322
91532 81253
09462 07373
47276 70856
03479 59241
94554 18640
19021 56584
70144 45090
04968 56061
52832 36514
20802 39128
46143 46638
22662 08106
28505 06689
09576 24905
68826 04133
36370 16393
95916 59340
64397 05508
02509 27534
54520 90528
44596 23531
01791 81084
31967 06395
85386 25834
59360 87848
81878 92801
24785 11136
17762 07646
86696 19155
10037 19425
87706 42235
19799 04132
94741 55372
39569 13351
91396 16242
84609 26286
45199 80127
66103 59708
56137 11321
75562 10170
37861 12551
82354 94331
61270 67122
46353 63277
G3340 96698
05509 43349
30322 56291
31365 36334
00342 30727
18850 43610
63637 47042
03284 24096
34924 67283
75946 90965
83250 44168
27984 89892
35905 44879
66469 61568
88259 03612
96714 97330
44799 58271
31531 16485
50250 48775
64340 34108
96184 64191
31079 89061
21304 88681
36607 79140
62025 05049
72858 07010
58076 87218
29618 38043
454S6 30345
36064 58249
89529 46622
01135 99264
45847 85836
06765 89749
80223 69513
45471 18610
50672 49761
61255 24318
37739 88835
85013 03763
80842 58427
45640 07032
32797 27430
26690 69567
30936- 99987
04461 2S460
38482 2S012
04816 66451
81281 32626
43644 29794
06957 66554
23223 96491
73137 03S67
81718 63357
86311
96458
84173
35499
57991
05992
80198
19429
26262
18376
54051
71446
53952
54010
24425
85491
79648
30293
81245
09998
80494
23159
32970
91162
93468
83446
94238
92774
26397
46587
86173
53747
03141
896S8
64524
08530
98309
16475
26722
79559
67497
56559
40545
65085
77086
99212
60393
72573
76580
84 64 8
04210
73852
44752
5084 9
23148
S9768
10865
26773
23897
70640
06386
39946
49558
47982
01949
50203
42605
64807
29526
40239
42174
14601
21284
90929
05499
31305
96030
25760
86183
01343
82296
40386
81829
16582
48988
63226
05278
51470
41598
29070
75425
69947
37198
87826
82214
05660
92523
62702
02103
05533
3 8354
61813
03427
62353
77932
59370
75741
05229
76599
43704
21301
07905
65 1 20
48320
45987
55568
08478
75961
04522
09761
G-10
97
•
TABLE OF
RANDOM
833 83
15461
88997
96634
39343
86561
67600
87081
76544
08982
27512
89046
61975
79250
64579
61330
11838
37496
74484
83272
45991
21942
34406
28785
41740
17361/
67790
10353
36885
34317
11304 46345
40639
19572
34159
13487
32387
76475
72583
57269
17471
44765
26548
66533
61231
23375
29913
24245
78402
03791
79409
54902
27283
19483
87369
40624
97378
15645
87183
08818
47740
49996
90997
40690
73062
76063
24841
77021
90894
16615
85552
39430
08275
29116
76537
73400
98752
94428
82470
70234
41227
45475
89941
82220
08842
66320
30514
47330
42274
93579
00073
79317
11694
06965
89006
19931
62537
55575
41981
08748
87074
08966
20423
48407
68906
74563
92361
75481
22882
22919
33982
03375
06982
00338
60557
95867
32783
17767
06580
69379
09816
65864
15555
43592
80089
13779
17566
55197
55767
30887
96515
24730
14411
98243
03526
06581
66943
72967
97927
81196
78198
10415
16231
82188
84332
72217
51940
16252
86297
68166
36602
57329
94716
80613
52102
35220
00526
97050
74475
93497
37659
02508
02161
82227
82576
06123
81274
09518
38568
99416
32472
45765
64687
06419
90828
41937
54184
53475
57677
92683
64203
,17781
64522
40751
98591
54748
28150
09088
95562
66008
89617
19797
18631
16868
32211
63114
46266
86924
42113
16959
48797
96322
89434
67288
17497
94761
68684
54663
56219
14889
22523
08100
38128
66588
06899
77245
32835
57649
06567
40270
94958
53811
06706
05420
43164
6471 G
84933
35061
22454
65854
18339
99156
94403
32952
27225
82150
89664
56067
07766
90242
71143
09316
84551
48576
04613
00944
53807
43766
59023
77152
DIGITS
76187
51649
G9036
04387
43933
44799
33555
05868
05527
41848
21693
78499
77459
732)4
50062
89275
10818
38111
87939
44211
84445
77205
84394
40760
73845
44264
62994
23179
86523
35982
12518
86926
65650
14931
57011
02420
57224
07061
28379
2)115
65329
31960
22771
61051
03459
21882
77019
79658
47396
86300
81683
54726
46546
95474
54716
44776
41489
12313
88860
09769
99417
84362
36977
56369
33825
13830
51094
31691
97311
47805
95406
02098
86244
47511
92035
73327
08371
99302
13947
18310
19485
79705
80566
50682
96893
79302
54240
24684
30781
OHIO
94316
48751
43521
95198
95046
11998
42525
51396
77505
85222
90485
99587
62608
73296
11785
01961
57961
65696
97895
34882
16906
95057
64678
84564
58282
21304
54385
57337
66048
41470
40820
92984
23197
14041
50563
28696
06354
94094
43299
10142
00286
94458
84907
43064
89119
15864
14293
68163
50903
35519
40420
93463
00800
72462
56395
83136
84292
30992
22657
93321
02741
25523
50508
03878
62175
39667
48890
38895
43131
11725
00971
96152
59703
45999
66196
66646
19522
92783
06648
374 95
54913
04257
20390
70620
34744
77875
53562
73074
68772
17265
63881
77361
50224
90595
94544
41668
61055
121.13
41145
33638
97243
07806
86319
56303
25722
35570
07168
74833
90074
40452
11072
03346
07911
13655
47458
90785
42384
79738
90052
02784
61628
56409
32917
81762
33800
86475
00593
52298
73492
48076
20010
55845
23310
24208
17860
62172
19370
08400
77516
80402
48489
42531
46612
62830
18599
77855
53633
48039
14134
68254
17620
05044
83303
38751
74867
34989
00924
75152
03837
81996
G-ll
98
TABLE OF RANDOM DIGITS
06831
96252
31779
27898
69882
64019
24904
58171
13871
89377
19670
05642
68347
94073
69418
37362
10657
30353
18394
69196
27019
21118
87103
28468
72092
71887
49109
38508
96133
90349
10830
69091
08241
03284
50134
04387
59513
35837
46135
83284
22117
98269
28633
74369
67856
70564
17859
34684
79767
91568
Q1829
51339
40972
81840
92G68
77129
07083
86078
10011
23017
57516 33747
39268 60588
75711 82466
48817 14059
08090 69146
23561 85971
23013 91122
17388 59294
78371 28385
65182 72610
55368 14100
32794 67872
93934 48600
33249 37997
93142 22835
54096 83219
86772 63897
34028 97995
99224 17222
48806 36559
96947 64653
64208 04451
42406 33938
17682 89917
05984 30315
81910 01465
39518 98704
24524 30021
07701 33187
92150 05739
67765 74112
22564 50040
05855 02164
00234 25133
98118 71680
39302 64683
02982 13503
53872 27988
29658 00175
58387 81275
04755 78939
38916 03129
76087 79901
82251 11028
98250 26658
38852 56056
15G51 92455
50467 4G033
76233 62364
07000 G1530
57714 36082
24227 40195
76694 01622
95991 63797
73003 10659
64260 62543
16313 30365
33534 06819
62766 26166
28718 52823
47928 25269
98807 63587
82822 81613
69167 21525
05185 07689
48825 56146
05209 57436
29832 70231
24591 35234
57410 03567
44661 51925
81638 15428
74386 26018
07565 49325
04099 57757
95388 20259
28033 5.0836
77575 71142
67827 88394
92390 37895
34888 84796
90039 33356
49755 33329
82521 02331
63587 88638
91833 78352
37352 64350
44649 12306
28025 12444
09973 35046
10900 20721
61483 16991
57474 87900
39089 36203
78861 90887
03437 60288
60525 78336
83492 66904
54482 55713
99285 59135
42939 14792
50222 53976
05879 88394
04531 41654
28325 42983
39554 52239
33376 93929
96077 79507
08884 10437
24486 49071
04791 83512
41173 14877
79774 99563
12328 33723
88140 07208
20924 88534
66941 26823
35977 52543
04665 76107
11137 64692
72315 04347
62300 57453
45412 31415
11273 57294
82529 62334
44200 12426
09494 70331
06171 39750
52077 27402
11135 14382
60285
61376
23910
31528
34055
05896
25421
78775
57965
02598
68706
14510
76362
99969
16S66
44818
20898
28709
39405
48174
- 16077
92751
36325
28225
50918
28786
38625
97558
43613
52850
09311
01939
20810
03834
49340
47646
48859
24720
64766
71131
99167
88659
79072
26097
73684
70620
91221
24353
76309
48330
34087
90000
44999
40571
13091
27754
50790
60307
01908
12630
78733
43658
13940
45965
43951
55925
26579
38440
82773
03G84
48964
62341
69104
36G12
66180
80649
9219 4
15167
90667
23G26
98420
89517
46535
32736
70004
46840
10607
19187
89800
35908
45661
08168
29434
82946
34466
81721
97824
08008
14121
27827
70801
42474
97545
02971
50650
90034
44706
45433
75896
77513
90539
01072.
74452
40354
85952
45129.
70042
46466
59856
05918
11545
83261
33873
54328-
66090
51554
70167
96943
78155
32843
05749
45215
28747
31626
08538
69998
49469
89057
94851
11508
33617
30832
48719
25670
26498
21037
60670
35342
91264
77936
07900
73540
19446
74690
88593
82162
85075
39935
16171
18874
95853
77314
61549
36957
36356
44S26
51046
03SS7
26S06
53635
53454
05451
46798
40145
02547
22140
99322
S76S9
72881
40503
G-12
99
TABLE OF
RANDOM
40681
27353
22597
88915
79178
89713
63020
45133
71152
54318
94563
84957
44619
79713
09949
43027
68321
02813
47446
08517
51194
79763
80567
62318
21541
67373
65291
63392
50049
64763
13011
44976
94731
44841
58114
75053
10760
56728
67907
73573
00416
07842
61398
82483
92684
08104
19067
07653
11476
57271
03614
04739
91340
60151
25949
51781
71407
97071
01707
52119
74840
30355
24811
91014
44450
17855
86540
13831
52245
61860
01207
28820
12109
62958
47884
29475
55575
37654
91091
33918
87008
92552
81623
12154
48696
24644
01087
32311
77807
56658
46326
03892
41967
94372
32998
35039
82275
32560
11945
50878
51940
44169
83459
88888
07752
65375
34741
99245
09156
82529
93919
72535
35297
33351
69774
32641
23240
37301
36135
25186
40131
51356
32702
75474
84559
65093
45655
00947
97180
35175
91020
86594
87835
53859
50205
89051
71343
26912
15341
31012
66627
47292
87259
27395
34567
07313
43774
88701
56132
36069
13840
83975
89909
88547
08856
56422
38011
10458
65809
15295
75812
•82841
99809
33958
03468
78396
28235
26532
83318
77096
77050
98159
56449
08000
65445
45534
45029
84611
04753
49955
97612
39593
89037
03471
76022
95835
42224
66513
35514
19282
34916
94718
93210
03218
92353
46632
41268
35295
93493
61016
01487
64386
02269
15196
93712
44214
71437
59039
12657
80005
90468
99815
78139
69224
02220
74232
24251
70330
91262
09355
92253
94384
36540
11770
76555
53662
22108
08697
50312
91726
15458
76661
02770
47195
68630
53020
68646
01282
42227
39343
2825G
03-111
92796
77002
07332
87490
35299
62241
27197
04170
DIGITS
81568
96319
51098
71270
63812
33657
45481
41509
04687
33262
65244
53466
55985
27077
81993
28803
96663
86674
67775
55543
41301
24034
29986
79315
61613
77384
69945
86642
49238
31727
02487
68308
63610
64436
79719
06858
89809
12729
13637
70054
53713
96476
13096
08892
29976
28172
20924
86795
80075
74483
13799
24239
37699
61160
65534
71110
83590
03030
00655
26829
53425
76329
88396
25471
24939
99428
74067
55408
52533
50065
88218
55819
09726
67161
38420
95562
68096
03709
34564
53896
96053
47245
69520
09495
97197
93684
33336
01512
39831
85626
58406
24326
88509
63328
21618
87600
66917
92413
00939
75858
23211
26260
08693
29368
99956
61952
83897
09931
76427
69486
61954
52808
51707
61318
15122
02274
25956
08937
31372
06943
53634
28758
39890
72112
15426
46277
19665
24873
75652
72560
22739
94579
69359
17526
57074
05179
17404
23642
30470
35331
98159
40764
95925
13833
63765
16027
05491
37788
27276
57333
37066
42128
07117
10909
68721
99155
01271
36612
93163
18865
98967
60237
86604
34209
87042
3S217
99285
32993
85093
53164
38130
72304
32656
58223
09172
10020
56276
90596
89037
18424
08527
21418
56626
24739
06594
86647
84339
33670
50372
38939
34164
55546
57339
89379
94C90
32761
10767
22685
50950
78485
61311
10786
18485
81751
28908
17106
78632
91223
82971
78688
59965
69932
79094
04080
66786
68912
96661
67153
13462
2994 l
77366
83318
75211
63624
32330
37906
10009
28915
25505
75795
08611
30428
16774
55857
73 I ■ 1
72195
32849
66381
88405
875 10
05353
45197
37779
89154
38303
36179
59465
39318
01340
85298
G- 13
100
TABLE OF RANDOM
77365
84989
17521
86996
40216
98564
09578
08118
11418
42906
37171
91202
13275
49335
22201
00487
70218
83995
05943
43636
83115
05326
40730
17580
37854
79092
71196
44676
33512
01394
86555
33377
40446
57482
58101
93351
85950
99349
11620
62284
77773
19056
25171
18153
59858
76172
13078
84800
47831
82640
91260
90776
06058
42048
48396
89420
52217
44050
86788
46110
08916
58309
95173
47126
66805
63352
95840
49426
31106
26577
02415
34941
23716
59285
75770
34367
38621
74880
85545
47343
35893
44454
79677
08449
12614
23779
16329
55800
02894
85378
27758
86488
00731
24755
13278
26314
47193
73823
63567
62403
84758
66959
40133
78418
60601
88548
80290
36501
07586
31538
88657
43247
42762
39627
73595
96504
29518
41121
27162
41884
69659
67267
11682
64014
16S65
24976
56101
61342
33229
84141
49443
25755
35350
82605
09294
43174
84438
58429
55583
18290
15378
84917
59806
93088
43400
02761
77455
10139
41627
92S00
99323
87911
42880
08801
93694
68112
17668
69472
43554
66423
52709
33577
43011
55471
96038
28178
81438
03102
37690
44973
23042
05483
65965
03410
22330
94292
75630
73995
08657
04090
44200
88766
51670
30853
70096
41949
26318
85345
82316
47684
77096
45556
98245
41062
45512
64554
70172
95784
94559
56008
77870
10750
59312
20509
84899
84475
42203
41706
78431
51870
28460
69216
62943
82915
46264
39485
15469
00253
81603
64997
75513
78863
31309
00303
86477
35914
77883
12256
14994
95956
02840
55140
50096
8 ] 5 S 8
30186
34617
36056
99441
20370
76848
70620
16369
93716
18983
66488
70445
63247
35139
47988
28356
DIGITS
38060
22038
50035
54179
99247
78422
47268
88311
82475
95915
62982
63361
20829
66849
36574
75253
22841
62327
24613
64369
63229
93647
92765
92632
23253
il927
22321
90070
38307
99723
26629
12257
00015
53614
32100
33313
93210
92284
93675
88780
13337
70529
67141
76775
39334
02881
18501
15704
93947
66994
829C2
69114
75762
94297
98514
71987
95231
96141
15210
36768
81178
63576
01825
18772
54169
40801
67358
37237
04742
30815
06360
49221
97070
20811
93055
02245
62915
46770
76906
30021
21128
37971
99205
27334
50597
78085
61601
85516
80368
16427
87658
-93411
61897
23215
43797
53768
83621
16593
81942
19120
57108
44953
55535
47182
•76583
62513
46903
05660
59653
95970
60282
53768
72987
59165
93598
38587
37322
11SS0
32383
28128
08293
64331
61993
86565
47534
71359
04153
29544
73101
27893
27207
90180
61397
21835
03109
77373
47873
41884
81234
06291
17930
30694
05331
93144
397S2
83302
32455
27882
21304
98277
93650
38343
64739
03637
12498
37308
20955
58759
44993
01751
86833
20257
84274
12632
77578
46333
37079
81345
47852
40187
00437
77864
75060
03518
14S69
67839
36670
42546
47662
85563
09340
60682
56796
39238
82325
11335
17236
11016
77153
39994
50660
39978
68238
66138
55839
13110
54077
63713
83761
29785
63090
78224
59536
85265
47072
47386
20719
40068
47075
07306
05619
74543
75570
15802
87269
55681
95636
07712
2504G
11466
05800
78575
44646
04731
73909
C4968
70782
69739
59711
25704
46222
22502
71890
63559
99159
72598
264 87
84515
61891
84437
4 8841
20819
75031
52307
05976
04077
63015
04896
13C05
34246
G- 14
101
TABLE Of RANDOM DIGITS
61721
03748
38841
69166
03752
98963
01854
20841
52865
31500
23932
43062
33464
15924
24387
15671
70400
88477
85686
93199
73782
89043
22541
79933
57728
83102
95333
74207
71472
52329
46384
82071
00261
22333
43136
58386
47279
85564
56751
02884
31677
34913
92024
95851
73195
90341
27029
35388
10015
54091
53694
56321
51780
85766
24303
14321
34850
57577
81552
88279
05124
43526
80602
0843]
39622
04292
67049
37226
77648
62162
09273
84395
97382
42955
25730
15183
69840
80256
57175
06706
88721
47483
15683
85491
46116
43140
44368
16104
46863
53687
91908
49963
85656
41706
18596
96335
20856
03851
47753
99980
87866
14100
55056
01560
58002
78236
79903
57595
30611
49302
36780
08641
20571
13793
09612
18366
06852
71154
94608
70392
45576
91644
74141
23815
82267
89567
21054
47503
25472
75618
23892
65090
87940
33934
31962
31487
44209
43610
01733
05897
46686
41250
54473
98489
59263
71833
75595
31835
08056
46018
72439
98123
65087
40454
51519
77297
37843
69199
76739
18081
33099
33358
55914
34239
47499
95151
61859
09679
83413
91905
74862
50549
49476
62215
87910
10078
82651
08775
29037
36499
56261
21774
62041
84210
04967
06678
84070
69595
48871
86757
34845
41877
95482
84017
32677
80515
53345
11650
03594
64422
32368
38947
68635
82913
60872
80379
42553
16780
91837
61799
72433
90816
97471
61115
17983
87540
87245
61508
31508
36613
92059
84967
49256
33531
79632
12060
41495
77722
23111
04569
39434
85821
57004
00302
24395
49351
81841
20972
12359
52778
87831
38161
72475
26174
54460
25764
17666
45682
74833
92963
51219
78247
70734
10493
25093
09283
07363
71612
77927
61691
75728
31074
53262
70995
42071
11089
56188
53946
30159
59234
87000
97222
97795
16128
55709
37785
52626
28600
13567
45016
74270
98330
82464
44016
03638
47595
53203
37306
69859
22351
55542
52537
17487
95617
64009
25240
28245
51638
55394
00151
91130
08054
93015
83580
78969
30410
36607
00387
97499
10178
90293
58612
37471
28521
98765
92421
33333
76923
38256
78580
55790
91405
34801
64616
44550
71873
79425
03789
29375
04018
03661
47229
63104
29262
61523
53452
78524
02933
56326
83043
42334
71506
69013
64856
48793
24449
39005
58497
03063
68636
26742
43174
30123
39842
37466
87218
77848
38069
70385
36871
27066
20227
50363
44940
38920
04956
21448
09296
19038
615S8
23271
81891
31523
20613
46854
13071
81465
31184
23883
03637
59572
77446
83552
31265
38746
66428
34733
44085
58254
37004
22269
45986
60634
51370
17736
99133
90402
28771
43275
34353
56816
30889
15487
81497
75570
58820
85890
87243
84176
35053
14384
13438
39943
86175
28198
36927
18890
57426
28948
02750
43389
28230
64566
36542
10223
33125
98741
71329
21150
07281
23023
88794
40799
96828
01518
92546
81373
54006
67649
56869
11746
69577
07078
12507
5 8072
97801
26586
82586
54101
26852
11703
40814
67598
28132
64838
70339
45738
71862
56776
15540
26639
45691
2410G
42228
004 93
00978
03175
34398
14783
881 5 •
66030
15062
01204
23499
32555
70487
87652
27892
93641
51367
G7592
50929
27203
56495
44117
14954
28085
908 16
75750
72350
45191
88378
7890G
579G6
G1603
48400
13993
70089
69582
82222
G-15
102
TABLE OF RANDOM
26437
80025
68310
83961
94972
69541
94346
81840
32370
25073
51989
15674
90358
34235
61877
65898
34643
4G340
07789
14195
61946
15619
41994
19126
79120
26191
58514
42860
57235
13474
32411
39136
58948
60268
99980
64051
48551
64819
31103
49883
47127
02361
38690
70982
29182
39329
05966
85612
37608
56042
42828
19215
93119
74749
01231
80874
41559
70657
00870
33446
90700
42746
17453
07672
63371
22966
26175
15085
40523
28129
23185
09653
59384
54389
40749
19215
35070
48941
81116
75687
73472
47371
80840
87165
01834
52175
00848
56107
33893
95933
86051
97054
19618
14530
89367
27156
24240
12949
53482
82244
87998
56428
79586
36404
01Q07
85669
46650
58994
33647
46647
72948
48729
73049
80584
47339
21540
36102
51421
11801
11312
10561
63356
51047
34639
09604
74956
08278
00668
48373
85984
65867
59252
81216
25148
56346
82246
24061
78800
42684
94854
43654
12830
16350
56222
94356
73611
86402
78501
21602
96956
52567
15912
21393
69577
76935
50320
89614
49467
38904
31027
03104
14551
42975
40220
48905
58228
39598
51245
66151
59983
66624
52596
31664
89494
30520
59329
92875
19662
94247
27551
27090
08032
58956
52673
42640
43337
88990
66282
52586
98011
64398
88518
37040
85102
15091
24318
18295
38575
53256
87648
58004
95558
76439
94755
27424
55007
48908
54214
58152
73361
30257
96593
06269
70026
97970
69056
32439
09380
93591
30233
72705
98991
08381
34348
01119
87729
35885
64989
89065
34309
70255
49084
73091
12425
40711
89559
81801
835G3
980G1
73902
43423
81125
64492
96563
18382
66858
41507
53732
93995
68111
DIGITS
15323
72315
71272
28132
54926
32979
45546
37772
75378
11422
47304
69369
41499
12442
88491
77031
94179
76270
46 504
04596
28489
13988
02027
30324
97010
07138
13510
41715
08805
00892
17465
42040
49687
31346
42819
62627
81967
38604
68547
96808
55610
49353
56290
60863
64983
38353
37995
59683
00731
18332
43201
64648
15674
91649
11914
43475
14629
31571
80282
89053
01001
89043
83404
07292
13587
18961
59020
34377
10435
11318
20996
17178
64876
78199
93162
39424
98603
35416
80076
50499
64836
85357
16813
04063
35411
78114
71504
44275
28933
17598
44812
67239
81440
83040
22263
56538
00025
57788
49861
26344
80414
81540
93191
81564
14721
95550
95293
35374
00024
03356
61586
31920
94022
13529
44566
91129
05602
96582
58783
33707
61804
61413
55300
83284
28188
69808
04818
44925
83510
31342
20317
06429
04568
08591
54958
13041
27643
65513
73024
19866
41992
73954
19394
36346
99028
51555
18508
312S3
56948
64203
28055
93910
80495
48749
74114
94219
94105
58822
03309
94930
85275
35319
46262
04313
64939
41783
61760
11584
78088
10077
71663.
52906
79316
57414
97817
93414
99318
36369
85615
01150
42215
63610
37716
47706
33887
47748
14571
55132
98953
01724
31282
81875
82755
65581
88838
18675
68553
86497
83240
86151
92032
24447
86028
58404
23965
68394
83714
71766
11334
18851
93436
82123
06026
98997
19558
22169
72085
8898G
24298
80625
64586
81159
69887
78278
74752
99902
44016
00553
16017
96010
21213
35389
49504
44067
28793
76354
39S79
14777
64156
17614
09479
68388
01048
72345
42563
55100
64316
39013
32661
14126
G- 16
103
TABU OF RANDOM DIGITS
23930
04508
62244
35048
50242
67999
31536
25407
71989
45433
76128
69326
37504
75663
63223
43107
70135
10378
25207
30192
66520
29819
17478
56335
99276
92993
88457
18868
31188
41704
50626
20047
80318
92908
49020
16209
54947
20890
60384
32642
00692
11580
38646
09263
76877
05817
36856
13889
39609
55619
09979
34936
58781
30207
03578
22544
97243
55121
47763
61195
35083
82010
24906
04993
46431
41556
02842
16480
44772
65857
56834
11647
47412
10572
55006
78730
58522
66328
42258
91830
37013
23432
90997
73642
14550
51046
53319
51538
33494
74826
19205
64255
10816
06173
56554
41501
47109
14426
28435
57887
23344
07507
96976
48154
34808
28032
15431
28988
76876
45657
67901
03113
19937
54883
25893
91665
36071
66144
39757
97250
61769
41018
13717
67506
32708
34848
65378
43245
87766
56871
77088
87453
04413
30695
69255
20314
23215
99511
84106
59064
96232
51504
53689
76181
33408
69036
07589
74822
88940
65460
13738
24068
02481
10387
29920
74600
28080
75677
70120
52635
92218
25408
54086
32515
35057
92867
31816
86812
99924
16795
94886
07353
15406
50642
92785
59257
34168
98153
28959
30017
20527
69166
80257
83628
72616
91592
85581
67641
759S9
32625
48816
15453
91191
25441
48827
90870
16846
32853
57113
76232
57916
36540
48876
24557
94154
74998
21646
08l00
96762
54421
51631
88447
43773
49579
42127
85113
63840
02946
26197
182G8
48501
25356
64351
53802
01042
04500
41752
50272
47869
87046
77281
26539
49593
44291
30014
42832
78505
19022
48837
07545
79287
83125
22088
83259
28143
61286
87926
14350
22476
63834
35196
81343
6S565
02702
36712
97281
20012
41738
86025
77694
83317
90112
93949
49559
09920
90831
75864
52587
23624
34060
93588
29091
50338
02219
97553
75374
63667
94437
83366
28132
90384
84218
25670
91824
04963
06594
70740
57504
24616
74417
00774
58476
01209
56541
64937
80996
04156
27801
70923
31497
70484
24645
50762
15430
91115
48699
09595
55122
11918
33482
36071
66109
17267
28105
63786
21373
37358
24697
56603
67418
95880
51665
89278
42437
91040
S1053
79349
18214
40130
49031
89442
29442
59700
87168
14045
73824
91945
07276
35416
85776
73187
98680
81961
98681
653C1
84131
60475
18786
78258
17631
13497
95157
50069
433S5
87718
51044
24251
02261
81792
91891
12561
99033
53230
11211
20685
15939
93411
57289
00048
37763
94780
81716
1S045
36600
82148
00724
63963
49418
12463
14246
87633
82307
51079
78530
007G7
22316
71326
50810
69267
67190
94324
25247
02977
79492
35727
87555
97651
30440
98015
91648
12909
54789
99445
31740
68137
14130
40593
42443
36383
99755
25781
26751
46328
49251
70727
77363
80826
31876
06019
57262
92210
18463
27662
18257
87027
77851
15603
18574
30742
65091
84392
93948
64429
71724
41328
20478
20518
38000
44084
81 870
49969
24028
18581
07574
70122
94993
63242
75960
46855
7G179
97371
03322
13236
81729
94425
27380
91797
40621
00048
22858
81498
08934
00375
44786
82428
1284 2
30514
77783
97002
■ i 73 l
44151
94920
14 290
96262
4 9573
09113
22271
275 19
87724
09543
88498
00338
26288
63688
67312
82285
02392
96123
44 800
12062
43279
25288
06209
91206
74234
52353
64708
76276
40513
4 4461
G- 17
104
TABLE OF RANDOM DIGITS
08046 36409
09703 09718
11991 62233
66581 44108
39620 57106
87769 39700
22800 46020
31671 70640
19740 67126
98477 29360
44162 23558
84646 79401
11517 26546
23723 69366
50462 22377
16143 15307
03846 93854
05481 18913
14909 88639
07291 52235
13324 85026
23411 99184
98802 50684
28060 15375
47301 25731
61764 12059
41843 36863
34437 51523
84817 89509
59605 17571
89635 61029
48096 83826
33191 88105
28362 10330
92725 44352
28601 58253
53565 80880
14142 23014
35625 08967
91469 95135
39610 00784
22675 39720
04343 03434
72636 92860
10301 65954
28438 12095
52538 68238
57042 12043
93696 55833
59275 56115
00307 76848
15150 12559
43666 41823
02334 73021
77728 21112
79880 99857
83366 17999
66957 59801
39432 17914
10322 76444
44486 13991
10932 84684
47561 37322
20176 77793
80157 94845
50265 76233
13457 40936
85765 73483
21584 77470
24020 95439
98436 69226
68997 75425
82295 12312
29832 71902
95695 86757
32220 76922
24696 13344
82974 62369
92780 01660
54922 33311
72451 90971
24547 82738
03651 75057
85125 41800
66605 15579
63801 49976
61494 39794
84170 89253
20656 76386
40981 32231
49950 60606
34632 11489
41010 '42467
90188 95428
08799 77258
22965 33139
89072 73444
56241 84032
27957 53862
90556 41624
06544 73800
48601 18018
60781 08689
37012 10019
96576 28880
27086 30022
53985 84182
99430 47260
85577 17764
75864 09351
62924 24284
98562 03080
79761 69868
08578 25986
65096 75214
77579 91011
33080 99793
36367 29919
29496 77953
74311 74301
42324 89429
09422 86423
28999 21845
90558 48449
07810 20140
14569 24160
84575 74705
70442 43052
28742 25154
14841 01759
31358 45762
91475 04419
12095 65696
36654 65721
18521 12846
39196 44522
68559 14620
38625 72945
66912 53757
89218 76965
34634 11531
28191 34920
43959 24762
24552 26271
42124 90038
37335 53079
66299 20081
33035 98671
20616 08143
90476 45777
24015 79070
48673 03361
20251 28101
88727 00786
37852 59924
20492 39242
42750 20850
48890 34388
87392 29767
97059 49260
57169 12474
09604 37234
64789 32920
91271 31977
15480 32292
79907 01952
06852 70904
38701 32250
87597 48164
88185 13537
55120 81504
24390 72157
50568 70866
00879 50989
93917 50656
00454 23428
41441 92740
13488 97462
48462 27592
16133 56442
60531 68531
20946 97051
95553 69333
99671 84159
91485 26744
12874 06277
20068 19067
89638 33247
90431 91558
99074 11543
68790 75934
65463 30600
96636 58251
32555 23412
43715 80636
69930 66076
50734 57896
16065 30554
90574 33788
02888 60316
99794 27796
48382 09514
02735 08872
32673 97938
23410 50693
30230 51684
01601 44892
45216 59786
08111 65098
04091 70727
83105 51730
18721 38085
73246 07933
55813 74212
71910 85616
20705 15996
25382 94252
G2122 98417
75404 70551
31696 77981
59984 46071
24342 07676
39934 27109
57179 07476
34408 47343
28188 29120
27584 49771
14572 37202
52773 73471
40009 54067
66374 93852
87105 06788
03015 18570
34817 84437
08468 28975
97803 02422
92101 23120
16890 86490
26154 59669
9] 372 33612
78933 50385
29353 33312
529S5 43897
89296 99236
90786 20574
79968 78530
77313 42102
12228 04807
85343 65949
79013 88325
G-18
105
TABLE OF RANDOM
22719
92549
10907
35994
63461
17618
88357
52487
79816
74600
25267
35973
80231
6C039
50253
88594
69428
66934
27705
51262
60482
33679
03078
•
08047
39891
30753
19458
02849
30366
83892
60551
24788
35764
57453
06341
35612
09972
98891
92625
70599
43713
18448
45922
55179
18442
73998
97374
66685
06639
34590
14971
68806
49122
16124
61905
78976
48382
25242
97656
51686
37868
82946
73732
63230
85306
01666
48114
95183
02628
05355
56638
70054
19427
24811
37164
43973
07496
17405
08966
65989
05540
72301
36504
00137
90375
95141
07885
94399
41145
50210
75954
68499
42308
38387
52363
97905
05301
98496
20682
68082
23458
57782
67537
38813
00377
03954
14799
63187
46191
22805
52251
06804
85959
20974
73104
62361
59105
39338
59358
69193
54954
90337
99346
60442
90933
70773
03331
84228
01405
61494
68702
08331
08923
83173
67081
39599
33465
96705
41458
34670
54958
34935
16858
16523
54262
98124
08864
36485
78766
52802
43099
88373
80091
35058
35755
88667
44515
80435
17140
32588
87009
95736
76930
71090
27143
70581
40618
16631
54178
44737
03723
25551
03816
97612
99833
49943
30139
07932
29267
01934
71559
30728
83499
65977
37442
75500
16143
79028
81790'
57747
59894
59543
13668
27197
51979
29757
26942
08736
15184
73650
87650
08162
90596
70312
84462
84094
70059
86833
23531
31749
92301
17194
06003
99847
12781
26641
990S8
65294
37138
75881
04920
93233
46959
14735
15153
25417
97570
91045
09929
75140
98874
96989
84371
87624
74090
82127
82000
84618
58572
56716
26311
59516
98602
47197
31139
76176
03499
17999
84361
63898
DIGITS
83659
24494
53825
97047
79069
50436
88823
19806
33960
30928
63457
97444
13799
35853
03149
63941
77660
66418
84755
29197
34068
81957
02985
83113
36981
80912
91335
41703
79401
97251
10178
91896
70819
46440
98356
95484
34858
13499
28966
88287
31186
91047
37949
76542
79361
17935
79544
15475
74765
11199
22047
17229
46703
39727
16753
15537
73857
35398
91783
92825
56988
15570
98029
42208
00190
97627
74554
91267
31240
34723
71641
50515
88231
99539
75745
68017
56975
94080
93689
98889
22891
22205
27777
84803
39220
92423
13303
09621
94153
18691
64563
02843
45577
93125
25294
68537
70220
78282
02396
10002
93873
97813
10039
25457
28716
50502
08810
19572
48024
58206
15009
25485
09306
24721
04187
15586
57695
89518
59788
04235
58323
83183
90041
44236
90815
72084
24713
39851
01431
60841
87472
47980
08802
95495
78745
55385
25484
71068
15155
85371
63310
50348 -
53457
39440
80411
56315
43523
06513
50899
86432
47556
98602
71744
70442
92312
98708
93010
98590
23656
85664
95229
24799
02313
17436
20273
02544
81368
08078
46740
52583
06779
47619
12901
60179
23780
19584
13356
35803
90284
97565
72526
53123
99948
59762
19952
37972
54981
10079
17490
15215
38403
23989
38549
82968
53300
51130
59167
89866
06030
88929
07653
80962
96692
07030
62470
23930
04763
89322
67576
38627
38729
88072
92589
61828
36504
12627
19461
69536
64419
82306
28306
76351
28109
86078
4522 4
43926
90282
99088
93605
03547
71983
62424
62130
44470
74 7 ■ 5
79862
5989G
50702
31938
18336
2763 1
64619
01504
77617
30219
97861
63620
23931
87903
9 3 566
G- 19
106
TABLE OF RANDOM DIGITS
13962 70992
43905 46941
00504 48658
61274 57238
43753 21159
83503 51662
36807 71420
19110 55680
82615 86984
05621 26584
06936 37293
84981 60458
66354 88441
49602 94109
78430 72391
33331 51803
62843 84445
19528 15445
16737 01887
99389 06685
36160 38196
05505 45420
85962 19758
28763 04900
42222 40446
43626 40039
97761 43444
49275 44270
15797 75134
04497 24853
95468 87411
01420 74218
74633 40171
46662 99688
10853 10393
68583 01032
75818 78982
16395 16837
53892 15105
66009 26869
45292 93427
34033 45008
13364 09937
03343 62593
46145’ 24476
37703 51C58
12622 98083
56043 00251
43401 35924
18053 53460
65172 28053
72300 11641
38051 59408
47267 35303
16239 50595
21636 68192
35804 44862
18792 41487
03290 87971
36493 63013
55875 71213
16194 92403
96191 04794
36460 62353
96973 70437
15934 75807
56652 91797
77764 33446
50934 43306
45945 62000
77705 28891
44016 79662
92795 00458
54460 22083
82240 79159
51492 36483
95895 24102
52512 03951
39856 73527
43879 07613
30647 88711
71047 14401
97092 79137
59576 04887
03013 90372
67938 29733
24258 93051
00538 57133
40963 69267
91829 65078
92326 70206
41621 79437
00535 88122
93332 09921
62507 19530
17420 30593
17689 56977
70085 28067
28308 55140
32125 81357
02190 83634
43548 30455
16508 82979
29066 02140
62509 61207
84294 38754
23577 79551
16614 83053
60022 35415
68181 57702
83025 46063
80951 80068
14714 64749
00721 66980
97803 78683
46561 80188
45284 25842
41204 70067
75190 86997
76228 60645
12106 56281
92069 27628
71289 05884
89279 43492
4416S 38213
70280 24218
07006 71923
21651 53S67
78417 36208
26400 17180
01765 57688
74537 14820
30698 97915
02310 35508
89639 65800
66012 70305
07686 31840
92002 63606
60867 39847
86816 29902
84755 34053
42003 58684
00812 16749
20852 02909
49510 75304
74665 12178
47076 23310
43097 83976
82554 90270
04670 70667
78984 29317
96246 73504
33354 70680
56561 79018
87750 46329
86222 66116
50002 32540
37963 23322
00066 40857
46839 26598
14596 04744
04800 32062
73531 70073
59510 76913
18880 66083
60665 57636
45248 78007
36305 42613
69481 30300
88532 71789
66761 88344
03261 89199
41078 86326
50968 96719
23395 72640
94582 29215
09271 68396
45347 88199
99476 45568
38724 15712
10741 58362
74899 87929
83281 72038
12312 56299
58912 21883
27971 16440
21631 81223
66664 75486
34273 25196
46544 95665
39626 06080
19848 27319
73243 98185
86568 49336
29983 67645
89336 35630
41425 66862
45542 22831
22499 68467
02196 10638
36070 37285
65911 38583
87251 75608
94047 57096
59964 50681
52947 20134
87950 13952
25294 20941
72584 84576
88307 92282'
57149 08642
17975 50063
67912 97670
55304 43572
38408 50031
80220 12139
67364 72416
77086 49557
80435 24269
20498 35645
71176 35699
02081 83890
89398 78205
85534 00533
89616 49016
15847 14302
98743 84455
47278 90753
25306 57483
41257 97919
39637 64220
56G03 93316
78135 53000
07515 53854
26935 67234
10551 15091
66944 99856
72122 99655
27130 90420
14200 97469
60043 30530
66769 94729
23542 35273
98115 33460
02290 40357
45486 03698
79858 52548
18138 40564
23023 70260
78460 47833
G-20
107
TABLE Of
RANDOM
42013
25126
49296
38839
98092
66261
56987
46342
70656
04614
99218
43326
71220
47549
69609
60246
70506
12969
83611
57725
36193
05504
57510
24880
43433
00531
71458
96341
59955
54799
74737
91290
58472
75246
44996
53061
21680
80352
70951
15425
08614
40071
68920
64920
23340
96656
96439
54118
52156
52621
62095
88876
35524
81750
08680
77889
92840
57213
80607
03600
16918
23456
81198
75611
25074
46268
35453
53423
93232
96635
55888
65437
40317
22775
57810
25423
35242
78919
09390
37512
89078
42669 .
29644
78077
72494
13192
42580
66330
68901
44233
70931
04040
92715
84711
50352
77128
77829
88384
34423
38977
37100
95870
34423
68405
52871
10308
26146
30767
59339
47405
01822
07742
73964
01142
16459
07393
92846
14103
35259
30109
50735
71154
23048
03035
08385
07419
04879
07820
33621
56625
50087
54480
86002
35638
98404
71772
45715
74504
54733
80412
45714
59014
12114
18042
90519
59220
80301
51824
76885
85646
10764
53574
99564
08495
80459
17678
48295
83757
65027
35491
25137
13748
72617
05969
41288
73983
90100
48318
64269
19759
99383
86972
98698
53377
78399
81463
95646
47319
48775
93940
47218
25488
68262
21410
61186
81340
41579
58825
22003
49490
87900
38409
86023
52902
65419
55171
74690
78509
82507
74217
72273
88384
07084
32642
58395
31315
92691
65161
01439
80177
14727
40472
08302
00582
81954
83748
71311
64473
73025
90187
88824
0G478
50725
76185
50468
15674
10172
11070
5625G
01G49
27554
23402
41542
24214
93388
37635
96312
73S91
16729
11725
07476
42396
95 670
49941
51549
66005
72644
19812
65399
48215
DIGITS
9G100
44205
85129
46749
47707
26422
32479
41453
82281
65793
05780
01070
70739
29282
98507
10209
67627
07864
05937
31892
20377
33928
54749
73464
40652
63186
22416
45953
94761
58992
62216
27970
50154
44759
77127
12816
51622
32075
85276
14589
05380
28335
25114
61683
57618
13824
59450
01023
11607
67538
17349
89230
03916
67328
28455
58153
38089
99100
73014
31305
48084
03581
64703
27349
74763
01540
07102
35254
17330
03758
31889
32922
03784
05018
37517
13982
05485
86728
34392
30716
16407
04518
27476
60810
25292
62951
2S750
39622
68054
11176
92935
37042
56655
97889
87259
88885
79735
22965
69877
98333
15661
85110
84313
99862
10233
18099
88450
98937
72828
61186
36271
07333
02936
50903
53965
60824
52938
31191
27402
55803
61502
23161
94518
63237
16715
85884
49636
57122
98079
14220
27118
02877
02755
85210
29357
18241
88087
40118
06232
93326
52413
93567
24945
85998
17555
16102
74986
65006
53715
19746
85802
76505
36292
40744
19788
46418
67883
72615
65192
84193
08094
72739
95361
06969
94802
81850
24789
55982
30526
22G76
75624
77124
78996
42364
04273
51645
60109
18278
29681
77883
89952
11764
79953
56457
95497
30865
37291
68696
04454
88205
63324
88553
23217
25332
21388
61944
45093
20674
95483
23757
87752
57079
29525
06486
47759
42240
87554
50096
89808
01816
46590
43884
17637
88473
20390
37261
3 S3 89
62432
31440
59825
38948
23682
11328
77542
86781
07564
38895
0 1 649
51479
G53D7
67693
29967
67-177
01991
12243
76610
39574
99565
36190
32008
07010
53100
48997
33188
29114
09132
25707
73C48
G0225
30702
G-21
108
TABLE OF RANOOM DIGITS
52534
82857
47299
48748
72888
88602
31385
63436
43035
10815
91400
63007
97273
32057
91951
80753
34577
58421
51026
28514
35885
86909
61780
30921
33258
93990
99581
70584
49811
43933
09614
57360
60566
71263
39899
06856
28724
93988
77589
22748
79287
76856
85097
14422
94957
63180
07117
50802
57008
72837
09472
93904
79062
09699
06683
15627
05471
52308
78528
25876
31677
96908
03890
21314
64503
65093
27865
69792
50778
30718
01874
79890
73607
21145
65168
70378
46175
35976
11715
13058
27728
79685
87000
81766
13756
39542
43035
24562
93335
00849
15083
24701
87498
56370
41122
38208
12759
03955
72612
18824
15282
40571
74608
54511
01418
36061
06128
71126
47235
87258
66755
02682
33789
88898
29899
36558
16521
10515
82211
47412
48090
82667
87063
61246
10231
63465
'99694
98810
44399
90063
96395
05290
86695
34823
17766
82253
29278
46716
17G03
16278
22288
14812
38440
61537
68293
35481
12317
84403
27489
14825
05628
23186
49976
51151
27859
23071
52184
85989
74678
20590
77886
44504
48977
07431
29133
99517
36561
13069
73593
96267
55302
19261
76761
17529
76210
44083
43083
43603
48769
75463
98302
35491
15837
75768
25722
56887
14082
29531
46695
63224
67921
91143
53255
79854
08527
29088
87873
31377
59474
68647
75682
95072
81979
08783
39007
17748
60659
16166
41789
99067
75168
24241
75997
82268
18396
75091
41347
29533
69180
76810
93673
57951
74687
75747
48063
69834
52374
59016
91240
18688
901 28
04581
02975
98263
59500
98G09
81140
50638
77S27
28671
49501
76986
33488
89038
45521
84477
05 314
10334
14684
25142
31705
13867
62620
68513
79149
07119
35964
30360
63656
60661
46330
12893
86602
03710
56516
06233
70431
42107
97639
90818
12960
84640
11301
05409
32044
14954
49446
70379
27056
95378
98163
43014
09500
47266
43147
32910
14649
52967
34718
90217
02732
73579
31711
52065
41789
88961
86536
54036
01747
59887
39134
22416
66211
31214
81730
82840
20825
22134
94528
53834
80250
90814
92145
73283
60898
32243
52658
83178
67131
95642
05079
55896
97865
93480
92630
69755
45829
86870
86083
32591
29480
63335
37586
03953
15324
57574
20158
04989
41399
84132
66845
35060
75773
07576
75952
70458
73336
17085
22792
20258
63856
60915
16317
60816
49287
93985
91898
29157
*53154
15095
03361
80922
66412
35269
15562
59691
15381
93119
31477
83235
39794
18043
04686
49861
88349
42883
40735
95238
44447
54255
89280
86992
56403
48722
89742
67634
46388
46708
48283
64313
68072
81028
50708
40678
75296
68187
86422
66783
00748
81409
53810
50390
21892
36258
76361
84137
25824
33136
56998
20918
31306
19685
45540
78390
39250
34628
01825
11804
67831
49082
13943
25544
59446
50749
55514
96623
84077
66487
06917
78976
66625
73375
40050
29995
30804
79911
69596
81584
80995
33835
13399
74312
58701
71350
85986
31290
64092
04332
60435
15943
64506
38531
09770
69281
78108
79611
16400
73810
00030
39514
35742
22967
65975
60427
04488
13149
36522
70276
69792
308G0
07832
99227
52971
09475
71006
84379
31381
99735
95153
94S18
96218
18273
302G0
04G03
41966
58102
92651
24201
25081
50459
26386
07564
31116
0G500
51750
48115
52182
04834
703G8
69631
G-22
109
TABLE OF RANDOM
77012
07384
73077
58917
90883
99688
96577
36515
53327
27830
20302
92144
50915
29248
36120
87101
03409
76898
41137
43948
81969
35233
89022
76526
43304
34807
08126
85164
30912
62625
80291
09797
06976
65531
94969
00849
40816
97682
40753
67140
34082
67803
78386
96338
90435
48144
36678
28842
99910
91250
71923
97743
68311
35887
84390
97766
61888
77653
78082
32839
18801
39524
79790
74616
77609
09013
01087
80078
15951
91875
13048
51611
74386
99985
44431
41789
61818
51838
46690
75215
58001
25588
78572
27581
72758
75657
91363
06883
63767
13608
59445
80665
88151
12051
63428
44889
04294
07799
67874
79841
81237
64397
68539
66659
52781
10679
50334
11422
02765
29241
58973
65467
38950
87853
16905
49234
68411
12338
15153
83208
36185
81850
31507
60906
23892
02697
19279
56989
81942
80964
55830
02431
93205
79197
74599
23957
75773
68884
31936
81490
06343
44395
4S564
42993
65735
39485
98566
02373
23953
30520
48876
74880
49887
86365
18299
13551
41581
09044
56419
16195
74692
76567
86266
19132
45849
29131
83732
75242
65232
08872
38528
48380
94012
44693
53843
45021
72055
37371
44018
98373
06474
23471
13782
32396
97506
83575
05580
81439
06635
02816
17007
74305
01821
41041
42674
37606
40561
54302
99589
22671
17936
91024
84985
03289
07721
34330
18439
69577
37771
6S254
69074
10171
17991
65383
51863
16723
63250
14038
39436
46531
97324
63679
10177
05637
62994
02085
54343
26238
58376
39827
56224
99229
54362
76943
13980
96214
94020
06341
78763
62643
67058
61329
23706
22885
44251
95044
15713
92819
23532
40332
DIGITS
74805
32390
45582
23330
69756
78936
03391
93326
41244
81366
11778
86G30
76882
41739
17986
86332
51689
07086
70734
05550
36463
83480
59540
47470
69287
53139
16842
09266
52532
46581
71925
26860
95874
35446
71293
09518
54907
73276
11899
98687
33261
72133
88780
99020
97004
19469
81431
72494
37623
22987
02619
02411
43127
51406
68460
10269
29426
55488
01517
88955
74732
61525
92718
25394
51080
76013
13021
62817
71591
97002
12773
90146
38524
22724
27506
86387
93567
37939
30734
19879
45851
25995
26819
21913
10179
42773
63539
18529
31925
28668
35053
01179
05254
•63537
42581
92780
71505
06464
76839
63347
60654
84232
53804
65075
27220
22632
91788
67316
68237
64200
90671
57147
30893
06623
41475
25784
40268
38287
73891
27376
59827
67797
62799
91022
79253
67913
08399
73386
94867
67321
87585
74438
83704
21945
15137
45020
55818
24592
84937
50474
44594
57843
70724
92870
32617
93264
31347
23349
38934
45635
97041
31641
05984
88948
70140
46709
05714
53352
19679
87224
02131
74225
04155
43997
62830
43279
00809
97046
28851
15337
24203
04579
95053
43817
62309
48304
90618
42059
97379
10602
53770
03116
51076
667S8
64104
51003
78830
02038
76344
89083
44803
36700
74785
25617
68049
34258
26432
06732
00600
93367
39729
45809
80821
39587
07684
90970
10173
35598
02336
74141
38535
01224
10097
14548
98917
29073
50638
25920
04575
7844 8
20462
61271
21702
84168
46679
35866
33967
79586
29719
47766
83508
22616
15S62
84 824
89884
83854
16712
91383
15935
82958
27633
82942
79253
40230
07629
49307
57167
24892
63015
43145
G-23
110
TABLE OF RANDOM
88115
59359
88857
19687
34108
28073
71035
12335
70915
34263
32924
78792
18933
91796
63082
79599
42519
05201
17045
39382
67006
80140
74512
12408
64096
53957
07994
42002
12668
50178
49498
88978
17442
68378
54770
18990
45671
72172
37095
63197
56316
57505
67778
56592
42765
90133
09824
25398
50303
93421
53760
25900
43391
18319
08120
24233
68519
57668
89044
21821
11980
81333
87078
85924
87322
72173
21019
66804
98240
86312
55332
133 84
41987
81401
08589
57607
25649
41487
81745
25535
69686
81509
19028
75140
03866
34130
16327
81730
80949
11124
85721
82231
09296
43409
80316
40694
73282
88363
23493
66853
28790
73555
39872
82425
67586
01488
66532
81455
26070
54050
95499
75165
80569
89454
25994
23246
93026
49835
68011
46709
54372
71661
98259
03429
90265
50667
67447
12042
93977
84144
39015
09690
22308
55079
46001
30848
98916
84404
69121
62466
03889
22848
43778
74537
75257
94392
05327
45485
23672
49212
68181
66796
01111
81046
03106
54283
10083
48124
66874
40560
48823
58942
76779
11831
71291
24114
27526
36778
52550
03349
58250
09433
49922
73517
05749
53805
24698
90621
44865
30020
67094
32424
78081
01866
06524
96327
08369
01352
81145
76239
96304
17442
26193
50470
40080
14320
29318
35603
67402
11237
17503
66734
92657
25594
48869
78373
76435
19095
11690
87307
78058
96964
06841
98848
17419
74417
70127
90585
33464
32119
05478
71773
34259
73504
17136
95594
70376
56991
94958
73025
86317
76771
66837
10831
54982
71728
32787
76084
68568
38031
39979
10146
27776
94907
33324
15592
60403
42603
96773
89004
DIGITS
33685
47395
85450
74431
53889
46352
13003
75724
91414
70539
95063
10456
61652
81171
64157
85426
78979
45796
77853
37515
48444
88584
30026
86203
69963
10182
60719
91408
52581
31505
03452
35732
66049
71522
78488
35698
27050
80879
22214
17387
46357
21105
62470
27862
30463
45316
67491
08712
49107
89776
63323
15314
18931
06321
67593
50937
98675
93242
03575
52357
71992
37385
89058
03613
58247
94275
65750
39800
89690
79511
19763
15911
62758
90384
08462
45433
38792
67984
14297
03353
82198
64457
32441
90153
47008
64870
04745
32499
40333
61195
6S520
05796
57927
49096
43765
05007
88903
89201
38588
74264
04692
58763
73089
62844
07701
21033
34261
62446
04251
88138
26350
81331
66392
22865
38179
97573
41406
87120
23019
76957
78363
79075
69264
01258
25346
57085
92362
17519
44003
00728
521C0
62325
34030
86493
05479
64858
20484
41417
70154
54470
60289
91993
33513
47265
92628
40702
27590
45199
41120
28897
02797
46778
06137
74457
17698
20775
77508
24814
42647
61096
30891
75550
08406
35640
97312
27244
32784
31944
04514
79805
29521
11486
35378
02951
19991
79181
27710
77898
18641
25822
15797
50526
19737
46728
47806
27756
92892
40249
12677
20351
45962
27413
52596
74767
15419
10278
34135
11550
08956
78074
45477
07566
01028
98648
11852
86055
69098
79807
32699
21694
09237
80180
37075
15571
75381
49159
97364
98803
41313
52271
90957
04215
79673
59041
58532
72241
18772
83987
66214
96335
29193
64089
48005
22480
35522
65199
70118
82010
63048
89269
37254
91599
06189
53170
95295
87192
575G7
05696
98464
98800
G-24
Ill
TABLE OF RANDOM
70926
14068
90617
51352
05865
38294
02507
86133
45888
21711
51447
00598
36601
60566
32418
33733
65492
09115
87007
43944
98578
16717
53459
98243
68053
98045
35229
65436
97032
90692
11030
27678
40435
23421
30446
06398
01268
40461
42] 65
76730
66982
99502
99638
32288
81444
49990
41133
65203
58173
33477
22975
87537
49981
83262
55604
56363
46172
55878
38017
28757
25239
51964
68059
75456
39179
59897
48512
00334
45937
19369
07445
43199
11331
84333
24530
52821
36525
86483
01485
27152
04483
39213
14609
02255
65310
85207
37425
3552S
59376
85614
36385
78567
05346
74610
26141
55407
39812
30331
60144
17516
46331
84545
74655
37810
71052
04897
76974
58825
06219
35829
66731
13895
78598
34046
33819
43230
46708
41391
27181
83392
66454
90538
67155
16330
47634
15390
36462
55477
37908
88709
46247
72875
26162
79014
84536
55637
15060
33992
51861
89417
02487
37297
82484
66076
52244
42610
30603
43360
37782
74207
76181
27103
98753
17717
75804
24240
59688
23292
40949
74821
81005
08991
34680
03514
44197
56871
37208
97581
82371
26370
33208
81662
43605
2055S
79985
43803
95466
93094
97246
31204
39723
01384
22765
93642
60124
62515
76499
84234
06259
51069
45055
24644
30258
39939
53071
69681
82442
84755
30753
38850
83385
60015
99787
68177
43030
04458
50325
13625
59771
52638
35754
46420
40662
91784
10383
101G2
66613
00105
17031
85743
89831
87771
78854
87869
25562
55684
77321
42361
69034
44115
52365
07152
2S678
69439
55376
33636
30300
46185
47790
80994
38313
14021
53007
04659
93123
12929
16404
65222
46174
52721
DIGITS
25126
21435
69981
06479
54942
98619
05872
54301
87716
26002
06444
18754
79000
29678
33535
90683
36936
70086
26343
44499
14785
94556
24145
73756
02966
92839
48741
46015
60649
78986
68355
41264
56845
25972
24239
80605
64851
45178
40698
45023
22186
99057
35949
63798
62111
09119
34541
41143
46943
46256
56229
84786
38692
16164
86948
23228
36018
72170
51051
75235
09456
92300
65626
48879
31402
41725
17979
02825
84411
90936
07944
18773
94012
01441
40655
22479
34278
29029
82444
32543
22945
48013
36887
71101
33008
97070
30842
27193
62451
28179
87177
19154
53851
05824
59090
98353
6938a
48352
58137
77898
47561
38516
00995
29132
674 66
94137
86723
33959
58960
78467
31321
28214
15552
79956
93786
83917
50354
06317
82244
64964
26177
91044
95720
98046
97875
79835
02268
34899
43576
94090
95251
08529
38081
20459
00237
48441
81158
34236
95130
56722
52682
24153
95903
16593
18839
42717
30680
04798
49349
80247
70789
38568
18708
96245
97479
74395
15182
28469
39961
16523
25332
59596
78425
98515
94769
49617
59215
38569
14739
48414
90844
17530
99091
10285
21540
85156
37718
08525
91170
63419
99086
45153
32542
47145
48575
60919
55124
78419
58554
9454 0
2G932
18676
192S5
62417
63764
46942
61530
59202
110S7
15121
09512
56402
52055
69511
95801
03817
31659
90580
61424
19064
86003
18461
37487
C7G63
29044
46022
84098
48084
05707
94180
86955
25525
10040
73737
90766
03720
97262
71890
16199
59265
06525
59029
29933
27542
745 1 S
17002
12405
42203
99491
543S0
86269
29475
28220
71 108
33211
30713
10441
13115
06313
78965
G-25
112
TABLE OF RANDOM
11767
41715
96921
39440
91713
10209
39469
04395
96949
68306
88035
86619
10325
12403
59223
01488
22623
75963
52672
08033
85453
72323
32385
04738
68076
94870
60073
79608
75998
05122
92793
48899
87556
46924
20939
02048
90603
58746
02696
73115
99402
91657
18017
77315
39059
52804
36184
32274
65204
35397
74967
53533
93594
69969
16216
15360
86221
06240
68606
05993
53092
10820
71341
56926
4S072
78293
43707
65260
46559
21593
24698
22898
26339
77971
47433
36341
31972
45946
23649
94999
70032
05924
91583
26358
42395
58505
19927
12491
29716
88554
73594
99247
47006
04316
15214
76445
56970
29913
49346
49418
25906
22504
11638
73444
50364
30906
29090
62259
64926
45247
65174
27188
78410
88819
89691
95707
46159
04585
08264
31148
86800
89098
64605
45971
11658
27050
19535
80967
86429
53087
10321
30484
20157
44523
17221
81688
67931
83947
92274
47572
87754
63269
20414
97007
85234
61003
95084
61292
17324
93461
92634
41808
82881
62269
335S6
43023
46101
12756
91289
97S32
56571
76602
83541
73035
54212
02277
75958
49212
59055
91260
26333
27670
05556
64366
57386
58163
45678
12771
96906
76195
24866
01275
00882
31104
25970
86997
96175
69773
38015
23916
64237
20191
40654
S6516
81157
50601
68108
35854
45951
96090
76183
41550
85252
38048
61986
59038
73354
29214
64984
42285
08430
83898
82979
99138
72201
28493
91724
84455
17948
67633
00322
75838
71501
37001
36824
99942
82603
23184
2G29G
50994
97872
36870
47178
G9926
36075
64219
065 80
2G192
82GG6
74G07
58098
55G23
26057
28G19
79776
89G24
83227
0G730
1G023
23771
DIGITS
01252
95477
90091
74570
47814
59930
43058
74922
84796
25716
80176
03721
42071
86811
58308
94360
23673
80897
68904
98109
97592
1 9285
41760
42244
51078
18855
98943
26426
84879
74388
72246
53768
14024
09495
40912
25929
51870
61184
65085
78295
24381
21328
36197
89852
69923
44192
06055
60314
10940
34627
97183
95154
37719
90074
06928
28257
80451
90422
20624
31777
70936
33884
63004
81011
90241
61172
05802
48592
96801
88425
41759
74193
54506
04385
71026
27633
01609
19345
83854
65117
85283
36548
48571
90295
65056
84743
75150
20811
. 92332
52934
68184
50502
00906
58323
81340
89565
90371
02911
18781
49995
29434
37229
81270
17091
08384
63145
97190
79048
25472
63993
71654
85623
76958
93888
34121
55333
66354
20732
83733
71859
89650
14679
29076
11295
26756
24524
45176
58099
21062
93277
52332
02171
69984
24729
45615
05921
73696
13267
12007
36060
02765
25037
08013
58209
32893
48671
92398
73811
32577
03895
15208
06382
92818
07525
18506
03007
11112
83193
38078
10928
82112
39610
98224
02571
03610
88372
70664
91292
17350
78812
17327
G0852
92021
15754
55988
16623
54681
38763
44930
12599
06468
5S772
11493
25244
57906
94438
43706
85667
S718S
72475
18779
32641
89064
70199
22278
18262
21094
13284
03783
47529
96431
58408
90223
36116
13558
99793
79106
35548
59039
40442
37238
62822
29049
66756
80217
89500
41013
08398
42274
57451
74950
60G32
11372
43392
66004
21524
46967
28332
19674
32822
93302
04530
10172
04809
9G867
31539
77593
73076
41422
56992
69449 •
97532
09986
G8SC5
92882
51774
40547
13335
80053
88100
G-26
113
TABLE OF RANDOM
99275
48612
21216
65329
47006
93487
83437
17776
85952
25025
77638
96966
33408
52567
97394
13771
86099
85457
58571
84468
82422
08792
07864
18509
17314
79394
17748
90396
44781
82857
15053
36157
18243
03108
81691
30831
20830
21955
49948
55957
61512
40712
24620
52733
44361
52270
08623
15054
40687
92854
69103
56560
84932
19661
06307
73582
54875
08117
98969
71713
91009
80511
72733
51864
93842
57300
92584
28176
93034
51982
92344
93509
93644
67316
55786
92749
83442
68882
04917
60100
42831
12508
45484
77529
12684
07745
53194
02923
61074
63854
45498
5S291
87859
53926
31865
09182
74356
98937
05305
44177
66926
27548
13360
74005
81863
29434
65828
22535
71027
81963
42571
68007
13720
72268
36932
44191
51743
00755
11342
96156
74446
78425
06622
18035
10454
01361
80115
72935
17163
22449
12978
51982
49118
56362
57711
61774
37757
07413
39789
32552
38043
01415
45193
84171
52383
15829
42557
52816
20654
41230
65919
70072
05256
51571
82292
42819
32053
60657
82161
35440
23139
91838
52934
54293
84798
19405
64597
82153
40667
49899
07288
45243
60807
81236
70539
69116
89344
12029
01539
93894
63194
11499
17269
88825
33188
45783
92486
36117
48960
28351
07396
88455
49617
31643
59540
89360
23385
55210
93043
02738
73831
35096
11635
69913
59826
52665
80524
66871
10050
20685
65846
39590
21711
76563
70545
53627
91900
09405
76537
98930
70669
44663
26954
84605
51598
62677
12248
24848
02140
01131
83555
56534
67758
71368
26859
83G97
77759
52073
04864
55059
44903
84173
97008
84 837
53 936
49014
65018
85266
95013
10543
DIGITS
81802
25488
71983
53254
49130
36775
48054
51516
34250
80153
44738
82972
74641
10629
27328
13977
68318
67241
81211
50595
57017
41471
01334
83346
52276
73286
98281
05360
64793
89261
95429
61175
63251
51012
30760
13305
47123
90904
83261
63990
69509
14503
27507
11978
53166
34969
25843
05886
23848
37815
56052
78502
97906
53173
20703
04025
91705
35226
26130
20635
41062
34805
54917
58877
06764
67445
81231
35754
08862
16353
46115
81226
81580
56533
«
28894
60970
89024
26833
22520
14141
74732
97088
83012
10059
29112
76031
53621
82550
48493
04735
91237
32265
51667
11757
85115
41774
56282
83432
18409
59954
47185
45649
98578
33918
26819
89151
85892
46253
32153
62668
83209
50630
86254
99242
84871
70667
92793
64207
00908
20585
00769
82604
23280
31513
80496
53094
44751
89764
63157
10031
857S9
99400
99659
94439
72369
79649
50218
18721
43983
44445
92519
94553
32365
46859
74074
92652
20289
18515
59762
77168
43086
03342
00323
34974
27538
03414
06554
36616
95862
14257
35913
01191
24708
34713
37519
84924
49530
56359
42477
08924
14403
92228
85675
29187
93505
65818
59005
07675
24657
68510
65639
63508
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91511
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78996
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6 ■■ l
74324
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4 4 G 9 2
3 2436
G2278
G- 27
114
48891
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71583
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86398
63642
71121
13701
71134
33767
331
…[truncated]