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To divide a 40lb block of steel into four pieces such that the sum of the weight of pieces is 40lbs, and then with the help of a balance be able to weigh any weight from 1 to 40 lb, divide the block into 1lb, 3lb, 9lb, and 27lb pieces.

Arrange the weight in various combinations, using both sides of the scale. With the following chart, you can weigh any 1lb increment of weight from 1lb to 40lb.

Left - Right = Total (27 coded as T to make columns align)

1000 - 0000 = 1 (1 on the left, none on the right)

0300 - 1000 = 2 (3 on the left, 1 on the right)

0300 - 0000 = 3 (3 on the left, none on the right)

1300 - 0000 = 4 (etc...)

0090 - 1300 = 5

0090 - 0300 = 6

1090 - 0300 = 7

0090 - 1000 = 8

0090 - 0000 = 9

1090 - 0000 = 10

0390 - 1000 = 11

0390 - 0000 = 12

1390 - 0000 = 13

000T - 1390 = 14

000T - 0390 = 15

100T - 0390 = 16

000T - 1090 = 17

000T - 0090 = 18

100T - 0090 = 19

030T - 1090 = 20

030T - 0090 = 21

130T - 0090 = 22

000T - 1300 = 23

000T - 0300 = 24

100T - 0300 = 25

000T - 1000 = 26

000T - 0000 = 27

100T - 0000 = 28

030T - 1000 = 29

030T - 0000 = 30

130T - 0000 = 31

009T - 1300 = 32

009T - 0300 = 33

109T - 0300 = 34

009T - 1000 = 35

009T - 0000 = 36

109T - 0000 = 37

039T - 1000 = 38

039T - 0000 = 39

139T - 0000 = 40

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