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To weigh things , there are only four weights available in a shop . Using these, we can measure from 1 kg to 40 kg's at once. Identify the four digits and explain your answer.

1,3,5,27 1,5,9,30 1,5,7,39 1,3,9,27

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1 solution

Wes Pomeroy
Apr 9, 2015

We are talking about a balance scale, where there are two sides. We can put a combination of these weights on one or both sides to find missing weights up to 40

1 = 1, 2 = 3-1, 3 = 3, 4 = 3+1, 5 = 9-3-1, 6 = 9-3, 7 = 9+1-3, 8 = 9-1, 9 = 9, 10 = 9+1, 11 = 9+3-1, 12 = 9+3, 13 = 9+3+1, 14 = 27-9-3-1, 15 = 27-9-3, 16 = 27+1-9-3, 17 = 27-9-1, 18= 27-9, 19 = 27+1-9, 20 = 27+3-9-1, 21 = 27+3-9, 22 = 27+3+1-9, 23 = 27-3-1, 24 = 27-3, 25 = 27+1-3, 26 = 27-1, 27 =27, 28 = 27+1, 29 = 27+3-1, 30 = 27+3, 31 = 27+3+1, 32 = 27+9-3-1, 33 = 27+9-3, 34 = 27+9+1-3, 35 = 27+9-1, 36 = 27+9, 37 = 27+9+1, 38 = 27+9+3-1, 39 = 27+9+3, 40 = 27+9+3+1

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