### Brain Teasers

# 4 weights

Lester has 40 kilograms of wheat. He has a simple balance and 4 weights of whole number denominations. The 4 weights are such that he is able to measure any whole number amount of wheat from 1 to 40 (no fractions). He can use a combination of two or more weights on any side of the balance as required. He can also use one weight on the left side and two or more weights on the right along with the wheat to weigh the required amount if necessary. What are the 4 weights Lester has?

### Answer

The weights Lester uses are 1,3,9 and 27 kg.For 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39 and 40 kg, he just needs to put the wheat on one side and the right combination of weights on the other side.

For 2, 8, 11, 26, 29, 35 and 38 kg he needs to put the wheat plus the 1 kg weight on one side and enough weights to make 1 more kg than he is trying to weigh up on the other side.

For 6, 7, 24, 25, 33, and 34 kg he needs to put the wheat plus the 3 kg weight on one side and enough weights to make 3 more kg than he is trying to weigh up on the other side.

For 5, 23, and 32 kg he needs to put the wheat plus the 1 and 3 kg weights on one side and enough weights to make 4 more kg than he is trying to weigh up on the other side.

Similarly,

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

...where negative numbers indicate weights that are on the same side of the wheat and positive numbers indicate weights that have been placed on the opposite side of the wheat.

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## Comments

I think we can go on to 5 weights, etc. by just multiplying the highest weight by 3. Eg : Here we can multiply 27 by 3 to get 81 so that for 5 weights we can get 1,3,9,27 and 81 for a weight of 121 . Next for 6 weights just multiply 81 by 3 and add up the weights to get the quantity which can be measured using these weights.

this was too hard-I didn't understand a word. (Actually I did-LOSER)

Very Confusing but very good.

Good teaser. It's easier if you have seen similar problems before.

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