Answers to Contest Center puzzles, riddles and brainteasers
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 Pan Balance        Many people immediately jump to the answer that you should buy weights of 1, 2, 4, 8, 16, etc. ounces. This is because they learned in school that these can be added to make any whole number, for example 21 is 16+4+1. So you could weigh a 21-ounce object by putting it in one pan, and placing weights 1, 4 and 16 in the other pan.        People who consider the problem more carefully will realize that you can put the weights on either pan. Using weights 1, 3, 9, 27, 81, etc. you can add and subtract them to make any whole number, for example 21 is 27+3-9. So you could weigh a 21-ounce object by placing it in one pan along with the 9-ounce weight, and putting 3 and 27 in the other pan.

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