A man loans his friend his only 40 pound weight to weight grain on a balance scale. A week later the friend brings back the weight broken into 4 pieces. However, the man is happier now, because he can now measure anything weighing 1 to 40 lbs. (Note: the measured weights are in whole numbers. So he cannot measure 1.5 pounds.) What are the weights of each piece?
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Some other answers are posted online... but no NOT work:
1, 9, 10, and 20... you cannot get 3
1, 2, 8, and 29... you cannot get get 4
7, 8, 10, and 15... you cannot get 19
5, 7, 8, and 20... you cannot get 9
BTW a 121 pound weight broken into 5 pieces will give you every integer up to 121.
You'll need 1, 3, 9, 27, and 81
permutations and combinations of these weights on the the balance scale covers all even numbers from 2 to 40
once the right combos for the range 2 to 40 are determined the odd numbers fall in between so when the balance scales shift between two consecutive even numbers the odd # is determined
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