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There is a king that has 10 servants that collect taxes for him. The taxes they collect are in the form of solid gold coins that weigh 10 grams each. The king finds out that 1 of his 10 men is stealing from him by scratching 1 gram out of each gold coin he collects in a way that you cant tell just by looking at the coins. The king is very upset by this and he wants to execute the man that is stealing so the next time they all come in to give him the taxes they collect he gathers them all in his room and stands them in a line. In his room he has a scale, with only ONE measurement he can find out which man is stealing from him. Assuming that the king can open up the bags of any of the men and measure whatever he wants in that single measurement, what does he do to have his answer in ONE measurement?

The king will open up all the bags of his collectors and he will do the following. He will take 1 coin out of the first bag, 2 out of the second, 3 out of the third, 4 out of the fourth ..... and so on up to 10 from the tenth bag. He will then measure all the coins he took out in one measurement and if 1 gram of the total weigh is missing he will know it was the 1st man, if 2 grams are missing the second, if 3 the third and so on..

Edited by elochai
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one of my favorite puzzles ... that's why it is already posted - check Weighing I. ... I have dedicated one whole page to such Weighing Puzzles

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