Ten bags in front of you on the floor are each full of newly-minted 1oz platinum bars. All of the bars look exactly the same, but all the bars in one of the bags are rejects and each bar weighs 1 gram less than a certified bar. You have an extremely accurate scale capable of measuring weight to the gram, but you are only permitted to use the scale once to make only one weighing. Using the scale only once for one weighing, how do you determine which bag has the bad bars?
The solution is to number the bags 1-10. Take from each bag a number of bars equal to the number of the bag - one bar from bag number 1, two bars from bag number 2, and so forth. Weigh them all together. The result will be light by a number of grams equal to the number of the bag that contains the light coins.
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