There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of an ounce off. You also know that all the other coins weight the correct amount. You are allowed to use an extremely accurate digital weighing machine only once. How do you determine which set of 10 coins is faulty?
2026-04-28 14:17:55.1777385875
The 100 Coins Puzzle
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Assuming that all normal coins have a uniform weight:
I think you would want to number the sets $1,2,\ldots,10$. Then take $1$ coin from the first set, $2$ coins from the second set, $i$ coins from the $i$th set, and $10$ coins from the $10$th set. Then the weighing machine will display the correct weight minus $n$ hundredths of an ounce. Then the faulty set is the one from which you selected $n$ coins.
You could also do this by selecting $0,1,2,\ldots,9$ coins. I'm not sure if either strategy fails for any edge cases.