Chests of Coins
There are ten chests of coins which each chest labeled 1 to 10. The coins in each chest are supposed to weigh 1.0 grams, but one chest has coins which weigh 1.1 grams. You want to find out which chest contains the coins which weigh 1.1 grams.
You have a digital scale which will allow you measure the exact mass of any coins you choose to measure the total mass of. Using the scale only once, what is the minimum number of coins do you need to determine which of the 10 chests contains the 1.1g coins?
(You will determine which chest contains the 1.1g coins based on the reading on the digital scale, so think about what would be the minimum mixture of coins needed when using the scale only once).
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1 solution
Measure on the scale 1 coin from chest 1, 2 coins from chest 2, 3 coins from chest 3, ... and 9 coins from chest 9, which amounts to a total of 45 coins. The mass on the scale will then be equal to 45 + 0.1n, where n is the chest number of the chest which contains the coins with mass 1.1g. If n=0, then none of total 45 coins placed on the scale had a mass of 1.1g and the coins in chest 10 weigh 1.1g. Therefore, a minimum of 45 coins are required to determine which chest contains the coins with masses 1.1g.