# The counterfeit sovereigns

This week's puzzle is a weighing problem. I have adapted it from one given in Martin Gardner's book: "Mathematical Puzzles and Diversions".

## The puzzle

The first eleven are being paid their match fees in gold sovereigns. Each player gets a stack of ten gold sovereigns. One stack of coins however is entirely counterfeit, but you do not know which one. You do know the weight of a genuine gold sovereign and you know that each counterfeit sovereign weighs one gramme more than it should. You may weigh the coins on a pointer scale that indicates the weight of the coins on its pan. What is the smallest number of weighings necessary to determine which stack is counterfeit?

## The solution

A single weighing can identify the counterfeit stack! You take one sovereign from the first stack, two from the second, three from the third, and so on up to all ten from the tenth stack. You weigh the whole sample on the weighing scale. The number of excess grammes in this collection gives you the counterfeit stack. For example if the collection of sovereigns weighs six grammes more than it should then the sixth stack, from which you took six sovereigns, each weighing one gramme more than a genuine sovereign, is the counterfeit stack. If there is no excess weight then the eleventh stack is the counterfeit one.

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