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Scott Duke Kominers

Kominers’s Conundrums: To Catch a Counterfeiter

Hundreds of coins, but which are the fakes? A scale can do the job — if you know how to use it.

One of these stacks is not like the others.

One of these stacks is not like the others.

Source: Bloomberg

In this golden age of printing money, it seems like a great time to enjoy a coin-weighing puzzle — a type of Conundrum that has been gaining currency since the birth of cash itself. This one features enough change to put Scrooge McDuck in the mood for a swim.

You have 20 stacks of 20 identical-looking golden coins — but all the coins in one of the stacks are counterfeit! (The coins in the other 19 stacks are real.) You know that counterfeit coins are heavier than genuine ones. And you have an electronic scale that can determine the exact weight of any number of coins, but its batteries are almost fully drained.