In the United States, coins have certain thicknesses. If a stack of these coins is exactly $14$ mm high, how many coins are in the stack?

contest-math arithmetic

Solution 1:

Adding an odd number of coins results in a $5$ in the hundreds place. So to get $0$ in the hundreds place, you need an even number of coins.

Adding any pair of coins results in an odd number in the tens place. So to get a $0$ in the tens place, you need an even number of pairs. That is, the number of coins must be a multiple of $4$.

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