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Mathematics

Frobenius Coin Problem and the Largest Unpayable Amount

Quick fact

For two coprime denominations a and b, the largest nonrepresentable amount is ab – a – b. For the classic chicken nuggets problem with 6, 9, and 20, the largest non-orderable number is 43.

Why this is interesting

You have two coins, say 3 and 5 cents. What is the largest amount you cannot make? Surprisingly, there is a simple formula—and for some sets of coins, the answer can be surprisingly large.