2021 JMPSC Sprint Problems/Problem 19

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Problem

As an April Fool’s prank, Sean hacks his teacher’s digital clock and switches each digit to a certain letter. Right now, the hacked clock displays $\textbf{M:AT}$. $14$ minutes later, it displays $\textbf{A:TM}$. If no two digits represent the same letter, find the value of $\textbf{A} \times \textbf{M}.$

Solution

asdf