2021 JMPSC Sprint Problems/Problem 19
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 . minutes later, it displays . If no two digits represent the same letter, find the value of
Note that if the changes to in just 14 minutes, is at the end of an hour, meaning that is either or . If , T must be if minutes later is a new hour. However, at time minutes after will be instead of a new hour number. Thus, . If in minutes it is due to be , then it is between 4-o'clock and 5-o 'clock currently. Thus, from , . From (), we can guess that . Then we have and . Checking, the times are indeed 14 minutes apart! We want , so the answer is .
(wow this is my *one* actual contribution to the AoPS wiki!)
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