12-hour digital clock

Question:

Suppose you have a 12-hour digital clock where the number representing the hour is always the same as the number representing the minute. That is, the clock can only show times like 8:08, 9:09, 10:10, etc. What is the smallest time difference between two such times?

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Solution: 49 minutes.
It is very tempting to just subtract the times 9:09 from 10:10, etc., and get 61 minutes, or if you’re careless to get 101 minutes. However, think of the times closest to one another, 12:12 and 1:01, and you will find the difference is 49 minutes.

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