Take your time…
Hint: When we’re talking about palindromes in numbers, we have to ignore punctuation so that 2:42 is read the same way backwards and forwards.
If you think you’ve solved the puzzle, skip ahead to the answer, or read on for our explanation:
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If we think about all the possible palindromic times, we’ve got ones like 1:01 and 2:02 where you just repeat the hour in the number of minutes, but you can also add a digit in the middle: 1:11, 2:12, 5:35, etc.
Using that technique, we can get the interval down to 10 minutes — between 1:01 and 1:11 for example. Is it possible to get it smaller?
If we use two times within the same hour, no, we can’t get it any smaller than that. However, there is nothing saying that we can’t span two different hours.
We want the largest number we can get in a single hour, followed by the smallest number we can get in the next, which means that our first number should end in :59 and our second number should end in :01. 9:59 and 10:01 work nicely!
To get anything smaller, we’d need a number ending in :00, but that would have to be 0:00 for it to be palindromic, and that time does not exist on a 12-hour clock.
Therefore, the smallest interval we can get is two minutes.
This puzzle was adapted from one from Braingle.