Mirror Clock: 13:31
Read the puzzle
A 24-hour digital clock shows 13:31, which reads the same forwards and backwards (a mirror time, like 12:21). How many minutes until the clock next shows a mirror time?
How many minutes until the clock shows the next mirror time?
Try the next hour: 14:??
70 minutes
The next mirror time is 14:41, 70 minutes later.
How to solve it
A mirror time on a 24-hour clock has the form AB:BA: the minutes are the hour digits reversed.
Step 1: check whether another mirror time is left in the 13 hour. Reversing 13 gives 31, so 13:31 is the only one; nothing later in that hour works.
Step 2: try the next hour. Reversing 14 gives 41, and 41 is a real minute value, so 14:41 is the next mirror time.
Step 3: count the gap. From 13:31 to 14:31 is 60 minutes, and from 14:31 to 14:41 is 10 more, so the wait is 60 + 10 = 70 minutes.
The usual wrong answer is 60 minutes, from assuming mirror times come exactly once an hour at the same minute. They do not: the minutes change along with the hour, from 31 to 41 here, so the gap is one hour plus 10 minutes.
Quick check: 13:31 plus 70 minutes is 14:41, and 14:41 read backwards is 14:41.
