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The ten digits of a digital clock are shown below.
I have a $12$ hour digital clock which shows the time, using four digits, on a piece of glass, so it can be seen from both sides. At what time between $3$ o'clock and $10$ o'clock does the time look the same from both sides?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.