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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.*