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Back in Time

Age 14 to 16 Short Challenge Level:
Beatrix has a 24-hour digital clock on a glass table-top next to her desk.

When she looked at the clock at 13:08, she noticed that the reflected display also read 13:08, as shown.

How many times in a 24-hour period do the display and its reflection give the same time?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.