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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 $13$:$08$.
 


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 which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.