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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.*