Back in time

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?
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Problem

 
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Back in Time
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.