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I'm assuming that you mean such times as 23:00, 22 :01, 21:02 etc  where 23 + 0 = 23, 22 + 1 = 23 and 21 + 2 = 23, then there are 23 such different times where the total of the hours and minutes sum to 23.

 

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13y ago
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Q: How many times in 24 hours does a digital clock add up to 23?
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