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An hour has 60 min. Assuming the clock has only the hour and minute displayed, every hour 1 would appear at 1, 11,12,13,14,15,16,17,18,19,10,21,31,41,51. Counting 11 as once there are 15 1s in an hour. In the 24 hours, only 0,2,3,4,5,6,7,8,9,22,23 have no 1 s in them. Therefore 1 aooears 165 times in those times. As for hours 1,10,11,12,13,14,15,16,17,18,19,21, there is always a 1 in the clock. This makes 1 appear 12*60 times which is 720 times. Therefore in total, 1 appears 885 times in a digital 24 hour clock.

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