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Ken's Puzzle of the Week

Sequential Digits on a Clock

- How many times in a 12-hour period (i.e. 1:00:00 to 12:59:59) can four
sequential digits be read on a digital clock? For example, 11:23:40 shows
"1234". Five Digits? Six? Zeros may be the first digit in
a sequence, but not the first digit on the display.
- Same question over 24 hours on a 24-hour clock (1:00:00 to 24:59:59).

Source: Original.

Solution

Mail to Ken