Ken's Puzzle of the Week

Sequential Digits on a Clock

  1. 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.
  2. Same question over 24 hours on a 24-hour clock (1:00:00 to 24:59:59).
Source: Original.
Mail to Ken