While on a walk the other day I passed an auto body shop whose hours were 9:15am - 4:30pm. Aside from the oddly specific opening hour, I noticed that, between the two times, no digits were repeated.

(a) If I assume that I'm using a 12-hour clock, and that I'm never open at midnight, what are the longest and shortest hours of operation I can have that still have no repeated digits in my two times?

(b) What if I'm using a 24-hour clock?

[NOTE: assume no leading zeros for the hour, but leading zeros in the minute in order to always have a two-digit minutes value.]

(In reply to Longer duration, 24 hour clock by Steve Herman)

24 hour clock:
A longer duration would be 1:04 to 23:59 for 22 hours 55 minutes.
Where Day Light Savings Time is observed with the closing day of the summer hours, and where the clock is set back at 2:00 or 3:00 in the morning, the durational length is 23 hours 55 minutes. (Some places in the world that observe DST reset their clocks at an earlier hour, such as the European Union at UTC 01:00, thus the longer duration may not be longer if you were located in the European Union.)

(I had found this answer for the operational hours before having spied Harry's solution, which is the same, but it was your DST comment, Steve, that prompted me to look for the solution for DST.)

Edited on November 13, 2014, 12:01 am

Posted by Dej Mar on 2014-11-13 00:00:12