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.]

I think that would be 2:34 am - 10:59pm, which is 20 hours and 25 minutes.

Edited on November 12, 2014, 3:24 pm

Posted by Steve Herman on 2014-11-12 15:20:35