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 Longest duration, 24 hour clock (spoiler) by Steve Herman)

In 24-hour time, wouldn't it be 0:14 - 23:59?  I don't think the 0 hours would count as a "leading" zero, as it is necessary for the specification of the hour. 1425 minutes.

Posted by Charlie on 2014-11-13 08:07:14