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.]

Actually, there is a longer hour of operation possible, one day a year, if the shop is in an area that has Daylight Savings time.  1:46 - 23:59, is 23 hours and 13 minutes on the day when switching from Daylight Savings Time to Standard Time.

Posted by Steve Herman on 2014-11-12 19:30:18