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.]
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