If a valid time on a 12 hour time period has the hour hand and minute hand switched, how many times will that result in another valid time? I have found 11, which is when the hour hand points at the same place as the minute hand. I know there is much more, but I can't figure it out.

Answer 1

Do you mean the physical clock hands are switched? No problem. I mean, the hands still point to places on the dial, right?

If you mean the digital time has hh:mm swapped to mm:hh, then any time from

01:01 to 01:12 is ok
and so on for the other hours. As long as the minutes are from 1-12, the swapping will produce a valid hour.

Answer 2

physical hands
they can't point to any place on the dial, because it won't be a correct time

Answer 3

Hmm. I'm still unclear. What is an example where switching the hands is invalid?