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.

Question

Math - Steve, Saturday, February 6, 2016 at 5:52pm
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.
Math - Andre, Saturday, February 6, 2016 at 6:01pm
physical hands
they can't point to any place on the dial, because it won't be a correct time
Math - Steve, Saturday, February 6, 2016 at 6:53pm
Hmm. I'm still unclear. What is an example where switching the hands is invalid?

For example, lets say a time is 6:30. The hour hand will point halfway between 6 and 7 and the minute hand will point at 6. If we switch the hands, then the hour hand will point exactly at 6 and the minute hand between 6 and 7. Then the time is around 6:32-6:33. But that isn't possible because the hour hand cannot be pointing exactly at 6. I think this is what the question is asking
Calculus - Steve, Tuesday, February 9, 2016 at 2:19pm
Hmm. In that case, you need times where both hands are exactly on numbers. So, there are 11 such times, exactly on hours.

At 2:00, say if you switch hands the hour hand will be on 12 and the minute hand will be on 2, so the time is 12:10.

Now, on a real clock, the hour hand will be a bit past the 12, but does that disqualify it?

So, I'd say your idea is good -- it captures all 12 times where the hands coincide. If we also allow the fudging above, then there are 11 other times, corresponding to

1:00 --> 12:05
...
11:00 --> 12:55

But, as you say, the hour hand will always be a bit off the mark.
Calculus - Andre post for Steve, Tuesday, February 9, 2016 at 11:33pm
I think there are more than 11
the person that gave the question said there were more than 11