You have two clocks One doesnt run at all The other loses an

You have two clocks. One doesn\'t run at all. The other loses an hour a day. Which clock will most often show the correct time. How often will each show the correct time?

Solution

The clock that does not run will show the correct time 2 times per day.
Suppose the other clock shows noon (12 o\'clock) (correct time 1) and goes backward
at 1 it will show 11
at 2 it will show 10
at 3 it will show 9
at 4 it will show 8
at 5 it will show 7
at 6 it will show 6 [correct time 2]
at 7 it will show 5
at 8 it will show 4
at 9 it will show 3
at 10 it will show 2
at 11 it will show 1
at 12 it will show 12 [correct time 3]
The clock that runs backwards appears to show the correct time 5 times.