jmc

Question

On a 12-hour clock, an elapsed time of four hours looks the same as an elapsed time of 16 hours. Because of this, we can say that four hours is "clock equivalent'' to its square number of hours. What is the least whole number of hours that is greater than 4 hours and is "clock equivalent'' to its square number of hours?

Accepted Answer

For two times to be clock equivalent, their difference must be a multiple of 12. We list the hours greater than 4, their squares, and the differences between them: array|c|c|c| 5 & 25 & 20 6 & 36 & 30 7 & 49 & 42 8 & 64 & 56 9 & 81 & 72 array We can stop at 9, since it is the smallest hour greater than 4 that is clock equivalent to 81, its square.