Surprising results from midday arithmetic

[xoder]

Times of day where a twelve-hour perfectly analog clock's hour and minute hands line up exactly

12:00:00.00
01:05:27.27
02:10:54.54
03:16:21.81
04:21:49.09
05:27:16.36
06:32:43.63
07:38:10.90
08:43:39.18
09:49:05.45
10:54:32.72

What surprised me most about this was the fact that there is no intersection during hour 11. Or, more accurately, there is an intersection at 60 minutes past the start of hour 11, which is both a) not included in my calculations, and b) congruent to 12:00:00.00 above.

What's sad is that this problem has been bouncing on and off in my head since HS calculus, 7 years ago, and calculus is not required to solve it (I probably could have done it in elementary school, arithmetically).

Comments

[zandperl.livejournal.com]

I've never bothered to calculate the exact times, but I forget when I figured out there's 11 of them. I guess once I knew that much, I figured calculating them was trival. :-P

It's also like how there's a different number of hours in a sidereal day (23.934) from a (mean) solar day (24), or the many types of months to astronomers.