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

[omgimsuchadork.livejournal.com]

I remember that problem! I first encountered it in seventh grade, at pre-school math club. I got the question wrong, and never bothered to work it out on my own, but I remembered that there were eleven times when the hands lined up (the question asked how much time would pass between one line-up and another; 65 5/11 minutes, for a total of eleven times in a twelve-hour period).