# A riddle of time

PocketKings
Posers and Puzzles 09 Feb '07 17:55
1. PocketKings
Banned from edits
09 Feb '07 17:55
Kind of like this one, read carefully.

At noon and midnight the hour and minute hands are exactly coincident with each other. How many other times between noon and midnight do the hour and minute hands cross?
2. 09 Feb '07 17:58
Unless there is some sort of trick this seems easy - ten times?
3. 09 Feb '07 18:05
10 times. The minute hand must pass over the hour hand once an hour (and once only), to go its full 360 degrees within the hour. The hands are on top of each other at 12, so don't cross again till between 1 and 2 (about 6 mins past, i can't be bothered to do the maths), then again between every pair of hours until 11 till 12, when they only cross again at midnight. Hence they will have crossed only 10 times BETWEEN 12pm and 12am.
4. 09 Feb '07 18:261 edit
I guess the trick is you are supposed to think:

1st crossing at roughly 13:05
2nd crossing at roughly 14:10
3rd crossing at roughly 15:15

etc.

10th crossing at roughly 22:50
11th crossing at roughly 23:55

Making eleven times. But of course the last of these, "roughly 11:55" is actually midnight and so doesn't count.