## Quick Clock Brain Teaser

Thanks to Riddles.com for this this quick clock brain teaser:

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?

Will unmask answers in a day or 2

Joe| Guest March 16th, 2007 - 2:27 am10. The first time it happens is a little bit after one, then after two, and so on until a little before eleven. After that the hands meet up again at midnight.

Prairie Kittin| Guest March 16th, 2007 - 7:51 am58

andrew| Guest March 16th, 2007 - 9:56 am11

jason| Guest March 16th, 2007 - 12:07 pm10

den| Guest March 16th, 2007 - 3:25 pm11 times. since it starts at 12:00 it will never cross again at any 12:XX but it will at all up till 11:XX. then they cross again at 12:00.

Frank| Guest March 16th, 2007 - 5:08 pmI count 10, corresponding to the crossings that occur after 1 through 10 PM. The post 11 PM crossing corresponds to the midnight crossing.

D| Guest March 16th, 2007 - 8:15 pmAt every hour, so not including noon and midnight: 11 times

Scott| Guest March 16th, 2007 - 11:34 pm12

Josh| Guest March 17th, 2007 - 4:13 pm10 times, it does not cross at 1:00

RK| Profile March 18th, 2007 - 11:31 pmyes, 10

ken| Guest March 22nd, 2007 - 1:11 am1:05.454545…

2:10.909090

3:16.363636

4:21.818181

5:27.272727

6:32.727272

7:38.181818

8:43.636363

9:49.090909

10:54.54545

The answer is 10

RK| Profile March 22nd, 2007 - 7:41 amhow did you manage to work out those #’s, Ken?

ken| Guest March 22nd, 2007 - 11:30 amThe angle that the hour hand makes is t/2, where t is in minutes. The angle that the minute hand makes is 6t.

Now you can use tan(6t) = tan(t/2). Then you solve that (you can’t just set 6t=t/2 cuz it’s a trigonometric equality with an infinite number of answers). I forgot all my high-school trig, so I had to dig around the web for the method.

Anyway, you find that the hands overlap roughly every 1 hour, 5 minutes, and 27.3 seconds.

RK| Profile March 22nd, 2007 - 5:15 pmThanks, Ken.

Frog stuck in a well - Smartkit Brain Enhancement News| Guest July 11th, 2007 - 1:03 am[…] Couple months back, a similar math brain teaser was posted. […]

Sofya| Guest July 26th, 2007 - 12:31 pm24

Tommy| Guest November 24th, 2007 - 6:11 pmThis question is approximately the level of a lesser middle school math competition, and probably many elementary schoolers could solve it, too. There is no need to use trigonometry to find the exact time either. No offense to anyone’s intellegence. Are there noticebly more interesting and challenging puzzles on this site?

RK| Profile November 24th, 2007 - 6:40 pmTommy: some of the problems on the site are relatively easy, some are hard.

so far, not many people have solved penny puzzle I put up, you can try that: http://www.smart-kit.com/s930/jumping-pennies/

The riddles, in general, are fairly difficult, you can try those too: http://www.smart-kit.com/scate.....s/riddles/

And the tangram is kind of fun and challenging: http://www.smart-kit.com/s895/baby-duck/

some of the puzzles in this group are hard also: http://www.smart-kit.com/top-1.....s-puzzles/