School-Safe Puzzle Games

## 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?

### 18 Comments to “Quick Clock Brain Teaser”

1. Joe | Guest

10. 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.

2. Prairie Kittin | Guest

58

3. andrew | Guest

11

4. jason | Guest

10

5. den | Guest

11 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.

6. Frank | Guest

I count 10, corresponding to the crossings that occur after 1 through 10 PM. The post 11 PM crossing corresponds to the midnight crossing.

7. D | Guest

At every hour, so not including noon and midnight: 11 times

8. Scott | Guest

12

9. Josh | Guest

10 times, it does not cross at 1:00

10. ken | Guest

1:05.454545…
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

11. RK | Profile

how did you manage to work out those #’s, Ken?

12. ken | Guest

The 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.

13. RK | Profile

Thanks, Ken.

14. Frog stuck in a well - Smartkit Brain Enhancement News | Guest

[…] Couple months back, a similar math brain teaser was posted. […]

15. Sofya | Guest

24

16. Tommy | Guest

This 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?

17. RK | Profile

Tommy: 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/