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: Clock Hands' meet!  ( 7277 )
« : May 19, 2007, 05:32:38 PM From Ria»



Clock Hands' meet!


How many times a day a clock�s hands (minute & hour) overlap?

 
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« #1 : May 26, 2007, 11:38:24 AM From anu»

23 times in a day,..the 24th time its the beginnin of the next day
« #2 : May 26, 2007, 12:44:46 PM From Ria»

23 is not the correct answer! Recently this question appeared in Bangalore Times' Mind Bender. The answer provided was 23 and I feel it is wrong.

The answer is 22.
Reason:

1:    12:00
2:    01:06
3:    02:11
4:    03:17
5:    04:22
6:    05:27
7:    06:33
8:    07:38
9:    08:44
10:   09:49
11:   10:55

The next one is 12:00 which falls in the next cycle.
Hence it is only 11 times the clocks hands' meet in one cycle.
In a day it is 11*2 = 22 times.
« #3 : May 27, 2007, 02:33:53 AM From anu»

its in a day,.... a day has 24 hrs,right,.....so..........
« #4 : May 27, 2007, 12:46:32 PM From Ria»

So?
In a clock full cycle the hands meet 11 times. In a day there are 2 cycles. Hence 22.
« #5 : June 11, 2007, 02:47:23 PM From Krishna»

My dear, its not like that you explained.In 1st cycle the hand meets 12 times and in second they meet 11 time and 12+11=23.

take it like this :--

1. 1200  am
2. 0105  am   
3. 0210  am
4. 0315  am
5. 0420  am
6. 0525  am
7. 0630  am
8. 0735  am
9. 0840  am
10. 0945  am
11. 1050  am
12. 1155  am
13. 0105  pm
14. 0210  pm
15. 0315  pm
16. 0420  pm
17. 0525  pm
18. 0630  pm
19. 0735  pm
20. 0840  pm
21. 0945  pm
22. 1050  pm
23. 1155  pm (not to correct time they meet approx.)

you have forgotten to add 1200.

If not convinced leave your digital clock for some time and count it on an analog watch.... ;)
« #6 : June 11, 2007, 03:14:18 PM From Ria»

Krishna, there are few errors in your example. Let me help you out in arriving at the right answer.
A clock hands doesn't meet 11:55. It is 12:00 at which they meet. Considering your approximation, lets say 11:55 is infact 12:00. This means you are adding 12:00 thrice. Once in the beginning, once in the end, and once in the middle. The last one belongs to the next day and hence cannot be counted. Therefore subtract one from your answer and the answer is 22.

« #7 : June 11, 2007, 03:55:32 PM From Krishna»

ya Ashish you are correct a nice catch. As in real time the overlapping time diffrence  is a little more then 65 min not exactly 65 mins. That means the interval between overlaps is 12/11 hour, which comes to 65.45 this exceeding time frame in a 24 hr day decrese one round of overlapping and hence its 22 if you count the  overlap at the midnight that begins the day, and also at the midnight that ends the day, the answer is twenty-three.

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« #8 : June 12, 2007, 12:07:51 PM From Narender»

Ashish is right if we don't consider the time 2400 which starts the next day.

But if we consider this then the answer will be 23.
« #9 : August 22, 2007, 04:51:44 PM From jigar_er_civil»

very simple in each hour they meet one time but at 12 u have to count only 1 time because 2time :) :) at 12 another day start so 23 is ans. :)
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