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Photo
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Stopping and Turning back hands of time


Best Answer Prime, 25 February 2013 - 08:46 PM

Spoiler for

 

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.

Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

 

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?

I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

 

Spoiler for actually, the answer is

Go to the full post


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19 replies to this topic

#11 bonanova

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Posted 21 February 2013 - 10:13 PM

There's more than meets the eye here.

I've gone back and forth and concluded a couple things.

 

Spoiler for First

 

Spoiler for Second

 

It's a very nice puzzle.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#12 Rob_Gandy

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Posted 21 February 2013 - 11:18 PM

@captainEd, the pic is not the start, both @ 12 o'clock is the start where the hands are moving clockwise, eventually the MH overtakes the HH causing it to stop but the MH keeps going until it reached the stopped HH again where then it reverses its direction (like bumping) while causing the HH to move again(resume running clockwise) . No double interpretations is intended here.

Spoiler for A little more clarification

 

There's more than meets the eye here.

I've gone back and forth and concluded a couple things.

 

Spoiler for First

 

Spoiler for Second

 

It's a very nice puzzle.

I agree now that I understand the OP a little more.


 

Spoiler for I still think that


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#13 bonanova

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Posted 21 February 2013 - 11:36 PM

Here's what I think.

Spoiler for Analysis


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#14 CaptainEd

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Posted 22 February 2013 - 12:29 AM

Oh dear! My epsilons didn't cancel. Oops. Way to go, Bonanova!
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#15 TimeSpaceLightForce

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Posted 22 February 2013 - 04:57 PM

Here's what I think.

Spoiler for Analysis

Spoiler for

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#16 Prime

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Posted 22 February 2013 - 10:15 PM

If I understood the statement of the problem right:

1). The hour hand changes its state from stopped to moving clockwise, or from moving to stopped every time the minute hand passes over it.

2). The minute hand continues moving in the same direction as before when it passes over the moving hour hand and reverses its direction when it passes over the stopped hour hand.

 

Spoiler for when they meet at 12

Edited by Prime, 22 February 2013 - 10:19 PM.

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Past prime, actually.


#17 TimeSpaceLightForce

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Posted 25 February 2013 - 12:57 PM

Spoiler for


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#18 Prime

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Posted 25 February 2013 - 08:46 PM   Best Answer

Spoiler for

 

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.

Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

 

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?

I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

 

Spoiler for actually, the answer is


  • 1

Past prime, actually.


#19 TimeSpaceLightForce

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Posted 26 February 2013 - 11:37 AM

Spoiler for

 

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.

Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

 

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?

I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

 

Spoiler for actually, the answer is


  • 0

#20 TimeSpaceLightForce

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Posted 26 February 2013 - 03:50 PM

This is the answer: Good one Prime! Thanks.

Spoiler for


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