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| Problem of the Week; |*---The Problem of the Week---*| | |
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| Topic Started: Nov 19 2006, 07:25 AM (1,090 Views) | |
| Admin | Nov 19 2006, 07:25 AM Post #1 |
Administrator
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(From The Art and Craft of Problem Solving by Paul Zietz) The Forty-One Rooks -------11/19/06------- Forty-One Rooks are placed on a 10 X 10 chessboard. Prove that there must exist 5 rooks, none of which attack each other. |
 
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| appu_xavier | Nov 30 2006, 03:08 AM Post #2 |
Poincaré Conjecture
  ![]](http://z5.ifrm.com/static/1/pip_r.png)
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this is impossible! |
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| Admin | Nov 30 2006, 03:32 AM Post #3 |
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No, it's not. Anyways, it's the Problem of the Week. It's not supposed to be easy. Hint: The method used to prove it uses pigeons and holes. 
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| Stephen | Nov 30 2006, 11:40 PM Post #4 |
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Smarter than the Average Amoeba
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?:-( There must be a pattern like this: pigeon, hole, pigeon, hole, and to the end of that row. Then, the next row alternates the same way, but hole, pigeon, hole pigeon.... Then as you go to the next row, it switches back to the first one, and on the next row the alternate way. |
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| Admin | Nov 30 2006, 11:53 PM Post #5 |
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:lol: No, not literally pigeons and holes. . . . . . . . . . . . . . Big hint: Pigeonhole Principle. |
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| KRK | Dec 2 2006, 01:39 AM Post #6 |
Poincaré Conjecture
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I have a question. 1. Can the 5 special rooks attack other rooks? |
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| appu_xavier | Dec 3 2006, 06:02 PM Post #7 |
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Poincaré Conjecture
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No ,I don't think so. |
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| Admin | Dec 3 2006, 07:08 PM Post #8 |
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Administrator
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The five rooks simply don't attack any members in their group. They can attack other rooks. |
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| KRK | Dec 3 2006, 10:36 PM Post #9 |
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Poincaré Conjecture
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One case. Yellow=special rooks
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| Edwardted | Dec 5 2006, 01:38 AM Post #10 |
Twin Prime Conjecture
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i dont get what their asking |
| You cannot win without losing. | |
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| KRK | Dec 5 2006, 01:46 AM Post #11 |
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Poincaré Conjecture
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Read the posts if you dont understand |
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| Edwardted | Dec 7 2006, 01:00 AM Post #12 |
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Twin Prime Conjecture
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Yea.. like Karthik's answer, if there all on the same diagnol wouldn't it work no matter what?? Or perhaps I'm confused |
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| theSKINzFAN | Dec 7 2006, 02:30 AM Post #13 |
Mathematician
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why is it called pigeonhole....i didn't know pigeons lived in holes |
| Life is something to do when you can't get to sleep. | |
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| appu_xavier | Dec 7 2006, 04:47 AM Post #14 |
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Poincaré Conjecture
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They don't |
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| Edwardted | Dec 7 2006, 08:46 PM Post #15 |
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Twin Prime Conjecture
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.................So why is it called a pigeon hole? And what is a pigeon hole. |
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