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February 15th, 2012, 07:22 AM   #1
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A rather tricky puzzle. Can you solve it?

My maths teacher asked us to solve this puzzle today. I found it quite interesting, so I though I'd share it with you guys. I dunno if this is a piece of cake for you pro-mathematicians, but I found it quite challenging. Anyway, here goes:

You are give a chess board which has the upper left and bottom right squares torn out (Picture: http://srednja.hr/images/sah.gif ) Can that chessboard be covered in dominoes (2x1)? If yes, describe how, if not, explain why not.

Good luck
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February 15th, 2012, 07:31 AM   #2
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Re: A rather tricky puzzle. Can you solve it?

I solved it, started a website named Wikipedia, and copied my results there.

All in the last ten minutes!

http://en.wikipedia.org/wiki/Mutilated_ ... rd_problem
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February 15th, 2012, 09:50 AM   #3
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Re: A rather tricky puzzle. Can you solve it?

Hello, mobilefreak10!

This is a classic problem: The Mutilated Chessboard.
And, as expected, it has a classic solution.


Quote:
My maths teacher asked us to solve this puzzle today.
I found it quite interesting, so I though I'd share it with you guys.
I dunno if this is a piece of cake for you pro-mathematicians, but I found it quite challenging.

You are given a chessboard which has the upper left and bottom right squares removed.
Can that chessboard be covered in dominoes (2x1)?
If yes, describe how.[color=beige] .[/color]If not, explain why not.

Drag your cursor between the asterisks.

**
[color=beige]
The chessboard has 32 black square and 32 white squares.
Note that a pair of diagonally opposite squares have the same color.
So, the multilated chessboard has 30 black squares and 32 white squares.

A domino will always cover one black square and one white square.
After you place 31 dominos (and cover 31 black squares and 31 white squares)
there will be 2 white squares remaining, which canNOT be covered with one domino.[/color]
**
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