My Math Forum A rather tricky puzzle. Can you solve it?

 Applied Math Applied Math Forum

 February 15th, 2012, 07:22 AM #1 Newbie   Joined: Jan 2012 Posts: 5 Thanks: 0 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
 February 15th, 2012, 07:31 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 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
February 15th, 2012, 09:50 AM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

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]
**

 Tags puzzle, solve, tricky

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post BenFRayfield Applied Math 0 January 21st, 2014 12:58 AM YWorld Algebra 24 August 10th, 2012 05:05 PM arun Number Theory 3 November 25th, 2011 01:41 AM netmaxweb Algebra 1 November 15th, 2011 11:22 PM mrhesham Algebra 9 November 21st, 2010 08:01 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top