All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
Dominoes and checkerboard (Posted on 2013-07-23) Difficulty: 3 of 5
1. Two arbitrary squares of different colors have been removed from a checkerboard.
Is it possible to cover the remaining portion of the board with domino tiles so that each domino tile covers exactly two squares?

2.Assume that at every step we remove a pair of squares of different colors.
What is the minimum number of such pairs that need to be removed to assure that the remaining portion of the checkerboard cannot be fully covered with domino tiles?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution Comment 3 of 3 |
(In reply to Solution by Brian Smith)

Excellent part 1 proof, Brian!

As for part 2 extension, three pairs would suffice

|      XX XX     |
+  +  +  +  +  +  +  +  +
|XX   XX XX      |
+  +  +  +  +  +  +  +  +
|XX              |

Edited on July 24, 2013, 2:45 pm
  Posted by Steve Herman on 2013-07-24 14:44:19

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information