perplexus.info :: General : Dominoes and checkerboard

Dominoes and checkerboard (Posted on 2013-07-23)

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

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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

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