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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    
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Some Thoughts First thoughts (and part 2 spoiler) | Comment 1 of 3
Part 1) Mathematical intuition says that the answer to part 1 is yes.  And perplexus logic says that the part 2 question only makes sense if the Part 1 answer is yes.  So I guess yes, since intuition and logic are in agreement.

Part 2) Two pairs are enough to ensure that the remaining pairs cannot be tiled.  Just isolate one of the corners, removing its horizontal neighbor with one pair and its vertical neighbor with the other. 

  Posted by Steve Herman on 2013-07-23 15:08:14
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