perplexus.info :: Just Math : Rectangle Color Rigor

Rectangle Color Rigor (Posted on 2014-09-23)

Some unit squares on an infinite sheet of squared paper are colored green such that:

Every 2x3 rectangle contains precisely two green squares, and:
Every 3x2 rectangle contains exactly two green squares.

How many green squares are there in a 9x11 rectangle?

*** Based on a Russian Math Olympiad problem.

No Solution Yet Submitted by K Sengupta

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: This seems too easy

| Comment 2 of 4 |

(In reply to This seems too easy by Jer)

The problem, I expect, is proving that it is always 33, for any 9x11 and any tiling.

That is not too much more difficult, so I agree that this is a relatively easy problem. I don't have time to write up the proof, but it is not hard to show that the only tiling that works is one where every third diagonal is solid green, and the other diagonals are uncolored.

Posted by Steve Herman on 2014-09-23 10:58:35

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