Painting a chess board

Is it possible to fill an 8x8 grid with 32 red squares and 32 black squares such that no 2x2 square has 2 reds and 2 blacks?

No Yes

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4 solutions

David Vreken
Apr 14, 2019

Here's another way:

That's how I did it. :-)

Erin Schnaedter - 2 years ago
Vu Van Luan
Apr 17, 2019

Here is another way to do this.

Mihaly Hanics
May 3, 2019

Here is one, where not only there is no 2-2 square, but there is no 4-0 or 0-4 square either. Divide the 8x8 into 4 2x8 lines, and make all the lines: RRRRBBBB RBRBBRBR All colours appear 32 times in the square. Also, can somebody please tell me how to use "enter" in a TeX text please.

Geoff Pilling
Apr 12, 2019

One way:

Start with a standard chessboard and paint rows 2 and 6 red and rows 4 and 8 black.

I was just about to post a picture of a different colouring, then realised it was just a reflection of yours! You say "one way" - do you know of others (apart from reflections and rotations of this one)?

Chris Lewis - 2 years, 2 months ago

Good question! I wonder how many "ways" there are if you don't count reflections and rotations...

Geoff Pilling - 2 years, 2 months ago

Your construction is not clear to me.

Atomsky Jahid - 2 years, 1 month ago

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The rest of the chess board is left as it was (alternate red and black).

Alex Burgess - 2 years, 1 month ago

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