Painting a chess board

Probability Level 2

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

Geoff Pilling by Geoff Pilling , 53, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

4 solutions

David Vreken
Apr 14, 2019

Here's another way:

7 Helpful 10 Interesting 27 Brilliant 0 Confused

That's how I did it. :-)

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

Here is another way to do this.

6 Helpful 4 Interesting 9 Brilliant 0 Confused
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.

2 Helpful 2 Interesting 2 Brilliant 0 Confused
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.

0 Helpful 0 Interesting 0 Brilliant 2 Confused

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

Log in to reply

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

Alex Burgess - 2 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...