- #1

DaveC426913

Gold Member

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Possible?

Here's what I mean:

2 colours: a pie cut into 2 pieces, one of each colour. Both pieces are the same shape, both are bordered by the other colour(s).

3 colours: a pie cut into 3 pieces, one of each colour. All 3 pieces are the same shape, all have every other colour as a neighbour.

4 colours: a pie cut into 4 pieces, one of each of 4 colours. But 2 pairs colours do not share a border, sinced they're kitty corner. (It is possible to do it by moving into the 3rd dimension - a tetrahedron will do nicely, but that's cheating.)

Is there a way of making a pattern (no matter how complex or convoluted) such that each colour has the same shape (tile), and each borders every other? And is in only 2-dimensions?

What is the maximum number of colours that one can accomodate?

I doubt there's anything practical that I could use at work, but now I have an academic curiosity.