×

# It is too ambiguous

For any set of points $$S$$, we say that $$S$$ admits distance $$d$$, if there are two points in $$S$$ such that the distance between them is $$d$$.

We wish to colour every point of the plane with finitely many colours in such a way that no colour admits distance 1. Let $$X$$ be the minimal number of colours for which this is possible.

Can you show that $$4 \leq X \leq 7$$?

Can you find the exact value of $$X$$?

Note by Sharky Kesa
1 year, 8 months ago