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 \(X\)?

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