CEMC Pascal, 2003

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, each of the 15 small squares is going to be coloured. Any two squares that have a vertex in common or share a side must be a different colour. What is the least number of different colours needed?

(A) $3$ (B) $4$ (C) $5$ (D) $8$ (E) $9$

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