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UKMT Grey Kangaroo, 2019

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Prab painted each of the eight circles in the diagram red, yellow or blue such that no two circles that are joined directly were painted the same colour. Which two circles must have been painted the same colour?

(A) $5$ and $8$ (B) $1$ and $6$ (C) $2$ and $7$ (D) $4$ and $5$ (E) $3$ and $6$

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