UKMT Pink Kangaroo, 2022

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Cuthbert is going to make a cube with each face divided into four squares. Each square must have one shape drawn on it; either a cross, a triangle or a circle. Squares that share an edge must have different shapes on them. One possible cube is shown in the diagram. Which of the following combinations of crosses and triangles is possible on such a cube (with the other shapes being circles)?

(A) $6$ crosses, $8$ triangles (B) $7$ crosses, $8$ triangles (C) $5$ crosses, $8$ triangles (D) $7$ crosses, $7$ triangles (E) none of these are possible

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