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Problem 63

Combinatorics Difficulty 1.2 Find the answer CEMC Gauss (Grade 7) · Canada · 2016

A cube has exactly one face painted as shown.

The other five faces of the cube are not painted. If the cube is rolled, which of the following could be the same cube?

(A) (B) [[IMAGE1]] (C) [[IMAGE2]] (D) [[IMAGE3]] (E) [[IMAGE4]]

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Rolling the cube does not change the size of the painted triangle.

For this reason, we can eliminate answer (A).

Rolling the cube does not change the number of painted triangles.

For this reason, we can eliminate answers (D) and (E).

Rolling the cube does not change the orientation of the painted triangle with respect to the face of the cube that it is painted on.

For this reason, we can eliminate answer (C).

Of the given answers, the cube shown in (B) is the only cube which could be the same as the cube that was rolled.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.