Maths Olympiad Prep

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Combinatorics Difficulty 5.2 AIME, harder Find the answer

A cube is created by folding the figure shown. Which face is opposite the face with 1 on it?

Pick one

Solution

Folds occur along the five edges between adjoining faces in the figure shown.

ANsWER: (C)

Consider the face numbered 3 as being the bottom face of the completed cube.

First, fold upward along the four edges of the face numbered 3 (the edges between 3 and 5, 3 and 4,3 and 6 , and 3 and 2 .

After folding upward, the faces numbered 2,5,42,5,4, and 6 become the four vertical faces of the cube.

The final fold occurs along the edge between the faces numbered 1 and 2 .

The face numbered 1 becomes the top face of the cube after this fold.

Since the bottom face is opposite the top face, then the face numbered 3 is opposite the face numbered 1 .

ANSWER: (B)

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.