Which face?
Which faces are opposite each other when this net is folded into a cube?
Age
14 to 16
Challenge level
Problem
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It is placed on a table with the face
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Which face is at the bottom?
This problem is taken from the World Mathematics Championships
Student Solutions
Folding up the net
Imagine folding the net into a cube, starting with the face
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So the face
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Considering edges
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Imagine the top and the base of a cube. The top shares a (green) edge with each side that isn't the base. The base shares a (blue) edge with each of these sides. These sides only share one edge with each other.
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Some of the green and blue edges are shown on the net to the right. It is enough to see that when the face
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