Which face?
Which faces are opposite each other when this net is folded into a cube?
Problem
The net on the right is folded into a cube.
It is placed on a table with the face
on top.
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
, and continuing until it reaches the top.
So the face
is at the bottom when the face
is at the top.
Considering edges
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.
Some of the green and blue edges are shown on the net to the right. It is enough to see that when the face
is on the top, the face
is at the bottom.