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At Q the ant can choose first to go left to T, then right to W.
Otherwise, at Q it can go right to R and then left to W.
W is the corner diagonally opposite to P and is reached by either route after three edges (and no fewer).
So after exactly three more edges, the ant must reach the corner opposite W, that is, P.
So the ant will return to P after travelling along 6 edges.
Crawl Around the Cube
Age 11 to 14
ShortChallenge Level 
At Q the ant can choose first to go left to T, then right to W.
Otherwise, at Q it can go right to R and then left to W.
W is the corner diagonally opposite to P and is reached by either route after three edges (and no fewer).
So after exactly three more edges, the ant must reach the corner opposite W, that is, P.
So the ant will return to P after travelling along 6 edges.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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