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Crawl Around the Cube

Stage: 3 Short Challenge Level: Challenge Level:1

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, $P$.

This problem is taken from the UKMT Mathematical Challenges.
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