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To visit $S$ requires a journey from $P$ to $S$ and one back. To visit $P$, $Q$ and $R$ and return to the mainland requires at least $4$ journeys, so at least $2+4=6$ journeys are required to visit all four islands and return.



This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.