205.Five Pirates and the Gold
★★★puzzlesJane Street
Five pirates of distinct seniority must divide 100 gold coins. The most senior proposes a split; all pirates including the proposer vote, and if at least half approve the split stands. Otherwise the proposer is thrown overboard and the next most senior proposes. Every pirate is perfectly rational and prioritises survival first, then gold. How many coins does the most senior pirate keep?
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Solve the two-pirate case first, then build upward. Each proposer only needs to buy off the cheapest pirates — those who would get nothing if the proposal failed.
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