Five pirates split 100 gold coins
Asked at Jane Street, Citadel, SIG
Five pirates, ranked P5 (most senior) down to P1, have looted 100 gold coins and must divide them. The rules:
- The most senior pirate proposes a division of all 100 coins.
- All pirates (including the proposer) vote. If at least half vote yes, the proposal passes. A tie counts as passing.
- If it fails, the proposer is thrown overboard, and the next most senior pirate proposes, repeating.
Every pirate is perfectly rational and prioritizes, in order: (1) staying alive, (2) getting the most gold, (3) all else equal, seeing other pirates thrown overboard.
What does P5 propose, and does it pass?
Show a hint
Solve from the smallest case up. What happens if only P1 remains? If only P2 and P1? Work forward.