Five rational pirates must split 100 gold coins by vote, or someone goes overboard. How?
Five pirates, ranked by strict seniority, must agree on how to split 100 gold coins. The most senior proposes a split; all five vote, and it passes with at least half in favor, including the proposer's own vote. If it fails, the proposer is thrown overboard and the next pirate proposes instead. Every pirate wants to survive first, then maximize their own coins. How should the senior-most pirate split the coins?
Reveal the answer
Propose 98 coins for themselves, 1 coin each to the third and fifth most senior pirates, and nothing to the second and fourth. Working backward from a two-pirate case (where the senior one simply takes everything), each pirate learns exactly which colleagues would get nothing if the plan failed — and can buy their votes for just one coin each, securing the 3-of-5 majority needed to pass.
— Ian Stewart, A Puzzle for Pirates — Scientific American, May 1999