Solution
The Pirate Gold Problem
Show the problem again
Five perfectly rational, greedy pirates must divide 100 gold coins. The most senior pirate proposes a distribution. If a strict majority (more than half) vote against it, he is thrown overboard and the next most senior proposes. Pirates prefer more gold, prefer to live, and will vote against a proposal if indifferent. How many coins does the most senior pirate keep for himself?
Worked solution
The answer is 98. Working backwards: with 2 pirates, the senior keeps all 100. With 3, the senior gives 1 coin to the junior (who gets nothing if the senior dies) and keeps 99. With 4 pirates, the senior bribes the pirate who gets nothing in the 3-pirate game for 1 coin, keeping 99. With 5, the senior bribes the two pirates who get nothing in the 4-pirate game for 1 coin each, keeping 98.
Source: From Ian Stewart, 'A Puzzle for Pirates', Scientific American (May 1999). Statement written for AxiomIQ.