## Bloodthirsty Pirates (Solution)

Work backwards:

If only Pirate 1 is left, he will get all 1000 coins.

Pirate 1 -> 1000 Pirate 2 -> X Pirate 3 -> X Pirate 4 -> X Pirate 5 -> X

If Pirates 1 and 2 left, Pirate 1 will not accept any proposal because he he knows that if he rejects Pirate 2’s proposal, Pirate 2 will be thrown overboard and Pirate 1 will get all 1000 coins. Pirate 2 is doomed to get nothing.

Pirate 1 -> 1000 Pirate 2 -> X Pirate 3 -> X Pirate 4 -> X Pirate 5 -> X

If Pirates 1, 2, and 3 are left, Pirate 3 will offer Pirate 2 one coin and give himself the rest. Pirate 2 will accept knowing that if he rejects then he will get nothing. Pirate 3 will also accept, so it will be accepted by a majority.

Pirate 1 -> 0 Pirate 2 -> 1 Pirate 3 -> 999 Pirate 4 -> X Pirate 5 -> X

If Pirates 1, 2, 3, and 4 are left, Pirate 4 will offer Pirate 1 1, Pirate 2 2, and give himself the rest.

Pirate 1 -> 1 Pirate 2 -> 2 Pirate 3 -> 0 Pirate 4 -> 997 Pirate 5 -> X

If Pirates 1, 2, 3, 4, and 5 are left, Pirate 5 will offer:

Pirate 1 -> 2 Pirate 2 -> 0 Pirate 3 -> 1 Pirate 4 -> 0 Pirate 5 -> 997