Goldman Sachs 5 Pirates Puzzle: Answer [Solved]

Answer: The most senior pirate keeps 98 coins for himself, gives 1 coin to the third pirate, 1 coin to the fifth pirate, and nothing to pirates 2 and 4. The plan passes 3 votes to 2.

The Goldman Sachs 5 pirates puzzle is one of the most famous game theory brain teasers in finance interviews: five pirates must split 100 gold coins, and a rejected proposal sends the proposer overboard. The answer is a 98-0-1-0-1 split, found only by reasoning backwards from the end of the game. This walkthrough shows every step.

The Rules of the Puzzle

Five pirates, ranked from the most senior (pirate 1) down to the least senior (pirate 5), loot a chest of 100 gold coins. They agree on a voting procedure:

• Pirate 1 proposes a split of the 100 coins.
• Every pirate votes, including the proposer. A plan needs at least half the votes to pass, so 3 of 5.
• If the plan fails, pirate 1 is thrown overboard, and pirate 2 proposes a new split to the remaining crew. The process repeats until a plan passes.

The pirates are perfectly rational, with clear priorities: stay alive first, take as many coins as possible second, and if two outcomes are otherwise equal, watch a rival go overboard.

This exact question appears in a Goldman Sachs interview experience (Set 14), where the candidate was asked the 100 gold coins and 5 pirates puzzle in the managerial round.

How to Solve the Goldman Sachs 5 Pirates Puzzle

The trick is backward induction: start from the smallest possible game and work upward. Each pirate knows exactly how the game would end if everyone ahead of him died, so you can work out precisely what each pirate would accept. Here is the chain, step by step.

Step 1: Two pirates left

Suppose pirates 1, 2 and 3 are gone, and only pirates 4 and 5 remain. Pirate 4 needs half the votes of a two-pirate crew, which is 1 vote, and he always votes for his own plan. So pirate 4 keeps all 100 coins and pirate 5 gets nothing. Pirate 4 survives no matter what he proposes.

Step 2: Three pirates left

Now pirates 3, 4 and 5 remain. Pirate 3 needs 2 votes out of 3, so he needs one ally. He looks one step ahead: if his plan fails, the game drops to the two-pirate case, where pirate 4 takes everything and pirate 5 gets zero.

Pirate 5 knows he gets zero if pirate 3 dies, so he votes yes for any plan giving him at least 1 coin: 1 coin beats zero, and at zero he would rather watch pirate 3 go overboard. Pirate 4, on the other hand, knows he would get all 100 coins in the next round, so he rejects anything below 100.

The cheapest ally is pirate 5, at 1 coin. Pirate 3 proposes: he keeps 99, pirate 5 gets 1, pirate 4 gets 0. Pirates 3 and 5 vote yes. The plan passes 2 to 1.

Step 3: Four pirates left

Pirates 2, 3, 4 and 5 remain. Pirate 2 needs 2 votes out of 4, so he needs one ally besides himself. If his plan fails, the game drops to the three-pirate case: pirate 3 gets 99, pirate 5 gets 1, pirate 4 gets 0.

So pirate 4 is the cheap vote again: he gets 0 in the next round and accepts 1 coin. Pirates 3 and 5 get 99 and 1 next round, far too expensive to buy. Pirate 2 proposes: he keeps 99, pirate 4 gets 1, pirates 3 and 5 get 0. Pirates 2 and 4 vote yes. The plan passes, since at least half is enough.

Step 4: All five pirates

Now pirate 1 proposes, and he needs 3 votes out of 5. If his plan fails, the four-pirate outcome kicks in: pirate 2 gets 99, pirate 4 gets 1, and pirates 3 and 5 get 0.

Pirates 3 and 5 are the cheap votes: each would get 0 in the next round, so each accepts 1 coin. Buying pirate 2 (who would get 99) or pirate 4 (who would get 1) costs more. Pirate 1 proposes: he keeps 98, pirate 3 gets 1, pirate 5 gets 1, pirates 2 and 4 get 0. Pirates 1, 3 and 5 vote yes. The plan passes 3 to 2.

That is the answer: 98-0-1-0-1. The senior pirate survives and keeps the maximum gold any proposer can keep.

The full backward-induction summary

Pirates remaining	Proposer keeps	Others get	Votes
Pirates 4 and 5	Pirate 4: 100	Pirate 5: 0	Pirate 4’s own vote is enough
Pirates 3, 4 and 5	Pirate 3: 99	Pirate 5: 1, pirate 4: 0	Pirates 3 and 5 vote yes (2 of 3)
Pirates 2, 3, 4 and 5	Pirate 2: 99	Pirate 4: 1, pirates 3 and 5: 0	Pirates 2 and 4 vote yes (2 of 4)
Pirates 1 to 5	Pirate 1: 98	Pirates 3 and 5: 1 each, pirates 2 and 4: 0	Pirates 1, 3 and 5 vote yes (3 of 5)

Traps That Catch Most Candidates

Keeping all 100 coins. The greedy first instinct fails: pirates 2 through 5 all get nothing and vote no, preferring to watch pirate 1 go overboard. The vote fails 1 to 4.

Splitting the coins evenly. Giving 20 coins to everyone passes the vote but leaves 78 coins on the table, and it shows you never worked out what each pirate would accept.

Offering 0 to a pirate who gets 0 in the next round. This is the subtle one. A pirate who gets zero either way votes no, because of the tie-breaker: with the coins equal, he prefers seeing you go overboard. You must offer him at least 1 coin to flip his vote.

Reasoning forward instead of backward. Starting from the five-pirate case and guessing feels natural, but it never converges. The puzzle is built to be solved from the end: two pirates, then three, then four, then five.

Misreading the vote threshold. The rule is at least half the crew, including the proposer, not a strict majority. With four pirates, 2 votes out of 4 is enough, which is why pirate 2 only needs to buy one ally.

What the Interviewer Is Testing in the Goldman Sachs 5 Pirates Puzzle

Strip away the pirate costume and this is a game theory interview. Here is what the interviewer is listening for:

• Backward induction. Can you solve a multi-stage problem from the end instead of the beginning? This is the core skill the puzzle tests, and it is the same thinking behind pricing options and planning trades.
• Thinking from the other side’s perspective. The solution requires you to figure out what each pirate expects to get if the current plan fails. In markets, every price you quote gets answered by a counterparty who has done the same math.
• Handling indifference and tie-breakers. Strong candidates state their assumptions out loud: what happens when a pirate is indifferent between two outcomes. The bloodthirsty tie-breaker is what makes the 1-coin bribes work.
• Clear, structured communication. The interviewer wants to hear the chain of reasoning in order, with each step building on the last. Rambling through cases out of order is the most common way candidates lose the thread.

Do not just memorize the 98-0-1-0-1 answer: interviewers can tell when a candidate recites it. The hire signal comes from deriving it live, out loud, from the two-pirate case upward.

Common Follow-Up Questions

Can the senior pirate keep all 100 coins?

No. Every other pirate gets 0 and votes no, each preferring to watch pirate 1 go overboard under the tie-breaker. The vote fails 1 to 4, so 98 is the maximum the senior pirate can keep and survive.

What if the pirates are not bloodthirsty?

The standard solution assumes the stated tie-breaker: with equal coins, a pirate prefers fewer rivals. Without it, a bribe equal to the next-round payoff may not flip a vote, and the clean 98-0-1-0-1 result breaks down. State your tie-breaking assumption in the interview.

Does the answer change with a different number of coins?

The pattern scales: with 200 coins, the senior pirate keeps 198 and still gives 1 coin each to pirates 3 and 5, since 1 coin beats a next-round payoff of zero.

Try Another Interview Brain Teaser

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• Two Doors Riddle: One Guard Lies, One Tells the Truth [Solved]: the one question that works no matter who you ask.