2. 100 Gold Coins
Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).
The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.
What is the maximum number of coins the captain can keep without risking his life?
Added 1 January 2007 · Updated 5 July 2026
Hint: Each pirate cares first about staying alive, then about getting as many coins as possible. A pirate will vote “Aye” only if the proposal gives them more than they would get after mutiny. Side deals, promises, and revenge votes do not count, because the pirates are selfish and treacherous.
What happens if there are two pirates? Who completely loses out? What happens if there are three pirates? Who completely loses out? What happens if there are four pirates? Which two pirates completely lose out?
Solution:
98
The captain says he will take 98 coins, and will give one coin to the third most senior pirate and another coin to the most junior pirate. He then explains his decision in a manner like this...
- Pirate 1: most junior, keeps 1 coin.
- Pirate 2: fourth most senior, keeps 0 coins.
- Pirate 3: third most senior, keeps 1 coin.
- Pirate 4: second most senior, keeps 0 coins.
- Pirate 5: captain, most senior, keeps 98 coins.
If there were 2 pirates, because pirates 3,4 & 5 had walked the plank, then pirate 2 would be the most senior, and he would just vote for himself and that would be 50% of the vote, so he's obviously going to keep all the money for himself.
If there were 3 pirates, because pirates 4 & 5 had walked the plank, pirate 3 has to convince at least one other person to join in his plan. Pirate 3 would take 99 gold coins and give 1 coin to pirate 1. Pirate 1 knows if he does not vote for pirate 3, then he gets nothing, so obviously is going to vote for this plan.
If there were 4 pirates, because the captain had to walk the plank, pirate 4 would give 1 coin to pirate 2, and pirate 2 knows if he does not vote for pirate 4, then he gets nothing, so obviously is going to vote for this plan.
As there are 5 pirates, pirates 1 & 3 had obviously better vote for the captain, or they face choosing nothing or risking death.
| Pirates left |
Winning proposal |
| 2 |
Senior pirate keeps 100. |
| 3 |
Captain keeps 99, gives 1 to Pirate 1. |
| 4 |
Captain keeps 99, gives 1 to Pirate 2. |
| 5 |
Captain keeps 98, gives 1 each to Pirates 1 and 3. |
Comments (24)
The pirate question could use a disclaimer. This basic game theory problem shows that the other pirates wouldn't accept 1 gold coin each and would rather walk away than take something perceived as 'unfair'. The solution isn't quite that simple.
I think I have an alternative and better solution to the Pirates problem. The original problem is that five pirates have obtained 100 gold coins and have to divide up the loot.
I believe I have a better solution to the Pirates problem regarding the distribution of gold coins among the pirates.
If pirates 1 and 3 vote against the captain, then the Captain gets mutinied, and a new redistribution is proposed. Why would they be content to get simply one coin?
In the '100 Gold Coins' puzzle, if pirates 1 and 3 vote against the captain, then the captain gets mutinied, and a new redistribution is proposed. Why would they be content to get simply one coin?
The solution to puzzle 2 and 3 needs a more detailed explanation. Is the most senior pirate the captain or the most senior of the rest?
In the scenario with five pirates and 100 coins, pirate 4 should take all 100 coins since he can secure a majority vote by himself. Pirate 5 would be grateful to receive even a single coin, allowing pirate 4 to keep the rest.
hello,
i have a proposition for question (2.), `100 Gold Coins`:
knowing that two of the pirates get nothing and two of them get each 1 coin, what if one of the pirates which gets 1 coin will not vote `Aye` for the captain, knowing that the other two who gets nothing won`t be pleased and won`t vote `Aye`, either ?
in the statement there is never mentioned that the captain will kill any of the pirates who dare not vote for his proposal.
so now there will be three against two, the captain and the other pirate will be overpowered and thrown overboard, and will remain only 3 pirates to split the money.
well .. i want to propose another solution which will surely get the captain with most of the money, without risking any mutiny.
the amount of money that will get each of the pirate if the sum will be split equally, is 20 coins/pirate. the captain will give to two of them 20 coins each, assuring himself that they won`t be losing anything either way, and then, he will take the rest of the sum, meaning 60 coins.
Knowing that two of the pirates get nothing and two of them get each 1 coin, what if one of the pirates which gets 1 coin will not vote Aye for the captain, knowing that the other two who get nothing won’t be pleased and won’t vote Aye, either?
The reasoning in '100 Gold Coins' seems faulty. If one pirate who receives 1 coin does not vote 'Aye', the captain and the other pirate could be outvoted, leading to a different distribution of coins.
The 100 Gold coins honestly doesn't make sense. If the captain was to take 98 gold coins and give 1 to two other members, wouldn't the members just fight back? Honestly who would want just one coin?
The 100 Gold Coins puzzle doesn't make sense. If the captain takes 98 gold coins and gives 1 to two other members, wouldn't they just fight back? They are all greedy, so they would likely mutinize and split the coins evenly instead.
The language in the 100 Gold Coins problem is confusing and requires clarification to improve understanding.
What about the thieves logic puzzle?
The second and third pirates could vote against the captain and redistribute the coins among themselves, which would give them more than just one coin each.
En el problema de los 23 prisioneros y 2 interruptores, el líder necesita esperar 44 veces, pero si solo lo giran una vez, ¿por qué no contar siempre 23? 23 es menos que 44.
The solution to the 6 pirates 1 coin problem is incorrect. The most senior pirate should give the coin to the 3rd most senior pirate to secure votes.
The puzzle involving 98 coins and 5 pirates is ambiguous. The captain should give 2 coins to ensure the other pirates choose his outcome, as they are treacherous.
If there were 2 pirates, pirate 2 being the most senior, he would just vote for himself and that would be 50% of the vote, so he's obviously going to keep all the money for himself. If there were 3 pirates, pirate 3 has to convince at least one other person to join in his plan.
The voting strategy for the pirates seems flawed. If pirate 1 knows he can get nothing if he doesn't vote for pirate 3, wouldn't he also consider the possibility of a better deal if he waits for pirate 2's plan?
I suggest that the given solution fails to take into consideration that all the pirates are intelligent and treacherous. Were I the next senior pirate, I would promise the three lower grade pirates that if they would reject the Captain's proposal and make him walk the plank, then I, as the new acting Captain would share the 100 coins evenly among the remaining.
The logic is flawed. If (for instance) there were 3 pirates, and the captain proposes that he keeps 99 and gives 1 to Pirate 1, you claim that Pirate 1 would agree to this because it's better than the alternative (getting nothing). But it isn't true; because the alternative is making the Captain walking the plank and splitting the 100 coins with Pirate 2, 50-50.
The logic is flawed. If there were 3 pirates, and the captain proposes that he keeps 99 and gives 1 to Pirate 1, Pirate 1 would not agree because the alternative is making the Captain walk the plank and splitting the 100 coins with Pirate 2, 50-50.
The logic in '100 Gold Coins' is flawed. For example, if there were 3 pirates, the captain's proposal of keeping 99 coins and giving 1 to Pirate 1 isn't necessarily better than the alternative of making the captain walk the plank and splitting the coins with Pirate 2.
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