## Puzzle #3: Five Pirates and Looted Gold Coins

This puzzle was shown to me by an 11 year old (Smiti Mittal) and I loved the puzzle. I have come across many puzzles of this nature, but liked this one for its simplicity and possible variations. This is from a book of puzzles used in interviews in Microsoft.

Five pirates have looted 100 gold coins. Now they have to divide their loot.These pirates are very greedy and cruel,so they want to maximize their profit and they don’t shy to kill their pirates. For distribution they decide that senior most pirate will proposes a distribution of the loot. All the pirates will vote, and if at least half accept the proposal, the loot is divided as proposed. If not, the most senior pirate will be killed, and they start over again with the next senior pirate. What solution does the most senior pirate propose? So that he can get the maximum profit, and of course live to have it!

Clarification Note: Assume that all of them are very logical, want to live and are greedy!

Target Group: Age 10 and above, good for adults as well

Variation 1: For younger kids, assume that there are only 3 pirates and then do the puzzle. This puzzle will teach kids a good way to solve a whole class of logic puzzles.

Variation 2: For age group 10 and above or anyone else who does the puzzle, repeat the same puzzle with the following change – Whenever a pirate proposes a distribution, and the group votes, they need more than half to vote in favor of the proposal to have the proposal accepted. If not the pirate who proposed is killed. What should the senior most pirate propose.

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### 9 Responses to Puzzle #3: Five Pirates and Looted Gold Coins

1. sandeep singhal says:

Are the pirates greedy and cruel i.e. will they kill another pirate even if it doesn’t change their payoff ?

• Alok Goyal says:

If they know that they cannot increase their payoff from what is being offered, then they will not kill the pirate offering the deal.

• sandeep singhal says:

Thanks, thats helpful. Though if they acted like true pirates, they should be really upset at the allocation coming their way and hence keep killing if they can get the same payoff later 🙂

2. chaitanya says:

Classic one. Once a pattern is established, fun to do with more number of pirates.

3. Jatin says:

In the 5 pirate case when the seniormost pirate proposes, does he get to vote as well? If yes, then I guess it means that 3 guys/gals (including him) must agree for the allocation to stand. Right?

• Alok Goyal says:

yes, everyone votes including the one who proposes

4. Vats says:

Interesting puzzle – took a while to figure out (if Alok approves the answer :-). However, with this level of logic these guys should quit piracy and write their own content. If they proposed and accepted the said offer – they probably got hired !!!

Another assumption is that they never took a game theory or politics class.

5. A slightly different version of the original pirates problem (read that one first to get all the rules). 6 pirates, only one gold coin. as before, the pirates are super-smart, and they value, in this order: (i) their lives, (ii) getting money, (iii) seeing other pirates die. so if given the choice between two outcomes, in which they get the same amount of money, they’d choose the outcome where they get to see more of the other pirates die. how can pirate 6 (first one to propose a solution) save his skin?

Copy pasted this link from another site. Not posting the link here since the same page contains the answer as well.

• Alok Goyal says:

This is indeed a very interesting variation, I loved it. Will post this on my facebook as well. I will send you the solution separately.