Arrrrr Mateys!!!!

Captain Jack Sparrow and his motley crew (four others, five total) have just plundered 100 gold coins and now they must decide how to distribute them.

Pirates have a strict order of seniority: Jack is superior to Bootleg Bill, who is superior to Crooked Chris, who is superior to Dangerous Dan, who is superior to Eagle-Eye Eddie.

The pirate's rules of distribution are thus: that the most senior pirate should propose a distribution of the bounty. All of the pirates, including the proposer, then vote on whether to accept this distribution with two possible outcomes:


The offer is approved by a majority or a tie vote, and it happens.
The offer is rejected, and in the ensuing mutiny the proposer is forced to walk the plank, goes overboard, and dies. The next most senior pirate then makes a new offer to begin the system again.

All pirate live honorably by The Pirates Code, which is as follows:

Every pirate shall want to survive.
Every pirate shall want to maximize the treasure he receives.
Every pirate shall prefer to throw another scurvy scumbag overboard, if all other results would otherwise be equal.

Now unbeknown to most mainlanders, pirates are very rational folk, and will think through each decision very thoroughly. How much gold can Captain Jack keep for himself and how much must he give (and to which pirate) to ensure he maximizes his treasure and stays alive.

i don't totally understand the constraints, or they're quite abstract.

how exactly is an offer accepted or rejected?

The most senior pirate suggests a plan to the other pirates on how to divide the gold i.e.:

A (Jack) gets 50 pieces
B gets 30
C gets 10
D gets 8
E gets 2


After a period of logical contemplation, all of the pirates, including the one who proposed it, while personally (best self-interest) following the rules of The Code vote to accept/reject the plan.


If it is accepted (or a tie) by the vote, the gold is divided as per the plan and the pirates then do what ever pirates do with their gold.
If the plan is rejected by the vote, the most senior pirate who suggested the plan is forced to walk the plank, and meets his fate in Davey Jones' locker. The next most senior pirate devises a new plan, which is then voted on.


For instance, if in the plan above B,D,and E voted against A's proposal, Captain Jack (A) is disposed of, and B then devises a new plan which is put to the vote of B, C, D, and E. The process continues until there is an agreement.

I'll admit that I never solved this (I do know the solution), and you will be surprised at how much gold Captain Jack can keep for himself. I think there might be a community effort required here, assuming there is no cheating. The implementation of the code, is just a way to say that each pirate will follow the rules, while wanting to stay alive and keep as much gold to themselves as possible.

I'll leave it at that for now, and start posting hints later this week if it gets stalled. Anymore questions? Fire away!

Why, in the example above, did B, D and E reject the proposal, while (I assume) C accepted the proposal? What's in it for C?

Those numbers were chosen quickly just to make an example.

However, the reason to vote against the proposal would have to fit the Pirate Code, the rules of distribution, and seniorit. In the scenario mentioned, it could have been that D and E thought they should be getting more gold. It might have also been that B thought that if two other rejected the proposal, and he joined them, he would be the new Captain and get a chance for significantly more gold (or death). Perhaps C thought that getting 10 gold coins was better than getting what D or E was offered.

There are many possible distributions, most ending in death, but the best solution to this puzzle from Captain Jack's perspective, will probably amaze you.

I will offer one strategy (hint) right now.
What do you think would happen if Captain Jack offered to keep it all for himself? Right. He would die. That would leave B to make the next offer. Would this pattern continue to leave E with all the gold??

If you answered "yes" then you need to reread the puzzle.

Good luck (I hope I haven't said too much)!

Why, in the example above, did B, D and E reject the proposal, while (I assume) C accepted the proposal? What's in it for C?

yeah this is what i was trying to ask. it all seems too arbitrary to assign an integer value to the answer.

Here's my thoughts. If A's distribution gets voted down, then B can propose to take 99 and give 1 to E. E has to go along with this, because if not, then C could propose 99 for him and again 1 for E for which E has to accept. Otherwise, if A, B and C all die, then D can take it all, as E cannot sway the vote (ties go in favour of the proposer). So E can't afford to let A,B, and C to die.

So E should really accept the first reasonable offer he gets. So lets say that A gives E 1 coin. A needs just one more vote to pass (3/5). If B rejects he can walk away with 99 coins. (as stated before, E must go along with every offer or he gets nothing). So B can safely vote against A. C and D know what's going on, so A really needs to sway either C or D. If it is up to B, C and D get nothing. So A only needs to give C 1 coin, and C must vote ok.

So.. A's distribution is:

A - 98
B - 0
C - 1
D - 0
E - 1

To play it forward now.. B will reject - hoping for control. C realizing this must take his 1 coin and walk. Same for E.

If C or E reject, and A is killed, then B will work with E - give him 1 coin and if E vote yes, it will pass and C and D get nothing. If E votes no... then this repeats with C working with E and again offers 1 coin. So E can really do no better than 1 so he should accept the first offer from A and kill no one.

So E can really do no better than 1 so he should accept the first offer from A and kill no one.

you make some valid points, but the code says a pirate would like to kill another if all else is equal. so if he could get 1 from B or C, E would rather kill A or B.

Larry and others,
I'm sorry I haven't replied earlier. I think there might be an error (tiny) in your logic. I'm not sure right now, and unfortunately I don't have the time to think it out properly. I will get back to this thread as soon as I can.

cheers

Larry,

You are correct.

In your discussion what threw me off was your reasoning for why to offer C 1 coin, but D nothing, when you stated

"So B can safely vote against A. C and D know what's going on, so A really needs to sway either C or D. If it is up to B, C and D get nothing. So A only needs to give C 1 coin, and C must vote ok."

I was thinking that A could have given D 1 coin (instead of C) and gotten the same result. However this is flawed, as D knows that if A, B, C are killed then he gets everything. D would rather take 100 vs. 1.

Well done.
BTW, I discovered that there is a Wikipedia (http://en.wikipedia.org/wiki/Pirate_puzzle) entry on this puzzle. Hit it up if you want a full explanation. Apparently the puzzle can be extended logically to 200 pirates or more even without increasing the gold!