Pirates Divvy Up the Booty (August '22 Challenge Question)

If you are brave you could keep all 100 gold coins for yourself. Explain to the youngest and the third youngest that, yes, they could vote against this proposal and kill you, but then it would be down to four pirates and under the inevitable proposal of the second oldest they would both still get zero coins, so there would be nothing to gain by killing you. As you state, "It's not in the interest of the youngest or third youngest to let it get that far (down to four)."

If the second to youngest joined the youngest and said they want more say 19 each or just less than a 5th of it each and the fourth eldest would agree if he could get some too. Would this change the deal

The fourth eldest is the same as the second youngest. So I assume you meant third eldest.

The problem is that these are pirates: although they are forced to follow the rules laid down by the puzzle master; they can easily renege on any agreement they have made in any previous round of negotiation. So even if the youngest three vote down the first proposal they are then in the hands of the second eldest and any one of themselves.

This is amazing logical work! Well done. This old scurvy dog walks away with 98 doubloons.

The easiest way to identify this is to work the problem backwards. Pirate #1, the youngest of them, gets 100 coins. But to get to a single pirate, what needs to happen beforehand?

At some point prior you need to have 2 pirates, the older pirate (#2) would propose he gets all the coins and represents the voting power to do that. What stands in his way?

Pirate #3 could propose a splitting the loot into thirds, but the other two pirates would certainly want more and could vote to increase their shares by killing him. Or he could propose he gets all the coins, but he needs at least one other pirate to vote his way. It would make sense to offer this to pirate #1, as he could end up with nothing in a two pirate vote.

In a four pirate vote, pirate #4 should propose to buy pirate 1 or pirate 2's vote; whoever is the lowest bidder, in what a logical pirate would see is literally a one-or-none situation.

The trend applies to 5 pirates. Pirate #5 should buy the cooperation of the other odd-numbered pirates, as they are either left with 1 gold coin or none at all.

Everybody but the oldest gains if the vote fails and the oldest one is killed. If the oldest is killed, there are 100 coins to be divided 4 ways. The same logic applies when there are only four left, etc.

The youngest 3 will vote no the first time, the youngest 2 will vote no the second time and 3rd time. On the last time, the youngest will vote no, kill the next youngest and get all 100 coins.

So, the oldest might as well give all 100 coins to the youngest and save 4 lives, including his own.

The oldest pirate proposes to give each buccaneer 2 gold coins, and invest the rest so that they will have a payout of 2 gold coins every time they hit a port in perpetuity, enough for wenches and rum for ever....and then hatches a plan to knock them off in an accidental sort of way, one by one.....over time the split is then divided between fewer and fewer number of mates increasing the payout to those that survive each time, so no complaints...the last two need to be eliminated together lest the last remaining mate gets wise....Long John Silver taught me that....

"Aaaaarrrggghh! A shark just bit off my leg."

"Oh no! Which one?"

"How do I know........ These sharks all look the same to me?"

The second oldest pirate sees what happened to the oldest one,and knew,logically, that he could be next..so he explained it to the other pirates.

The rest of the pirates,also being logical, turned on one another, killed everyone older than himself.The original 2nd oldest had stood back and watched the mayhem unfold.He was the most logical, fastest,meanest,greediest,strongest and the most bloodthirsty, experienced,and skilled at killing so he killed all survivors and took all the gold for himself.It was a ballet of bloodshed.He was ankle deep in blood when the fighting was over,and he was the only one left alive.

He threw all of the bodies over the side to the sharks,and he celebrated by having a slug of brandy that had been taken from a French ship.

He lived well and prospered till he challenged a one legged pirate with a parrot on his shoulder.He lost the fight,and Long John had enough money to quit pirating and open up a chain of seafood restaurants which are still popular today.

Moral of the story:Never bring a sword to a gunfight.