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

Posted July 31, 2022 12:00 AM
Pathfinder Tags: challenge question

You yourself have joined Anne, Charles, Billy and John from last month's adventure.

Pirates are notoriously bloodthirsty and greedy, and this group pirates are all extremely logical. You have 100 gold coins to share as a group.

Here are the rules for splitting the booty:

The oldest pirate proposes a division of gold coins.

  • If at least half of the crew votes in favor, coins are split and everyone is happy
  • If the vote fails, the crew kills the oldest pirate and the next-oldest pirate makes a new proposal with the same rules.

The proposal process continues until one is accepted. Individuals are allowed to make voting blocs.

As the oldest pirate, how many gold coins do you walk away with? Please explain.

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#1

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

07/31/2022 11:00 AM

98 for yourself

1 for the youngest, and 1 for the third youngest.

If it gets down to two the second youngest takes all (his own vote is half the remaining crew). Not good for the youngest.

If it gets down to three the third youngest would take 99 whilst offering the youngest 1 to vote for that split. Not good for the second youngest.

If it gets down to four the second oldest would take 99 whilst offering the second youngest 1 to vote for the split. So its not in the interest of the youngest or third youngest to let it get that far.

So with five the oldest offers those two (the youngest and third youngest) 1 each to vote for the 98, 1, 1 split.

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#2
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Re: Pirates Divvy Up the Booty (August '22 Challenge Question)

07/31/2022 1:16 PM

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)."

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#8
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Re: Pirates Divvy Up the Booty (August '22 Challenge Question)

08/17/2022 5:56 PM

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

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

08/18/2022 4:50 AM

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.

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

08/25/2022 4:35 PM

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.

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#3

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

07/31/2022 2:01 PM

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.

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

07/31/2022 3:38 PM

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....

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

07/31/2022 6:03 PM

They were interviewing a pirate on TV. I know he was a pirate, he had a wooden leg, a hook, and an eye patch.

Reporter: What happened to your leg.

Pirate: Off Bermuda, a shark got me leg.

Reporter: And you hand? What happened to it?

Pirate: In the Bahamas, a barracuda got me hand.

Reporter: How about your eye?

Pirate: In Florida, a mosquito flew into me eye.

Reporter: A mosquito???

Pirate: Arrr...It was right after I got me hook...

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#6
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Re: Pirates Divvy Up the Booty (August '22 Challenge Question)

08/01/2022 5:28 AM

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

"Oh no! Which one?"

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

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#7
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Re: Pirates Divvy Up the Booty (August '22 Challenge Question)

08/01/2022 8:28 AM

What does a pirate drive on vacation?

An RRRRRV

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