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#1 2006-07-31 15:36:06

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Five Pirates

Five pirates return from a mission of murder plunder on the high seas. They have 100 gold pieces that need to be divided amongst themselves.

The pirates, conveniently named A, B, C, D, and E have a seniority order. Even more conveniently, A is at the top of the list, followed by B, then C, D, and E.

The highest seniority pirate gets to propose how the gold is split, and then the whole group votes to approve of the split or not. The high seniority pirate gets 1.5 votes, and the other pirates get one vote. If the proposed split is approved, the gold is split up accordingly. If the proposed split is not approved, the high seniority pirate is killed by the other pirates, and the   highest seniority of the remaining pirates get to propose the split, with the same rules.

All the pirates are rational.

How does Pirate A propose to split the 100 gold pieces to get the maximum amount for himself, while ensuring the proposal will be approved by vote?


You can shear a sheep many times but skin him only once.

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#2 2006-07-31 23:00:25

Zach
Member
Registered: 2005-03-23
Posts: 2,075

Re: Five Pirates

30, 25, 25, 25, 20


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#3 2006-08-01 00:33:50

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,713

Re: Five Pirates

40, 30, 30, 0, 0


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#4 2006-08-01 02:17:18

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Five Pirates

Zach, MathIsFun, those answers are incorrect; please try again.

(I am interested in the logic you used to obtain those answers, though.)

The correct answer is rather non-intuitive.


You can shear a sheep many times but skin him only once.

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#5 2006-08-01 02:39:25

Patrick
Real Member
Registered: 2006-02-24
Posts: 1,005

Re: Five Pirates

40, 0, 0, 30, 30


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#6 2006-08-01 03:32:52

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Five Pirates

Patrick wrote:

40, 0, 0, 30, 30

Please try again. smile


You can shear a sheep many times but skin him only once.

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#7 2006-08-01 04:14:03

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Five Pirates

I could hide a hint or two if people wanted. The solution is VERY counter-intuitive. Had I not read the logic behind the solution, I never would have believed it.


You can shear a sheep many times but skin him only once.

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#8 2006-08-01 17:58:44

tt
Member
Registered: 2005-07-03
Posts: 32

Re: Five Pirates

99, 0, 1, 0, 0

Last edited by tt (2006-08-01 18:02:34)

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#9 2006-08-02 00:00:44

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Five Pirates

tt wrote:

99, 0, 1, 0, 0

Close. Very close. I think such a split would lose the vote.


You can shear a sheep many times but skin him only once.

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#10 2006-08-02 00:39:56

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Five Pirates

The captain will take 98 coins, and will give one coin to the third most senior pirate and another coin to the most junior pirate.

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. 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, 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 and 3 had obviously better vote for the captain, or they face choosing nothing or risking a horrible death.

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#11 2006-08-02 01:06:53

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Five Pirates

Devanté wrote:

The captain will take 98 coins, and will give one coin to the third most senior pirate and another coin to the most junior pirate.

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. 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, 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 and 3 had obviously better vote for the captain, or they face choosing nothing or risking a horrible death.

Correct answer and logic. excellent


You can shear a sheep many times but skin him only once.

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#12 2006-08-02 07:07:51

tt
Member
Registered: 2005-07-03
Posts: 32

Re: Five Pirates

98, 0, 1, 0, 1
Well, too late to correct my silly mistake! Devante got it right.

Last edited by tt (2006-08-02 07:11:49)

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#13 2007-11-30 03:27:38

Trob
Member
Registered: 2007-11-30
Posts: 0

Re: Five Pirates

has anyone else notices the solution to this puzzle on the main
website is flawed?

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#14 2007-11-30 04:06:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Five Pirates

I didn't even know this puzzle was on the main website.
Could you link it here?


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It wanted to be normal.

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#15 2007-11-30 15:00:22

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

Re: Five Pirates

Well, it is : www.mathsisfun.com/puzzles/5-pirates.html


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