Five Pirates

All_Is_Number · 2006-07-31 15:36:06

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?

Zach · 2006-07-31 23:00:25

30, 25, 25, 25, 20

MathsIsFun · 2006-08-01 00:33:50

40, 30, 30, 0, 0

All_Is_Number · 2006-08-01 02:17:18

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.

Patrick · 2006-08-01 02:39:25

40, 0, 0, 30, 30

All_Is_Number · 2006-08-01 03:32:52

Patrick wrote:

40, 0, 0, 30, 30

Please try again.

All_Is_Number · 2006-08-01 04:14:03

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.

tt · 2006-08-01 17:58:44

99, 0, 1, 0, 0

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

All_Is_Number · 2006-08-02 00:00:44

tt wrote:

99, 0, 1, 0, 0

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

Devantè · 2006-08-02 00:39:56

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.

All_Is_Number · 2006-08-02 01:06:53

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

tt · 2006-08-02 07:07:51

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)

Trob · 2007-11-30 03:27:38

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

mathsyperson · 2007-11-30 04:06:36

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

JohnnyReinB · 2007-11-30 15:00:22

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

Math Is Fun Forum

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

Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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

Re: Five Pirates

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