perplexus.info :: Logic : A Pack of Prudent Pirates

A Pack of Prudent Pirates (Posted on 2002-08-19)

After a long season of plunder, a pirate team of five Prudent Pirates has amassed a booty of 500 golden coins. Before they part their ways, the five decide to divide the treasure.

They that they will each propose a division strategy in order of their seniority: first the oldest pirate will propose the strategy for the division of coins. All five will then vote on it, and if at least half vote "Yes", the strategy will be used to divide the coins. If the majority rejects the plan however, the oldest pirate will be killed, and the whole process will be repeated with the remaining pirates, with the second oldest proposing his strategy.

Since all the pirates are very prudent, each one will want to claim as many coins for himself without getting killed. Given this, how many coins will each of the pirates (5 - 1, with 5 being the oldest) get, and why? What strategy will the oldest pirate propose?

Submitted by levik

Rating: 4.3750 (16 votes)

Solution: (Hide)

Consider a situation with one pirate. He will simply claim all the coins for himself.
With two pirates (2 and 1), 2 will propose a "strategy" where he gets all the coins, vote for it, and thus will walk away with all the booty, leaving 1 with nothing.
If we have 3 pirates, 3 will need one more vote to avoid getting killed. He knows that if his strategy is not adopted, he will be killed, and the situation will become the equivalent of a 2-pirate setup, in which 1 will get nothing. Thus, if 3 offers 1 a single coin, 1 will accept, since he will lose even that by declining the strategy. Thus 3 would be able to abscond with 499 of the coins, having given 2 nothing.
With 4 pirates, 4 will try to bribe 2, who would gain nothing in the 3-pirate scenario. 2 will have to take 1 coin from 4, or else take nothing from 3. Thus 4 will give 2 one coin, and get his vote for a total of 50% of the vote, leaving 1 and 3 emptyhanded.
We come to the 5 pirate scenario. #5 needs two more votes to reach the 50% threshold. He can get them by offering 1 and 3 one coin each. (Remember, they get nothing if 4 proposes his strategy). They will accept so as not to lose everything, and 5 will go home with 498 coins, leaving 2 and 4 with nothing.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
reverse logic	Axorion	2007-11-20 03:58:40
How I'd solve it	Michael Rudolph	2007-05-10 17:25:20
Fascinating Puzzle, and it has problems.	Tonio Loewald	2005-09-09 01:16:38
re: I beg to differ	Popstar Dave	2003-10-30 07:20:24
re: I beg to differ	DJ	2003-05-01 09:39:52
re: I beg to differ	Jon	2003-04-30 08:37:35
I beg to differ	pleasance	2002-12-05 06:31:17
the real solution	crazy-kook	2002-09-06 16:35:46
re(4): Applied Psychology	friedlinguini	2002-08-20 05:07:55
re(3): Applied Psychology	Jim Lyon	2002-08-19 17:35:43
re(2): Applied Psychology	levik	2002-08-19 11:38:34
re: Applied Psychology	friedlinguini	2002-08-19 10:46:52
Applied Psychology	Jim Lyon	2002-08-19 10:06:13
re: dont understand..	friedlinguini	2002-08-19 05:36:08
dont understand..	Cheradenine	2002-08-19 05:27:04
Solution	friedlinguini	2002-08-19 03:45:12
try this..	Cheradenine	2002-08-19 03:34:42

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