Pirates !

Five pirates have 100 gold coins.They have to divide up the
loot.In order of seniority,each pirate proposes a distribution
of the loot.All the pirates vote,and if at least half accept the
proposal,the loot is divided as proposed.If not,the most senior
pirate is eliminated,and they start over again with the next
senior pirate.What solution does the most senior pirate
propose? Assume they are very intelligent,extremely greedy,
and interested in surviving.



The most senior pirate knows that he needs to get two other pirates
to vote for his solution in order for him not to be eliminated. So why
would any pirate vote for him? The next most senior pirate would
surely see it in his self-interest for the senior pirate to be eliminated.
Letís start simplifying. If there were only one pirate, there would
be no puzzle. The pirate would take all the loot, and no one
would complain.
Now consider the situation with two pirates. Same outcome. The
senior pirate takes all the loot, and the other pirate can’t do a thing
about it as the senior pirate’s vote represents half of the voters.
It gets more complicated for the senior pirate when there are
three pirates. Let’s number the pirates from least to most senior:
1, 2, and 3. With three pirates, pirate 3 has to convince at least one
other pirate to join his collation. Pirate 3 realizes that if his plan
is not adopted, he will be eliminated, and they will be left with two
pirates. All of them know what happens when there are two pirates:
pirate 2 takes all the loot himself and pirate 1 gets nothing. So pirate
3 proposes that he will take 99 gold coins and give 1 coin to pirate
1. If pirate 1 has any self-interest at all, he really has no choice. If
pirate 1 rejects the offer, he gets nothing. So pirate 3ís plan will
pass two to one over pirate 2ís objection.
With four pirates, an even number, the senior pirate needs just one
vote other than his own to impose his will. His question now is which
one of the other pirate’s votes can be exchanged for the fewest number
of coins. Pirate 2 recognizes that he is most vulnerable. Therefore, pirate
4 knows that if he gives pirate 2 anything at all, he will vote for it.
A rule is emerging here. In each case, the senor pirate should buy
only the votes he needs, and buy them as cheaply as possible. Apply
the rule to the five-pirate case. Pirate 5 needs two votes plus his own.
The goal is to toss a coin or two to pirate 1 and pirate 3, the two
pirates in the most vulnerable positions. Both will be empty-handed .

if the senior pirate is eliminated and four pirates remain. So pirate
5 offers one coin to pirate 3 and one coin to pirate 1. Pirates 2 and
4 get nothing.

Click here for detailed solution.

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