# What is the maximum number of coins that pirate A might get?

262 views

There are 5 pirates, they must decide how to distribute 100 gold coins among them. The pirates have seniority levels, the senior-most is A, then B, then C, then D, and finally the junior-most is E.

Rules of distribution are:

1. The most senior pirate proposes a distribution of coins.
2. All pirates vote on whether to accept the distribution.
3. If the distribution is accepted, the coins are disbursed and the game ends.
4. If not, the proposer is thrown and dies, and the next most senior pirate makes a new proposal to begin the system again.
5. In case of a tie vote the proposer can has the casting vote.

Rules every pirates follows:

1. Every pirate wants to survive.
2. Given survival, each pirate wants to maximize the number of gold coins he receives.

What is the maximum number of coins that pirate A might get?

posted Jul 24, 2017

The answer is 98 which is not intuitive.

A uses below facts to get 98.

1. Consider the situation when A, B and C die, only D and E are left. E knows that he will not get anything (D is senior and will make a distribution of (100, 0). So E would be find with anything greater than 0.
2. Consider the situation when A and B die, C, D and E are left. D knows that he will not get anything (C will make a distribution of (99, 0, 1)and E will vote in favor of C).
3. Consider the situation when A dies. B, C, D and E are left. To survive, B only needs to give 1 coin to D. So distribution is (99, 0, 1, 0)
4. Similarly A knows about point 3, so he just needs to give 1 coin to C and 1 coin to E to get them in favor. So distribution is (98, 0, 1, 0, 1).
SO, The idea is based on the fact that what B will distribute if A dies (B would always want A to die). If A gives more coins to 2 people than B would have given, A wins.

Similar Puzzles

You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

+1 vote

5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme:

The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it.

If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?

+1 vote

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold.
What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?