5 Pirates and 100 Gold Coins | Puzzles for Interview - Interview Preparation PDF Download

Introduction

In this puzzle, we have 5 pirates - A, B, C, D, and E, who need to decide how to distribute 100 gold coins among them. The distribution process has some rules, and each pirate wants to survive and get the maximum number of coins possible.

Rules of Distribution

• The most senior pirate, A, proposes a distribution of coins.
• All pirates vote on whether to accept the distribution.
• The distribution is approved if at least half of the pirates agree (including the proposer).
• If the distribution is accepted, the coins are disbursed, and the game ends.
• If not, the proposer is thrown and dies, and the next most senior pirate makes a new proposal to begin the system again.
• In case of a tie vote, the proposer can have the casting vote.

Goal

Every pirate wants to survive, and given survival, each pirate wants to maximize the number of gold coins he receives. So, the question is, what is the maximum number of coins that pirate A might get

Solution

The answer is 98, which is not intuitive. Pirate A uses the following facts to get 98:

1. Consider the situation when A, B, and C die, and only D and E are left. In this case, E knows that he will not get anything because D is senior and will make a distribution of (100, 0). So E would be fine with anything greater than 0.
2. Consider the situation when A and B die, and C, D, and E are left. In this case, D knows that he will not get anything because C will make a distribution of (99, 0, 1), and E will vote in favor of C.
3. Consider the situation when A dies, and B, C, D, and E are left. To survive, B only needs to give 1 coin to D. So the distribution will be (99, 0, 1, 0).
Using the above facts, A knows that he just needs to give 1 coin to C and 1 coin to E to get them in favor. So the distribution will be (98, 0, 1, 0, 1).

Conclusion

In this puzzle, pirate A can get a maximum of 98 gold coins by using a clever distribution strategy that ensures his survival and gets the support of other pirates.