Thursday, April 19, 2007

Greedy Pirates

Five greedy pirates looted 100 gold coins and now to be divided amongst them. Having different seniorities, the most senior pirate proposes a way out. They will cast a vote and now if at least 50% accepts the proposal, the loot is divided as proposed. Or else the most senior pirate's head is chopped off, and they start again with the next senior pirate. What should be the idea in the mind of seniormost pirate to get the max coins?
Important : Given that they are intelligent enough to think about it :)

Solution
Lets minimize the problem for 3 pirates. To make it easily understandible for 5 pirate situation i assume they are C, D, E in order of decreasing seniority.
Pirate C needs to convince any of the other. So he contacts juniormost pirate E and tells him that if he dont vote him, then i (C) will die. And then in the next round D will vote himself and he will get all the money. In that case you dont get anything. Pirate C offers pirate E 1 gold coin to vote for him. He has no choice but to accept so as to have at least something.

Now 4 pirate situation. B, C, D, E in order of decreasing seniority.
Pirate B sees that if he dies the worst pirate will be pirate D (as it will be a 3 pirate situation with C,D,E). So he contact D and offer him 1 coin and explain him if he dies C and E will get the coins. So he comes to his side and votes for him.

Now our situation A, B, C, D, E in order of decreasing seniority.
Pirate A , sees that if he dies the worst off people will be pirate C and E(as with the situation in BCDE). So he contracts both of them with 1 gold coin offer for each. And takes away 98 gold coins