TADM2E 2.52

This problem is a famous game-theoretical scenario called the pirate game (http://en.wikipedia.org/wiki/Pirate_game). Assume the senior pirate gets to vote.

Where there is only 1 indivisible dollar: 2 pirates - The senior pirate gets it. 3+ pirates - The least senior pirate gets it.

In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die

Another Answer : Assume senior pirate also gets to vote.

Based on pirates inherent tendency -

a. They want to kill other pirates even if it does not affect their outcome -

2 pirates - Senior gets it.

3 pirates - Smallest gets it, because 2nd pirate will vote for kill. So, in order to live he must give dollar to smallest.

4 pirates - 2nd or 3rd smallest will get with 50% chances, because 1st will vote for kill irrespective of weather he gets the dollar or not. And 2nd or 3rd will vote for 4th if they get the dollar.

5 pirates - He is certainly going to die, irrespective of his proposal. Whosoever he chooses other three/four will vote against him.

6 pirates - Here 5th will vote for 6th irrespective of weather he gets the dollar, otherwise he is going to die. And 1st will vote for 6th if he gets the dollar, because if he doesn't he doesn't get the dollar(because the case will reduce to 4 pirates).thus, 6th will live and 1st will get the coin.

b. They want other pirate to live if it doesn't affect their outcome -

Senior most pirate always gets the coin.