Puzzle: Pirates and gold

9223 views

Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their ages. Pirate 5 is 50 years old, Pirate 4 is 49, and so on down to Pirate 1. To divide up the loot, they agree on the following:
The most senior pirate will propose a distribution of the booty. All pirates will then vote, including the most senior pirate, and if at least 50% of the pirates on board accept the proposal, the gold is divided as proposed. If not, the most senior pirate is murdered. Then the process starts over with the next most senior pirate until a plan is approved.
All Pirates are equally intelligent and selfish. Their preference is first to remain alive, and next to get as much gold as possible and finally, if given a choice between otherwise equal outcomes, to have fewer pirates on the boat.
Assume you are the senior most pirate in the group. Come up with a plan that maximizes your gold, and others will accept. How will you divide the coins?

3 Vote Up   |   Post Answer

By  Roshan





Shaan Shaan   10 years ago

If there were only 2 pirates, pirate 1 being the most senior, he would just vote for himself so he's obviously going to keep all the money for himself.

Now if there are 3 pirates:
pirate 1 already knows what happens when there are 2 pirates (pirate 1 takes all the money himself and gives nothing to pirate 2). So pirate 1 proposes that he will take 99 gold coins and give 1 coin to pirate 3. So, pirate 3 says, well, 1 is better than none, and since i know if i don't vote for pirate 1, I get nothing, I should vote for this plan.

If u work out on this futher considering the case for 4 pirates and then finally for 5 pirates u will reach this solution:
Pirate 1 = 1
Pirate 2 = 0
Pirate 3 = 1
Pirate 4 = 0
Pirate 5(me) = 98

Reply    7 Vote Up   6 Vote Up


Gagan Kshirsagar Gagan Kshirsagar   10 years ago

If there were only 2 pirates, pirate 2 being the most senior, he would just vote for himself so he's obviously going to keep all the money for himself.
so the distribution will be:
p1 = 0
p2 = 100
Now if there are 3 pirates:
pirate 1 already knows what happens when there are 2 pirates (pirate 2 takes all the money himself and gives nothing to pirate 1). So pirate 3 (senior most) proposes that he will take 99 gold coins and give 1 coin to pirate 1. So, pirate 1 says, well, 1 is better than none, and since i know if i don't vote for pirate 3, I get nothing, I should vote for this plan.
p1= 1
p2= 0
p3 = 99

now in next case, P4 (senior most) needs one more vote other than his own, so he will propose to one coin to pirate 2, as pirates 2 will get one (better than the above case) he will vote for pirate 4, so equation will be:
p1 = 0
p2 = 1
p3 = 0
p4 = 99

For the last case, Senior most pirate need to get two more votes, so he will propose to give 1 coin each to pirate 1 and pirate 3, which is better than the case if they don't vote (as they will get nothing so they will vote for pirate 5, so the equation will be:
Pirate 1 = 1
Pirate 2 = 0
Pirate 3 = 1
Pirate 4 = 0
Pirate 5(me) = 98

Reply    1 Vote Up   0 Vote Up