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Five pirates ........... 100 coins ................
24 Answers
Five pirates on an island have 100 coins to divide among themselves.
They divide the loot as follows: the senior pirate proposes a division and everybody votes on it. If at least half the pirates vote for it, then the motion is passed and the loot will be divided as suggested.
If not, they kill the senior pirate, and start over the same process: the senior pirate suggests, the pirates vote, and either the senior pirate is killed or the motion is passed as is.
Suppose you are the senior pirate. How would you propose to divide the coins? The pirates are all extremely intelligent, logical and greedy, and aren't suicidal or anything.
.... and no, the answer isn't 20 coins to each .....
They divide the loot as follows: the senior pirate proposes a division and everybody votes on it. If at least half the pirates vote for it, then the motion is passed and the loot will be divided as suggested.
If not, they kill the senior pirate, and start over the same process: the senior pirate suggests, the pirates vote, and either the senior pirate is killed or the motion is passed as is.
Suppose you are the senior pirate. How would you propose to divide the coins? The pirates are all extremely intelligent, logical and greedy, and aren't suicidal or anything.
.... and no, the answer isn't 20 coins to each .....
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one answer would be 34+33+33+0+0
You say they're all logical.
He wouldn't use the 20 each, as the logical thing to do would be for the others to reject this as they would get a minimum 25 each share from that point on. Nor would any of them want to take over as senior pirate after his demise as their life would be in jeopardy.
By offering 33 to each of two of them, he's ensuring they get a great deal, and since more than half would accept it the vote would be carried, he'd be better off and keep his life into the bargain...?
You say they're all logical.
He wouldn't use the 20 each, as the logical thing to do would be for the others to reject this as they would get a minimum 25 each share from that point on. Nor would any of them want to take over as senior pirate after his demise as their life would be in jeopardy.
By offering 33 to each of two of them, he's ensuring they get a great deal, and since more than half would accept it the vote would be carried, he'd be better off and keep his life into the bargain...?
The way to solve this is to work backwards .....
If the 3 most senior pirates have been killed and there's only 2 left - the most senior one knows that he can offer 100 for himself and 0 for the other - both vote and the notion is carried.
But before we get to the 2 pirate scenario, there would have been 3 pirates left. In this scenario, the most senior pirate offers to split the gold 99 for himself, nothing for the next senior pirate and 1 for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 2 pirates left, the lowest pirate will end up with nothing (2 pirate scenario), so all he needs to do is offer the lowest pirate 1 gold and he'll vote in favour.
Keep working backwards until you're at the point with 5 pirates ......
If the 3 most senior pirates have been killed and there's only 2 left - the most senior one knows that he can offer 100 for himself and 0 for the other - both vote and the notion is carried.
But before we get to the 2 pirate scenario, there would have been 3 pirates left. In this scenario, the most senior pirate offers to split the gold 99 for himself, nothing for the next senior pirate and 1 for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 2 pirates left, the lowest pirate will end up with nothing (2 pirate scenario), so all he needs to do is offer the lowest pirate 1 gold and he'll vote in favour.
Keep working backwards until you're at the point with 5 pirates ......
I think you're misunderstanding.
I'm working backwards to show how the problem should be solved.
When there are 5 pirates, the senior pirate offers to split the gold in which ever way he feels fit. Everyone votes (including the senior pirate) and if at least half of the pirates vote in favour then that's the end of it and the notion is carried. If less then half vote in favour, the senior pirate is killed and the next senior pirate suggests a split etc ...
I'm working backwards to show how the problem should be solved.
When there are 5 pirates, the senior pirate offers to split the gold in which ever way he feels fit. Everyone votes (including the senior pirate) and if at least half of the pirates vote in favour then that's the end of it and the notion is carried. If less then half vote in favour, the senior pirate is killed and the next senior pirate suggests a split etc ...
But under this proposed distibution couldn't the 4 lowest seniority pirates get together and agree to vote against and then split the loot 25,25, 25, 25.... or just the 2nd, 3rd and 4th might collaborate and agree to split it, say 34, 33, 33.
Or does that fail because the second knows that at the next step the 3rd, 4th and 5th might conspire and vote against o the second pirate is killed... and so on
Or does that fail because the second knows that at the next step the 3rd, 4th and 5th might conspire and vote against o the second pirate is killed... and so on
eltelioni - you are correct (at last lol :P )
Explanation:
Working backwards, If the 3 most senior pirates have been killed and there's only 2 left - the most senior one knows that he can offer 100 for himself and 0 for the other - both vote and the notion is carried.
But before we get to the 2 pirate scenario, there would have been 3 pirates left. In this scenario, the most senior pirate offers to split the gold 99 for himself, nothing for the next senior pirate and 1 for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 2 pirates left, the lowest pirate will end up with nothing (2 pirate scenario), so all he needs to do is offer the lowest pirate 1 gold and he'll vote in favour - otherwise he's end up with nothing.
But before we get to the 3 pirates scenario, there would have been 4 pirates left. In this scenario, the most senior pirate offers 99 gold for himself, nothing for the next senior pirate, 1 for the next senior pirate and nothing for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 3 pirates left, the 2nd lowest ranked pirate would end up with nothing (3 pirate scenario), so all he has to do is offer him 1 gold and he'll vote in favour and the notion will be carried, with 2 votes for and 2 votes against.
But before we get to the 4 pirate scenario, there would have been 5 pirates (starting point). The most senior pirate looks at what would happen if he was killed (4 pirate scenario) and works out that the lowest ranked pirate and the third lowest pirate would end up with nothing so all he needs to do is offer them 1 gold each and keep the other 98 pieces for himself.
Explanation:
Working backwards, If the 3 most senior pirates have been killed and there's only 2 left - the most senior one knows that he can offer 100 for himself and 0 for the other - both vote and the notion is carried.
But before we get to the 2 pirate scenario, there would have been 3 pirates left. In this scenario, the most senior pirate offers to split the gold 99 for himself, nothing for the next senior pirate and 1 for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 2 pirates left, the lowest pirate will end up with nothing (2 pirate scenario), so all he needs to do is offer the lowest pirate 1 gold and he'll vote in favour - otherwise he's end up with nothing.
But before we get to the 3 pirates scenario, there would have been 4 pirates left. In this scenario, the most senior pirate offers 99 gold for himself, nothing for the next senior pirate, 1 for the next senior pirate and nothing for the lowest pirate. Why ?? Well he knows that if he is killed and there are only 3 pirates left, the 2nd lowest ranked pirate would end up with nothing (3 pirate scenario), so all he has to do is offer him 1 gold and he'll vote in favour and the notion will be carried, with 2 votes for and 2 votes against.
But before we get to the 4 pirate scenario, there would have been 5 pirates (starting point). The most senior pirate looks at what would happen if he was killed (4 pirate scenario) and works out that the lowest ranked pirate and the third lowest pirate would end up with nothing so all he needs to do is offer them 1 gold each and keep the other 98 pieces for himself.
