Six pirates and Gold Coin distribution puzzle
The five pirates mentioned previously(http://puzzlefry.com/puzzles/gold-coins-puzzle/)are joined by a sixth, then plunder a ship with only one gold coin.
After venting some of their frustration by killing all on board the ship, they now need to divvy up the one coin. They are so angry, they now value in priority order:
1. Their lives
2. Getting money
3. Seeing other pirates die.
So if given the choice between two outcomes, in which they get the same amount of money, they’d choose the outcome where they get to see more of the other pirates die.
How can the captain save his skin?
If pirates are taken to be 6 5 4 3 2 1…with the number corresponding to the seniority-
Let’s then start with 2 pirates and go further as done in the 5 pirate puzzle problem,
2 pirates- 1 and 2. Obviously 2 will keep the coin.
3 pirates- 3 will give it to 1 and 1 knows he won’t get anything if he says no as when 3 pirate is killed, case 2 reduces to case 1.
4 pirates- 4 gives it to 2. who (since is intelligent) would say yes to.
5 pirates- 5 obviously won’t give it to 2. But even if he gives the coin to 4,3 or 1. All of rest three will say no to it. So, this condition can’t be stabilised . So 5 would be killed no matter what and we’ll go back to case 3 with 4 pirates.
6 pirates- 6 knows 5 would always want him to live or else if 6 dies, 5 eventually dies and we go back to case 3 where 2 gets the coin. So 6 wont give it to 2 as he would be rich one way or the other. Thus, he will give the coin to any of 4,3 or 1 . Any of them would say yes.
So 6,5 and (4/3/1) would poll yes and captain saves himself.
The captain, in order to save his life would give the only coin to the next senior pirate (the potential next captain). Seeing this, the rest of the 4 members would plan to kill the pirate. Once the member is dead, the captain would then decide to hand over the coin to the next senior pirate, who also gets killed and it goes on until only 2 members are left. At this point, the junior most member wouldn’t dare kill the captain alone and hence, the captain not only saves his life, kills the other pirates but also gets the coin.
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