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Posts : 576 Join date : 2010-12-06
| Subject: A Logic Puzzle Fri Mar 15, 2013 2:03 am | |
| Teacher asks us this:5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme: The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen? My response:- Spoiler:
Let the pirates be called 1-5 with 1 being the oldest.
If only 5 is left, he will take all the money for himself. ('+' means agreement)
5: 100 +
If 4 and 5 are left, he only needs 1 vote to have his way, which is his own. He can distribute it as selfishly as he wants.
4: 100 + 5: 0
If 3, 4 and 5 are left, 3 needs a plan that gets either 4 or 5 to agree. Since 5's vote is cheapest he chooses to encourage 5.
3: 99 + 4: 0 5: 1 +
If 2, 3, 4 and 5 are left, 2 needs a plan that gets two out of 3, 4 and 5 to agree. 4 and 5's votes are cheapest, so he chooses to encourage them.
2: 97 + 3: 0 4: 1 + 5: 2 +
If all pirates are left, 1 needs a plan that gets two out of 2, 3, 4, 5 to agree. 3 and 4's votes are cheapest, so he chooses to encourage them.
1: 97 + 2: 0 3: 1 + 4: 2 + 5: 0
Alternatively, if they will end up looting more treasure, they may find it more optimal in the long run to have more crew to man the pirate ship, or raft, or whatever else they use to find treasure. Then this would happen:
5: 100 +
4: 100 + 5: 0
3: 100 + 4: 0 5: 0 +
2: 100 + 3: 0 4: 0 + 5: 0 +
1: 100 + 2: 0 3: 0 + 4: 0 + 5: 0 +
This is if the next oldest pirate doesn't mind looking selfish, and thinks 100 gold coins is more valuable than an extra pirate to get work done, otherwise they will just continue looting treasure more efficiently with 5 pirates and eventually, they will gather enough gold coins so that they don't think they need any more to make a living and make their way back to the ports to trade their loot. Then, they'll have a violent confrontation where 1 dies and gets all his loot stolen, and it is the fittest pirate that survives and takes all the gold for himself and he lives happily ever after.
Then again, maybe pirate 1 realizes that on the way back to the ports with a healthy amount of coins, there's nothing stopping the other pirates resolving the distribution issue with the best or most strategic swordsman getting all the loot. Then he might decide that even though he has most of the loot, he distributes the wealth in such a way that starts a conflict that gets everyone teaming up on the best swordsman, giving him a fighting chance at being the only one left once they get to the ports.
Or maybe one by one, they get exhausted to death from staying awake to guard their treasure, and all that's left is a floating raft of gold coins for other pirates to loot as treasure.
Enjoy! |
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sirchief Admin
Posts : 61 Join date : 2010-12-04 Age : 29 Location : No where and everywhere.
| Subject: Re: A Logic Puzzle Fri Mar 29, 2013 1:58 am | |
| Just keep voting no, right? |
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