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: Pirate's Problem  ( 4122 )
« : May 13, 2007, 05:47:34 PM From Shrinidhi»



Pirate's Problem


Aboard the ship there are 5 pirates, numbered 1 to 5. Higher number indicates higher priority. A treasure chest containing 100 gold coins has been found. According to the rules of the pirate world, the highest priority pirate decides how the treasure is to be split. Then all the pirates, including himself, vote on the decision. If a majority vote against the split then Pirate #5 is thrown overboard, and the next in command takes over. The process is repeated until there is no majority voting against the way the split is decided.

The votes of the pirates are governed by the following factors:
- All the pirates are very mean. Each one would like to have the biggest share no matter what.
- A pirate values his life before money.
- A pirate will vote against any plan, unless that would cause him to be killed or to get less gold.
- If there are equal number of votes for and against a pirate, the pirate stays.

How should Pirate #5 divide the treasure?

 
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« #1 : May 25, 2007, 11:58:53 PM From spazinvader»

Pirate 5(Highest priority)=49
Pirate 4(Next to 5)=25
Pirate 3(Next to 4)=13
Pirate 2(Next to 3)=6
Pirate 1(Least priority)=7
I dont exactly know the answer.But is it right?Please reply to this.
« #2 : May 26, 2007, 12:12:25 AM From Poonam»

Pirates are very mean and hence they will try to keep even the last penny with themselves.

However lets solve this problem backwards.
Suppose there was only one pirate. He will keep all the 100 coins with himself.

Suppose there were two. Pirate 2 (higher priority) will keep all the coins with himself since he will vote for himself. Now pirate 1 will vote against pirate 2. Still the Pirate 1 will have all the money since there isn't any majority vote against him.

Priority:   1      2
Coins:     0      100

Suppose there were three. Pirate 3 (higher priority) wants majority. So he has to woo one of the 2 pirates. He will give one coin to Pirate 1. Pirate 1 will be happy, since he knows that if he votes against pirate 3 he will end up with no coins (above case). Hence he will vote for pirate 3. Pirate 3, now, has majority. He need not give anything to Pirate 2.

Priority:   1      2        3
Coins:     1      0       99

Suppose there were 4. Pirate 4 (higher priority) wants one vote for him apart from his vote for no majority against him. So he has to woo one of the 3 pirates. He will give one coin to Pirate 2. Pirate 2 will be happy, since he knows that if he votes against pirate 4 he will end up with no coins (previous case). Pirate 4 with Pirate 2 on his side need not give anything to the rest.

Priority:   1      2     3      4
Coins:     0      1     0      99

Now contining this series, in case of 5 pirates, Pirate 5 will have to just see who he needs to benifit. He has to just please those who will suffer otherwise in case of his exit. Obviously, Pirate 1 and Pirate 3 are right candidates as they will get nothing if he dies. He just have to give them one coin and Pirate 5 not only survives but rejoices.

Priority:   1      2    3      4     5
Coins:     1      0    1      0     98

 

« #3 : May 27, 2007, 05:48:39 PM From Ramesh»

Just thinking ...

Hey Guru,
whenever a high priority pirate divides the coin and gives only 1 coin to a pirate from which he seeks a "for vote".Why is it assumed that he will give a for vote for only 1 coin and would not give an against vote since the division is not equal. Are low priority pirates have fear of high priority pirates ::)

expecting an explanation..... ???
« #4 : May 27, 2007, 07:04:22 PM From rohit»

right guru :)
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