Six pirates and a gold coin

Puzzle Level :- Hard

PUZZLE

           Sixth pirate joined other five pirates mentioned in previous puzzle (http://solve-puzzles.blogspot.in/2016/10/greedy-pirates-and-gold-coins.html) and looted a passenger ship, unfortunately they got only one gold coin from ship

(All rules to mentioned in previous puzzle are applicable here to divide the loot)

They now need to divide 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 you(most experienced pirate) save yourself?

ANSWER

              By giving one coin to either 1st or 2nd or 4th Pirate  (Here you are 6th pirate and 1st pirate is least experienced one)

SOLUTION

             We can follow the similar approach mentioned in previous puzzle (http://solve-puzzles.blogspot.in/2016/10/greedy-pirates-and-gold-coins.html)

Until Case-4 there are no issues , we can follow the same logic.

     In Case-5 , Pirate-5 can't get 3 votes. 

Pirate-3 always votes against since he gets coin anyway in situation as case-4

Besides his vote pirate-5 can get one more vote by giving coin to either pirate-1 or 2 or 4.

He still need one more to save himself.  So in Case-5 always pirate-5 dies.

	Pirate-6	Pirate-5	Pirate-4	Pirate-3	Pirate-2	Pirate-1
Case-2					1	0
Case-3				0	0	1
Case-4			0	1	0	0
Case-5		0	1	0	0	0
Case-6	0	0	1	0	0	0

          In Case-6 ,  Pirate-6 gets his vote  and pirate-5 also votes him because he will die if Case-5 situation arises.  Pirate-3 votes against you even if you give coin to him because, anyway he gets coin if situation moves to case-4 

So You can get another vote by giving coin to either Pirate-1 or 2 or 4

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Greedy pirates and Gold coins

Puzzle Level - Hard

PUZZLE

       Five pirates looted 100 gold coins by raiding merchant ship and they want to divide these coins among themselves. These pirates are extremely intelligent ,cruel and greedy and each one want major share of booty.

       The pirates are ranked based on their experience. The most experienced pirate gets  chance to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. 

        If you are the most experienced pirate among them and got first chance to distribute coins, then what is the maximum number of coins you can keep without risking your life?

ANSWER

• Pirate-1(You)  ==> 98 Coins
• Pirate-2           ==> 0 Coins
• Pirate-3           ==> 1 Coin
• Pirate-4           ==> 0 Coins
• Pirate-5           ==> 1 Coin

SOLUTION

       First it looks impossible to get even single coin , because all other pirates can vote against your proposal to get even that single coin from you.

       Even if you not taken single coin also, they might vote against you since each one is such a greedy persons that they want all booty for themselves not giving anything to other pirates.

To solve this problem we need to follow the bottom to top approach.

i.e let's assume there is one pirate then obviously he gets the all the Coins

Now take case of 2-pirates

      First pirate distributes coins as 100-0.  Even second pirate votes against this proposal. proposal is accepted since first pirate got 50% votes since he votes for himself

Let's move on to 3-pirates case

           Apart from your vote, you need another vote to approve your proposal

The next experienced pirate(2nd pirate) will vote against you since he get 100 coins if you die (take look at 2-pirates case)

         You can give 1 gold coin to 3rd pirate and ask to vote in favour, he happily agrees because if he votes against you and move to 2-pirates case he gets no coins.

So you can distribute like 99--0--1 and you can get 99 coins without risking your life

Similarly for case of 4-Pirates

              Apart from you,  you need another vote to accept the proposal.

Next experienced pirate (i.e pirate-2) try to vote against you because he gets 99-coins if you die and situation moves to 3-Pirates case.

But Pirate-3 will favour you because he get 0-coins if situation moves to 3-Pirates case

    You can give 1-coin to 3rd pirate and get his vote.

So distributions is like 99-0-1-0 and you can enjoy 99 coins

Similarly this logic can be extended for 5 ,6,7 ... pirates

In our 5-Pirates case Distribution should be like  98-0-1-0-1. so that you can get maximum booty without risking your life.

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