Sequel : Story of Distribution of Loot

The five pirates mentioned previously 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.

How can the captain save his skin?

This is how he should save himself! 

 The Prequel of the story!

Captain's Life Saving Proposal in Sequel

First read the story of sequel!

Let's name all the pirates as Pirate 6,5,4,3,2,1 as per their seniority. Now, the captain should respond with the logic below to save his skin.

Let's consider the cases where there are different number of pirates left on the ship after getting rid of seniors one by one.

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CASE 1 : 2 Pirates

The captain i.e. Pirate 2 can keep coin with him & obviously vote for himself (1/2 = 50% vote) to approve the proposal.

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CASE 2: 3 Pirates.

The captain i.e. Pirate 3 offers coin to Pirate 1 to get his support (2/3 = 66%) on proposal. Since, Pirate 1 knows what is going to happen if Pirate 3 dies as crew reduced to 2 Pirates as in CASE 1.

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CASE 3: 4 Pirates.

The captain i.e. Pirate 4 offers coin to Pirate 2 thereby getting his support (2/4 =50% votes) to get approval on proposal. Again, here Pirate 2 is smart enough to agree on this proposal as he know what will happen if Pirate 4 is eliminated leaving behind 3 pirates on sheep as in CASE 3.

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CASE 4: 5 Pirates.
Now the captain i.e. Pirate 5 always will be in danger as he can give only coin to only 1 of remaining 4. So he can 'earn' only 1 vote in support of his proposal i.e. only 2/5 = 40% votes. Hence, there is no way his proposal get approval & he should be ready to die.

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CASE 5: 6 Pirates.

Here, Pirate 5 has to agree whatever captain i.e. Pirate 6 offers as if Pirate 6 dies the case reduces to CASE 4 where Pirate 5 can't save himself. However, if both Pirate 6 & Pirate 5 die, then CASE 3 comes into reality where Pirate 2 gets coin. So Pirate 2 would never agree on proposal offered by Pirate 6.

However, if Pirate 6 offers coin to Pirate 4 then he would take it happily as he knows that what will happen of both Pirate 6 & 5 are killed as CASE 3 comes into picture where he has to give coin to Pirate 2 to save himself.

If Pirate 6 offers coin to Pirate 3 as well & earn his support as Pirate 3 also knows what is going to be the case of both 6 & hence 5 get eliminated. The case will be reduced to 4 Pirates as in CASE 3 where Pirate 4 will offer coin to Pirate 2.

The Pirate 6 even choose Pirate 1 to offer coin. Again, Pirate 1 smart to think that what will be the case if 6 & hence 5 are killed. It will be the scenario as in CASE 3 where Pirate 4 offers coin to Pirate 2.

In short, the Pirate 6 will always get support from Pirate 5 always in any case & any one from Pirate 4/3/1 if he offers coin to any one of these three. 

That's how he will get support of 50% (3/6) group to get approval for his proposal thereby saving his own life on approval of proposal offered.

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Story of Distiribution of 100 Coins Loot

Five ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go “Aye”, the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.

If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?

He can take away 98 coins! How? Read here! 

The Captain's Undeniable Proposal

What was the situation?  

He can keep 98 coins! Surprised? Read how.

Let's number 5 pirates as Pirate 5, Pirate 4.....Pirate 1 as per their descending order of seniority.

Pirate 5 keeps 98 coins with him and gives 1 coin each to Pirate 3 and Pirate 1.

Now Pirate 5 i.e Captain explains his decision -

CASE 1:

 If there were only 2 pirates then Pirate 2 would have taken all 100 coins after obtaining his own vote which accounts to 50% votes (50 % of 2 = 1).

CASE 2: 

 In case of 3 pirates, the Pirate 3 would have offered 1 coin to Pirate 1 & would have kept 99 coins with him. Now Pirate 1 wouldn't have any option other than agreeing on deal with Pirate 3. That's because if he doesn't agree then Pirate 3 would be eliminated & all coins would be with Pirate 2 as explained in above (case 1) of only 2 pirates. So votes of Pirate 1 and Pirate 3 which account to 66% (2 out of 3) votes of group locks this deal and Pirate 2 would be left without any coin.

CASE 3: 

 Now in case of 4 pirates, Pirate 4 would offer coin to Pirate 2 & would keep 99 coins with him. Now, Pirate 2 know what happens if Pirate 4 gets eliminated. Pirate 3 would offer 1 coin to Pirate 1 & will take away 99 coins. So Pirate 2 would definitely accept this deal. That's how votes of Pirate 4 and Pirate 2 makes 50% (2 out of 4) votes of group to pass the proposal. Pirate 3 and Pirate 1 can't do anything in this case.

By now, Pirate 3 and Pirate 1 realizes what happens of Pirate 5 gets eliminated. They won't be getting any coin if Pirate 4 becomes captain as explained above (case 3). So they have no option other than to vote for the proposal of Pirate 5. 

This way, Pirate 5, Pirate 3 and Pirate 1 (3/5 = 60% of crew) agree on proposal of Pirate 5 where he takes away 98 coins with 1 coin each to Pirate 3 and Pirate 1.