Brain Teasers | Screwy Pirates

 Question: 

Source: Google

Five pirates looted a chest full of 100 gold coins. Being a bunch of democratic pirates, they agree on the following method to divide the loot: The most senior pirate will propose a distribution of the coins. All pirates. including the most senior pirate, who will then vote. If at least 50% of the pirates (3 pirates in this case) accept the proposal, the gold is divided as proposed. If not, the most senior pirate will be fed to the shark and the process starts over with the next most senior pirate... The process is repeated until a plan is approved. You can assume that all pirates are perfectly rational: they want to stay alive first and to get as much gold as the possible second. Finally, being blood-thirsty pirates, they want to have fewer pirates on the boat if given a choice between otherwise equal outcomes. How will the gold coins be divided in the end?  

 

Solution: 

 

Since the solution for 1 pirate would be trivial let me start with 2 pirates 

Let's assume pirate no 2 is the senior pirate 

The senior pirate(pirate no 2) would claim all the coins as he will always get 50% votes. 

 

Let's add one more senior pirate 3. Pirate 3 requires 2 votes(his own vote and pirate 1) in total. 

If he offers pirate 1 nothing, then pirate 1 will not vote for him. But if he gets voted down then pirate 1 will get nothing. 

So he will offer the pirate 1 one gold coin and get his vote and keep the remaining 99 gold coins with himself. In this way, he will receive 2 votes. 

 

When pirate 4 is added, he knows that if he gets voted down pirate 2 will not receive anything. So pirate 4 will offer pirate 2 one gold coin and keep the remaining 99 gold coins with himself. In this way, he will get 50% of the votes(1 from himself and one from pirate 2). 

 

Now coming to the 5 pirate cases. Pirate 5(the most senior pirate) knows that if his plan gets voted down both pirate 1 and pirate 3 will receive nothing. So he will offer pirate 1 and pirate 3 one gold coin each and keep the remaining 98 coins with himself. Thus he gets 3 votes for himself (pirate 1, pirate 3 and himself). 

 

In general: 

For the 2n+1 pirate case (where n= 49) the most senior pirate will offer 1,3,5...2n-1 each coin and keep the rest for himself. 


https://medium.com/@priyankadalmia2009/brain-teasers-screwy-pirates-c9709d1f7b43



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