You have five pirates, ranked from 5 to 1 in descending order. The highest ranked pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. And the process begins again. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)
Lets start easy, if we have only 2 pirates, pirate #2 will give all the money to pirate #1 so he can survive else pirate #1 would simply deny his proposal and take all the money. So pirate #2 is a starving pirate
If there are 3 pirates, pirate #3 would keep 99 coins give 1 coin to pirate #2 to win his vote else pirate #2 might ( 1 coin beats 0 coins) not vote for him even if he got nothing in the end, so we maximize pirate #2 profit and maximize pirate #3 profit, pirate #1 is the greedy and will settle for nothing but all the coins the problem is that only pirate #2 can give him the coins cause else he would never win.
If there are 4 pirates, pirate #4 has to give 99 coins to pirate #3 and 1 coin to pirate #2 else pirate #3 would not vote for him because he could do a better deal with him dead and pirate #2 would not vote because he would not get any money, so pirate #4 is a starving pirate
(Solution to puzzle above )
If there are 5 pirates, pirate #5 will have to conquer the starving pirate #4 and #2 ignoring the greedy #3 and #1, so he will just keep 98 coins to himself and give 1 to pirate #4 and 1 to pirate #2 maximizing their profit and his.