### distribute the gold coins

You have five pirates, ranked from 5 to 1 in descending order. The top 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. How should he allocate the gold in order to maximize his share but live to enjoy it?

1. A: 98 coins
B: 0 coins
C: 1 coin
D: 0 coins
E: 1 coin

try to solve it.

2. Assuming the pirates are very intelligent but equally greedy.

Lets solve this problem in the reverse direction.

Assume that there was only one pirate.. He would get to keep all the money.

Now assume there were two. In this case, the first will keep all the money.
Even though the second pirate will obviously oppose, fewer than half should disagree for the first to be killed which would mean less than one which is obviously not possible.

Now assume there were three pirates. The first pirate now cannot keep all the gold since two other will oppose him. So he can give some to the third to make him agree.
The third pirate has to agree to anything the first pirate offers as otherwise he would not be getting anything. The first pirate, being the greedy fellow, will offer him minimum which in this case is 1.

We can continue in this manner to solve the above problem in which the number of pirates is five. :)