Five pirates ........... 100 coins ................

[Gizmonster]

Five pirates on an island have 100 coins to divide among themselves.
They divide the loot as follows: the senior pirate proposes a division and everybody votes on it. If at least half the pirates vote for it, then the motion is passed and the loot will be divided as suggested.
If not, they kill the senior pirate, and start over the same process: the senior pirate suggests, the pirates vote, and either the senior pirate is killed or the motion is passed as is.

Suppose you are the senior pirate. How would you propose to divide the coins? The pirates are all extremely intelligent, logical and greedy, and aren't suicidal or anything.

.... and no, the answer isn't 20 coins to each .....

[Bodica]

We will label the pirates A, B, C, D and E, The solution is best explained by looking at what each pirate would propose, starting with the dogsbody, E.

D's and E's Proposals

E never actually gets to make a proposal, although he would award every single gold piece to himself if he had the chance. The problem is that D's proposal comes first, and D will always win this ballot as he holds the casting vote. Therefore, if pirates A, B and C were to be cast overboard, D would be able to propose the following and win:

D - 100
E - 0
C's Proposal

Being a reasonably intelligent pirate, C knows that if he gets to make a proposal through both A and B being thrown overboard, he would only have to offer E better than nothing to win the vote. Offering D better than nothing wouldn't work, as D knows that if C goes overboard, D would get the whole stash. C could therefore propose the following and win:

C - 99
D - 0
E - 1
B's Proposal

Also being reasonably intelligent, B has got out a small piece of paper and worked out all the above. To win the vote, all B has to do is to offer D more than he would get if C's proposal was adopted. Although D would be able to take the lot if A, B and C were to go overboard, D realises that in reality the game would never get that far, as C and E would gang together to make C's proposal win, as stated above. B can therefore offer D one more coin than he would get if B were thrown overboard, thus allowing B to win with the casting vote. The winning proposal would therefore be:

B - 99
C - 0
D - 1
E - 0
A's Proposal

At this point, A looks over at B scribbling on his small piece of paper and, with a smug grin, makes the following proposal:

A - 98
B - 0
C - 1
D - 0
E - 1
Knowing that, if given the chance, D will help B win B'

[Bodica]

Knowing that, if given the chance, D will help B win B's proposal and leave the others with nothing, C and E happily vote for A's proposal, thus allowing A to walk off with the fortune after a democratic vote. Brilliant, isn't it?

[keithlbw]

a = 32
b = 32
c =32
d =2
e =2

[Gizmonster]

The answer has already been posted:

A: 98
B: 0
C:1
D:0
E:1

With all the other pirates being logical and not suicidal, C and E will vote in favour of this and you'll end up managing to keep 98 for yourself.