Okay. I gave that pirate puzzle some more thought.
So let's go from the opposite end.
If only Pirate 5 is alive: he gets all the 100 bars - therefore he will only vote yes if he is given all of the 100 bars.
If Pirates 4 and 5 are alive: he will never win the majority with Pirate 5 since P5 can get a better deal in any case. Therefore Pirate 4 can maximally get 0 bars (in any case).
If Pirates 3, 4 and 5 are alive: P3 will take 50, P4 will take 50 (both will vote yes), and P5 will get 0.
, P3, P4 and P5 are alive: they need a majority vote therefore P2
, P3 and P4 must vote yes (we already know that P5 will always vote with a no) - P4 will vote no if he gets less than 50 bars, since he can get 50 bars if he lets P2
die and splits the bounty with P3. P3 will do the same. Therefore P2
would get 0, P3 - 50 and P4 - 50, P5 - 0 (P2
will get to keep his life).
, P3, P4 and P5 are alive: P1's priority is his life (requirement) and if he gets any goldbars, he'll be happy. P2
will be happy if he gets more than 0 bars. P3 or P4 will only vote yes if they get at least 50 bars. Therefore (if my assumptions are correct thus far):
P1 takes 48 bars and keeps his life. - He obviously votes yes.
gets 1 bar (he's better off than if P1 dies). He votes yes.
P3 gets 51 bars (he's better off than if P1 and P2
die). He votes yes.
P4 gets 0 bars. He votes no.
P5 gets 0 bars. He votes no.
We have 3 yes votes and 2 no votes - the majority acceps the solution, and P1 keeps his life.
Arniepie: any better now?