There are five rational pirates (in strict decreasing order of seniority A, B, C, D and E) who found 100 gold coins.
In addition, the order of seniority is known in advance so each of them can accurately predict how the others might vote in any scenario.
(In the previous round, one might consider proposing B:99, C:0, D:0, E:1, as E knows it won't be possible to get more coins, if any, if E throws B overboard.
But, as each pirate is eager to throw the others overboard, E would prefer to kill B, to get the same amount of gold from C.) With this knowledge, A can count on C and E's support for the following allocation, which is the final solution: (Note: A:98, B:0, C:0, D:1, E:1 or other variants are not good enough, as D would rather throw A overboard to get the same amount of gold from B.)
Ian Stewart wrote about Steve Omohundro's extension to an arbitrary number of pirates in the May 1999 edition of Scientific American and described the rather intricate pattern that emerges in the solution.