Math forum

Five pirates have come across a treasure of 1000 coins. According to pirate rules the pirate of highest rank must make a suggestion on how to divide the money. If a majority agree to his suggestion then it is to be followed by all the pirates. However, if the suggestion does not get a majority approval then the suggesting pirate is thrown overboard, after which time the remaining pirate of highest rank then makes a suggestion under the same rules. This process repeats, if necessary, until only the pirate of lowest rank is left, in which case he would get everything. Any pirate may suggest any distribution, rank does not guarantee getting more coins than anybody else. Assume that all pirates are infinitely greedy, infinitely logical, and infintely bloodthirsty, and that each pirate knows this to be true of every other pirate. The highest priority of each pirate is to get as much money for themselves as possible. The second highest priority is to throw overboard the other pirates. A pirate will vote to throw another one over even if they have no monetary gain by doing so, and even if it would cost them their own life, but would not if throwing them over would cost even 1 coin. How should the first pirate suggest dividing the money?