## Saturday, February 2, 2008

### Pirates!

$500$ pirates have just stolen a treasure of $100$ gold pieces, and they decide to share it in the following way: starting from the $500$th pirate, and going on with the $499$th, $498$th, and so on, each pirate proposes a way to share the gold (for instance, he says: "the pirate $1$ will receive $13$ gold pieces, the $2$nd $17$ gold pieces, ..."). The proposal is voted, and if it passes with at least $50\%$ votes (including the pirate that is making the proposal) it is accepted and the gold is shared. If the proposal is not accepted, the pirate is shot and the next pirate is going to make a new proposal, and so on. How many pirates will survive?
Note that each pirate only trusts himself, and their main purposes are, in order:
$\mathbf{\alpha}$) survive,
$\mathbf{\beta}$) gain as much gold as possible,
$\mathbf{\gamma}$) kill the highest number of other pirates.
Have fun! :-)

Update (17/02/2008): Solution posted! (show solution)