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Math Help - Pirate Treasure Riddle (Fun!)

  1. #1
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    Pirate Treasure Riddle (Fun!)

    Five pirates are trying to split up 1000 gold pieces. The rules are as follows:

    Pirate #5 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #4 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote.
    What is the most amount of gold pieces that pirate #5 can keep to himself, and what would his proposal be?

    The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.

    Assume that the pirates value their own life over gold, but would love to see their comrades die even if for no apparent reason. A tiebreaker means the pirate that made the proposal is thrown overboard.




    Now I solved the riddle, but I wanted to further develop it. For those of you that are interested, what would happen if there were an infinite amount of pirates? (Granted it can't be infinite as the gold runs out at some point)

    This is where I get stuck, i can't seem to figure the riddle out for an infinite amount of pirates.
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  3. #3
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    I would instead propose to say that the amount of gold any pirate could receive is zero.

    Not only would all the pirates kill each other over the gold [even if they DO value their lives over it, eventually the last two will defend themselves against each other], but you would have to have an infinite supply of gold to motivate calculation.

    Even if the infinite greed of pirates would justify an infinite number of them going after a pithy 1000 pieces of gold, they would never be done killing each other to dole out whatever infinitesimal sum of gold was agreed upon, so the answer would still be zero.



    Okay, that's all philosophical; fine, I'll do a little math.

    With only 1000 gold pieces to supply an infinite number of pirates, the equation becomes a limit.

    lim(S_n) = S

    but the actual equation would be expressed as

    lim(S_{\infty}) = 1000

    which would mean no single pirate would ever receive an appreciable amount of gold, even if one could separate each piece infinitely small and infinite number of times. The number tends to 0 so much that it may as well be zero.
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