• 📛Maven@lemmy.sdf.org
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    9 months ago

    “Equal” has a slightly different meaning in fair division problems. It doesn’t mean “the exact same quantity of matter”, so not being able to judge exactly 1/3 of the apple doesn’t super matter (though your seed problem can be solved by cutting diagonally through the apples rather than along one side), but rather, that each person gets a portion they value at least as much as the others; maybe some people are willing to take a smaller piece if it means they have no seeds, maybe some people are going to peel their piece so they care more about having the largest internal volume, maybe some people plan to plant the seeds and so they actually value them, maybe some people only care about having the biggest piece.

    In practice, for three people this can take as few as 2 cuts or as many as 6; since there’s two apples and we can do 2 cuts with one stroke here, there is a fair division solution, but it only works if things go perfectly:

    The first person cuts the apples into 3 shares they think are of equal value (perhaps they hate apple cores, so they cut one side off both as above)

    The second person points out which share(s) they think are the best

    The third person takes the share they consider to be most valuable

    The second person takes the share they consider to be most valuable

    The first person takes the remaining share, which, since they cut, they must consider equal to the other two.

    If the second person doesn’t think at least two shares are of equal value, the problem becomes impossible to resolve without more knifeplay.

    • ArbitraryValue@sh.itjust.works
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      9 months ago

      I think that one person can decide where to cut the first apple and another person can independently decide where to cut the second apple, so the problem is actually a little easier. I posted my attempt at a solution as the top-level post. (My solution does assume that all three people have the same preferences.)

      • 📛Maven@lemmy.sdf.org
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        9 months ago

        Yeah, that would work assuming nobody has competing preferences, nobody feels jealousy, and especilaly as long as the third person has no preference for the first apple. It’s servicable for this riddle.