this post was submitted on 04 Feb 2024
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What's bothering me is, mathematically that is the answer, but practically the apple is a non uniform shape so you cant really determine where a third of the apple truly is and it has seeds in the middle meaning two of the kieces will have seeds one the one getting the two cut off pieces won't so its not truly shared equally.
Cut the leaf off with the one slice then each person just eats a third of each apple with their teeth.
If you sliced vertically (still considering thirds) you would get more fair distribution of fruit-meat vs seeds
Yeah. It's a bad question. Why only one stroke? If you cut the apples into cubes and doled them out equally it'd be a much better and more equal experience. The problem presented is a lie, it's just a geometry puzzle.
What bothers me is how dangerous that procedure would be
"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:
If the second person doesn't think at least two shares are of equal value, the problem becomes impossible to resolve without more knifeplay.
If anyone is interested, there's this video by Up and Atom that neatly shows the complexity.
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.)
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.
I’m sure with some calibrating you could just cut off 1/3 of the edible portion. While the core-containing portions would be heavier, the edible apple weight would be the same. It wouldn’t be easy to do first try though