In one slice, cut a third off of each apple, and you’re left with 3 portions of 2/3 an apple each
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.
“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.
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.)
Or cut both of them in half and throw out half an apple.
Didn’t say all of the apple.
Line the apples up next to each other, I guess. Sort of like taking a single slice through multiple carrots on the cutting board at once. Harder to do with apples given their shape, but I’d the knife is big enough, or you’re counting a slice as “single continuous motion” then it is probably valid.
I can’t think of any other physical solution that isn’t a joke, so this is the most probable puzzle solution. In a D&D setting I might require a slight of hand check with a very low DC to pull off the single slicing motion.
Cut 2/3 of both apples leaving 2x2/3 segments and 2x 1/segments (2/3 cut in half for those of you who struggle with fractions)
Align the two apples so they’re off center to one another. One has 2/3 on the outside to the left, 1/3 to the right, the other 2/3 to the outside to the right, 1/3 to the left.
Bird’s eye view, the single line cutting both apples will leave us with the left 2/3 of the first apple and the right 2/3 of the second, and a third portions made of 2 thirds, or another 2/3 of an apple.
One cut, 2 apples, 3 equal portions.
No need to align them like that. Just place them one behind the other and cut off one third on the side (with a single stroke).
You’re right that they’re off-center from a first “symmetry line” you have to draw.
So: you place them on your cutting board. Trace an imaginary vertical bird’s eye view that passes by the center of both. Now based on that imaginary line, move both apples so they’re offset 2/3-1/3 from that line in each direction.
I thought about this at first but then two people get the core as part of their portion and one doesn’t :(
What the fuck is this single-use knife
With forensics being as good as they are now, they’ll probably figure out the knife you used the first time is the same knife you used the second time.
You really can’t have a favourite knife anymore. Gotta dispose of it right away or they’ll work out the pattern without needing to figure out the riddles you left behind at the scene. It’s cheating really, but the only thing you can do to prevent it is by taking the “single-use knife” approach.
What my group will do
Kill one person, yeah we are so dumb :D
With one stroke? Does your group only consist of level 1 wizards or is it some kind of legendary knife?
Stab a player… We can just reincarnate them after the puzzle
This was my vote except for reincarnating. I’m sure one of them deserves it. Probably. Maybe.
Whatever we can find some other fucker to help us in the tavern.
I play a cleric in my party. Previously, we’ve been asked to recover and return a certain plot-important NPC who didn’t exactly want to be transported…
We killed him, transported the corpse, handcuffed it, and then raised him at the destination. It’s a lot easier to transport a body than a live half-elf who is actively trying to escape.
Just say “Why don’t we just use the knife multiple times to cut the apples into quarters so two people get 3/4 of an apple while one gets half an apple? One person gets a quarter apple less than the other two but it’s not a big deal is it?”
Whoever complains about this approach gets stabbed.
