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.
Well, regardless, someone's getting hurt. Have you tried cutting two whole apples, one on top of the other? It's non-trivial! They aren't exactly stable and the rogue's gonna try to swipe one or both as soon as you move your own fingers out of the way. May as well get it over with and stab the rogue to start.
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.
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.
You tie the unlucky member to sacrifice. Maybe one with low fortitude.
And use coup de grace. Probably it will die
One shot with one stroke.
Technically it's doable ^^
I am fully awake now, and I can't believe I didn't think of cutting it not down the middle. Haha. There's a fairly easy way to calculate where to cut a sphere so that the sphere segment has a desired volume. Similar to the formula used in this video.
The first person decides where the first apple would be cut, such that he would be equally happy with either taking the larger portion or dividing up what remains.
The second person either says he wants that larger portion, in which case he's done, or he says he wants to divide up what remains, in which case the first person takes the larger portion and is done.
The third person decides where the second apple would be cut.
Either the first or second person (depending on the outcome of the second step) picks either the larger portion of the second apple or the two smaller portions.
The third person takes what remains.
The two apples are cut and their pieces distributed.
This doesn't guarantee a solution, since it's possible that the third person would have wanted the larger portion of the first apple. It only works if we assume that the first person, when given the motivation to cut fairly, does so with high precision. Otherwise the first person can, by screwing himself over, also screw over the third person.
No, you line the apples up under the knife and then slice once. Each apple can be moved relative to the knife and independently of the other apple.
I should have been more specific when I said things like
takes the larger portion
because what I meant by that is "permanently claims the larger portion as his own". The apple is not cut (once) and no one actually gets their pieces in their hands until step 6.
DM:
We're in Waterdeep, so the entire area is in a magical field, so detect magic is useless.
Also you cast a spell and thats a crime in Waterdeep, so you see a Karen of an Elf run off to find the guard
Player: I cast Identify on the apples.
DM: first one is fine, second one is a baby Mimic that attacks your finger as soon as you touch it to cast the spell. What's your AC and Roll Initiative.
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.
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.
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
"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.
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.
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.
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.
Four is just two twos but doesn't have three as a factor, so four still isn't equally shareable among three without either not sharing some or, hear me out, murder.
Two pieces equal to 1/3 of the total and two pieces equal to 1/6th. Everyone gets a third with 4 pieces, but one person has two smaller pieces that add up to a third. You can accomplish this by cutting one third off each apple with a single stroke,.
If we can go through multiple apples in a single stroke, then we can assume we're allowed to a) go through the same apple multiple times b) make curved, complex strokes c) murder party members.
