Commit harakiri obviously
4.5% of the population are psychopaths. 1.4% have a degree in maths.
coincidence?
This is how the hunger games started
you have the knife, ‘equally’ means you get all the apples
Comments full of people earnestly trying to solve the problem without breaking the law lol
Just cut them right down the middle. Four slices each person takes one and the last is left to rot. It says share equally not share the entire apple
Cut both apples into 10 slices each. And then, the richest person takes 18 slices. Because that’s how capitalism works, baby.
shouldn’t be that hard, but I understand that 94% can’t do it.
line up the apples, a line that will cut the first apple into 2/3 vs 1/3 will also cut the next apple in same proportion. 1 person gets the 2 sliced 1/3s
Apples are not homogenous, the underlying requirement when asking for “equal share” is that no one is dissatisfied with his/her share, or envy someone else’s share. The solution is a dynamic process :
After explaining it clearly to everyone, hover the knife above the left of the first apple as if you were going to cut it through but without doing it, move the knife slowly to the right until one of the three participants says he is happy with that share, cut the apple at that point and that participant gets that share. Then do the same with the second apple and the remaining unserved participants. Whoever doesn’t have anything after that gets the remaining two slices.
Since everyone “could have” spoke earlierto get a share, everyone has a share that they consider the best in their frame of reference and everyone is satisfied.
This solution also works with more than three participants
Edit: I just now realised the goal was to do it in a single cut
Stack the apples on top of each other, and proceed to do a single spiral cut down from the top stem, out towards the edge, and then back to the center in a single fluid motion. It won’t solve the problem, but it’ll look damn cool
Let’s assume you can stack the apples, and passing through both is still 1 stroke. That means cutting through 10 could still be considered 1 stroke.
Stack the apples.
Cut entirely through the top one directly in half.
Continue cutting through the second one.
As you cut through it, one of the people takes the top apple, rotates it 60 degrees, and puts it under the bottom apple.
Finish cutting through the now top apple and continue cutting through the now bottom apple (the original top that was already in half).
Repeat this until you’ve cut each into 6 pieces like this (picture not mathematically accurate, for visual purposes only).
Give everyone 4 each.
Actually, if you can peel them both with o e stroke, you cwn make apple sauce and serve eqaul portions quite easily.
You forgot about the cores.
Cores are non edible volume so you probably need to cut closer to 68-70%.
Damn you ruined it
My solution is cut both apples in half, and take two halves, because I am more equal than others.
Some animals are more equal than others…
Because the 6% are psychopaths capable of murder. I thought it was closer to 3% of the population though
Line em up and cut a third off both apples in one go? Everyone gets 2/3? Seems simple right? Consider the core. I don’t think it’s possible if you consider the core. You have to kill one of your friends.
You have to kill one of your friends.
You have to kill one of your friends.
Choose which one of your friends to kill.
Reach for the knife before someone else does.
You have to kill one of your friends.
Michael: See, the trolley problem forces you to choose between two versions of letting other people die. And the actual solution is very simple. Sacrifice yourself.
– The Good Place
Killing one of your friends might not be the optimal solution.
But one of your friends might think it is.
Rotate each apple 90 degrees so that core is parallel to the ground and perpendicular to the knife, now its split equally
If more than one person hates the stem part then yea it’s murder time
The core isn’t evenly distributed along the axis though, it’s like a small thingy in the center. Definitely murder time
This is actually the sandwich problem, which states there is exactly one slice that will split a sandwich of 3 elements into exactly 2 halves regardless of the shape or position of those elements. We don’t need the full proof, but the problem is continuous, so any desired ratio is possible, therefore you will always be able to slice an apple into exactly 1/3 and 2/3rds “good bits”, so a single slice will always be able to do the job.
I still struggle to visualize it. If we have two concentric spheres (or circles), how can you make a cut that slices both into ratios of 2/3 by volume/area?
diagonals
Or you could sacrifice yourself, you murderous bastard.
But then I would be dead.
Cut 1/3 up from the top or bottom?
(the apples! Cut the apples!)
cut one in half. then take turns each taking an equally sized bite
If you cut one in half then the two survivors get one whole apple each.
Bite bite pass
Cut both apples in half. One half for the blonde, one half for brownie, one half for the ginger, and the last half for the animals or something.
Last half for the painter of this picture.
:D
I will be the cpt obv
1/3 1/3
<=======]==o
2/3 2/3
Ok but like how do you know it’s 1/3 of the apple without any other tools.
You don’t, you only know it’s possible to do so thanks to the Ham sandwich theorem
What’s funny is that you’ve actually stumbled onto an entire problem that’s studied quite heavily. I remembered a Numberphile video about this. The problem is called “envy-free cake splitting”. It’s pretty straightforward. A split is envy-free if no one believes someone else got more than them. For three people this was figured out in 1960 and you can read about it here. It has been solved for N participants as well and you can read about the general problem here.
For two people, it’s obvious. One splits and one chooses. The first person is incentivized to make it even because they don’t know which they’ll get.
I was going to give a summary of the process for three people but it’s too much to explain succinctly. Just check the article I posted lol.
How is it obvious for two people, what if I have horrible manual dexterity and despite my best efforts, I slice the cake like 1/3 and 2/3, and the other person picks the bigger piece? I would very much envy the other piece
Your “cut” would not be complete until you believe you’ve made them 50/50.
here we go infinite cuts
Then have them cut and you choose. Easy. Now they envy your piece and having better dexterity as well.
Insert Thanos balanced meme here.
Let’s not go too deep on this alright
Right… right… but https://en.wikipedia.org/wiki/Envy-free_cake-cutting
if the cake is a 1-dimensional interval …
The Stromquist moving-knives procedure uses four simultaneously-moving knives…Consider a spherical cow perched above a black hole, facing the sunset…
I did not expect to see this today
To put that in perspective, for 2 people that would be ~4.3 billion
alright we better get started then
It’s just the upper bound. I have no idea what the process is lol.
Cut first, choose last. It’s as fair as you can get when eyeballing it
Only works with two people. For three you use Selfridge-Conway procedure which uses up to five cuts.
it is a magical long sword of apple slicing (+5 damage and THAC0 against apples, +1 otherwise)
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Just eat out the apples together, ignoring the knife. Just take a bite and pass the apple to the next person, repeating the process until there is just a core. Not very sanitary, but mission accomplished.
