this post was submitted on 21 May 2025
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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
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.
well you can't rule out the worst possible case, so lets get rolling
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)