How to cut a cake fairly for three people


#1

Originally published at: https://boingboing.net/2017/10/05/how-to-cut-a-cake-fairly-for-t.html


#2

“I Cut, You Choose” for Three: Steinhaus’s Method

Read More: http://locus.siam.org/doi/abs/10.1137/1.9780898717624.ch17

Let us eat cake!


#3

I prefer the moving knife procedure. It’s punishes being too greedy - I’m ok with that.


#4

ask everyone how big a piece they want? I guarantee in 99% of cases that’s going to be some quantity smaller than a third of an entire freaking cake.


#5

I bake cupcakes…no worries.


#6

I think it’s harder to find three people who want equal portions. Usually, it’s a fit of passive aggressive “Oh, I only want a sliver!” on repeat.


#7

They skipped the part where she gets to sell all her stock before she starts cutting. :thinking:


#8

Man, you have not dined with my kids lately


#9

The real challenge is to cut a cake into Pi pieces


#10

Weigh cake, divide total by three, cut pieces until 1/3 total weight is gone, serve.


#11

I learned this much simpler method from reading about how Civil War soldiers divided their rations of coffee and sugar.

Alice cuts the cake into three pieces as equally as she can, while Bob and Charlie watch.

Bob then turns his back.

In turn, Alice points to each piece and asks “Who shall have this one?”

Bob, unable to see what she is pointing at, replies in turn with one of the three names.

Charlie watches, and when all three names have been called out, distributes the pieces of cake accordingly.


#12

In what way is that passive-aggressive? Do you really think everybody wants to gorge themselves on as much cake as possible? That anybody who says they want a small piece must be dishonest?

Full disclosure: I sometimes don’t want any cake at all, and when I do, I skip the ice cream. But I demand more than my share of coffee.

@David_Guilbeaul Trick question! Cakes are not pies!


#13

Came here to say this. ‘One cuts, the other chooses’ was the clear rule in our house.

Now wondering if there’s a permutation that works for three people, eg A cuts twice; B chooses first; C chooses second. Is there a better way?


#14

But then Mary doesn’t get any cake.


#15

A makes first cut
B makes 2nd cut
C makes third cut
A chooses first piece
B chooses second piece
C gets the last piece.

It works because:
A has no effective input into the size of the pieces, but gets first pick so can select the piece that matches their desire (be it large or small)
B decides how big one of the pieces is, and more-or less decides how big the other two will be. If she deliberately makes the first piece oversize, then she’ll most likely end out with half of the remainder.
C is incented to make the last cut as fair as possible, because they’re probably going to get one of the pieces on either side of that cut.
Basically B & C are incented to cut fairly, or will be punished for not doing so.

Assumptions:

  1. Cake is a circle and cuts are radial.
  2. The cake is not a lie

#16

I prefer Tau pieces


#17

We have cakes, pies, and pastries for three occasionally at our house. This is how we manage:
Cut six pieces, give each person two.


#18

To cut a cake into three pieces only takes two cuts though…


#19

check your assumptions :wink:

Also, while true, in that case:
A makes first cut
B makes second cut
C makes first choice
B makes second choice
A gets what’s left

The general rule is to try and ensure whoever makes the most meaningful cut gets the last piece, then work your way down the stack of influence.


#20

“your promised reward is merely a fictitious motivator” Nice. I would have never have placed cake and a video game together.

“Popularized by the game “Portal” (found on Half-Life 2’s “Orange Box” game release for PC, X-Box 360, and PS3). During the game, an electronic voice encourages you to solve intricate puzzles using cake as a motivating perk. When you have “broken out” of the game’s initial testing phase (from threat of death), you find scrawls on walls of the innards of the testing center warning you that “the cake is a lie”.” UrbanDictionary