The Mathematically Correct Way to Cut a Cake

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Creator - Jade Tan-Holmes
Script - Alexander Berkes, Simon Mackenzie and Jade Tan-Holmes
Animations - Lester Chan

Chapters
0:00-1:42 The Cake Cutting Problem
1:42-3:22 Cut and Choose
3:22-7:29 Last Diminisher
7:29-10:03 Selfridge-Conway Protocol
10:23-11:51 Why the cake cutting problem is hard
11:51-16:28 Aziz-Mackenzie Protocol

[vigilantcosmicpenguin]

As computer scientists, our plan is actually to explain theoretical solutions so confusingly that eventually everyone else will give in and let us have the big piece. It's an optimal solution because I get more cake and you get me to shut up.

[chaoscope]

Note to self: do not invite mathematicians to a cake party.

[rustymustard]

Meanwhile in real life, Billie wants all the cake, Alex HATES cake but doesn't want Billie to have any. Charlie is completely over all this nonsense, killing his appetite so he tells Alex about Billie's Onlyfans. Now she's begging him not to text her boss the link and crying before throwing the cake in a fit of rage at Charlie, but misses, hitting Doug who was just walking by minding his own business.

[adityavardhanjain]

"Sharing is mathematically difficult"

New favourite excuse when my sister asks to share my food. 😂

[VaradMahashabde]

"Wedding photo for Mackenzie? Could she not find another pho-OH WAIT A MINUTE"

[justklaas]

Once I was fed up with my daughters complaining about the size of their slice of cake, and the topping. They thought it was all just so unfair. I had enough of that, so I threatened them to put the cake in a blender and pour each of them a glass. I thought it was a great solution since it fixes the disagreement over who would get the chocolate bit, the strawberry bit and so forth. They declined my offer and accepted the slices given instead.

[kentslocum]

3:00 "This is a huge drawback for anyone with more than one friend." It's bold of you to assume I have more than one friend. As someone who has no friends, the optimal sharing strategy is for me to eat the entire cake myself. 😊

[kjbunnyboiler]

Having watched this twice now I’ve decided to use the tried and tested methods mothers in families have used for years. Don’t let the kids see the other kids pieces of cake😂

[dudifluke]

Alex, Billie and Charlie may be happy but Simon definitely got the best deal. :) Good video.

[EdOne]

People in a birthday: Lets share the cake!
Me: Hold up
*Pulls out my phone to rewatch it*

[oguzozgul]

My identical twin and I used to share coke for instance, so we used to try to fill two glasses equally to the millimeter level accuracy, until we both were satisfied with the equality.. One drop to this, another two drops to that, and repeat. It sometimes took 20 minutes but who cares! Whatever is spilt onto the table, one of us put thier bare feet on it so that the other could not lick it off the table. so for me, it is fairly understandable why an envy free algorithm is so complicated :)

[StefanLopuszanski]

Hannah Fry did a great video on this years ago on Numberphile. Your video is great too and seems a lot more comprehensive. What motivated you to make this one?

EDIT: Oh. The wedding photo! That says a lot, lol.

[amarug]

This reminds me of an argument I had as an 8-year-old with my parents who cut a small cake in two exact halves, one for me and one for my 2 years younger and much physically smaller sister. I complained that equivalence in absolute size of a cake piece was the wrong metric for fairness, but rather "equivalent satisfaction" should be aimed at and thus, my hypothesis was, that the cake should be divided into the ratio of the sizes of our stomachs, which again could be estimated from our body weights. My parents were not impressed with my hubristic mini-essay of neuroscience and mathematics and just told me to zip it and be glad I have any cake, as many kids don't have cake at all, ever. 😅☠

[SapinskiMath]

As a teacher/fanatic of discrete math, I love everything that's here. I will admit, this is the one topic in the fair division chapter I skip only because I know how long it can take and resolving the whole envy issue. Divider-Chooser, Lone-Divider, Lone-Chooser, Sealed Bids, Markers, all fine. This is much tougher, but if you're willing to brute force the steps and no one minds the time it takes, then do it and let everyone walk away as happy as possible.

But the thing I love most about fair division as a whole is that it brings the whole concept of the value system to light. It spans so many financial, personal and/or political aspects, and you can't just say everyone should be happy with what they get just because of what you perceive to be all pieces being equal fractions of the whole thing. What you value is not the same as what your neighbor values.

Excellent video. I'll remember this one for the future.

[nobodysdeath]

This is the first time ever I've seen a scientist made a video about their discover in mathematics. That's wholesome on so manh levels

[suz]

this is so cool. I thought this video was gonna be about the better way to cut circular cakes but this is way better

[pedrobernardo]

It would be interesting to see it applied to land division, as it usually cannot be freely divided and the pieces must, usually, be continuous

[brianw]

It would have been hilarious if you and Simon had cupcakes at your wedding!

[Rynamony]

What happens if some parts change in value depending of the parts they're paired with? Like a situation in which Matt likes strawberries and blueberries equaly, but hates them together, then if he ends with pieces that contain both, suddenly his cake loses value. Or what would we do in a case in which consecutive pieces are more or less valuable than pieces from different parts of the cake? For example if instead of cake we think about time, someone might think that 10 consecutive minutes of something is worth more (or less) than two separate sessions of five minutes each?

[connecticutaggie]

Nice video. Note: I recall someone defining "fairness" as the condition when all parties are equally dissatisfied. I think that definition might make for an easier solution.😁