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# Equally sharing a cake between three people - Numberphile

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**Published on Sep 26, 2017**

Audible (30-day trial, free audio book): https://www.audible.com/numberphile More links & stuff in full description below ↓↓↓ This video features Dr Hannah Fry. More videos with Hannah: http://bit.ly/hannah_vids Hannah's website: http://www.hannahfry.co.uk Her book mentioned is "The Mathematics of Love". Envy free cake cutting (the paper mentioned): https://arxiv.org/abs/1604.03655 A clarifying note from Hannah: n^n^n^n^n^n is the maximum number of cuts in the n person case. Something we could have made clearer... Bob's trimmed piece still carries the status of his "first choice", so if Charlie leaves it, Bob will (must) pick it... otherwise he'll pick the one that was his original "second choice"... The upshot of this is that there's no chance Alice will be left with the trimmed piece after everyone takes their first piece. And Bob remains envy free under these conditions too. A trilogy of mathematical cake cutting videos... http://bit.ly/CakeCuttingTrilogy Editing and animation in this video by Pete McPartlan Discuss this video on Brady's subreddit: https://redd.it/72jyww Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

NumberphileTry

Albert BNo friends = No problems

boer harmsI'd just blend it, and divide by weight....

Scorpio SnakeThe one who has the knife , gets the whole cake .

LimeTime MusicSo this is what people who write exam questions spend their time doing

PROUD RACISTand this is why socialism doesn't work

PlayTheMindCake?! Should've been

Stark Talksthe title of this video is wrong. the exercise is not about getting equal slices but about satisfying preferences.

Jimmy KefferMoral: never share cake with a mathematician

INeedToSleepNow.comAmazing unintentional ASMR in this video.

Jaakko FagerlundEasiest solution to make a fair cut: Alice cuts and passes the piece. If both Bob and Charlie don't accept it, then Alice gets the piece. Then Bob cuts and Charlie either accepts or not. This way you can't get a large piece unless others agree to it.

BlobVanDamThis is why you never invite a mathematician to a birthday party.

NotoriousHDCOMMUNISM INTENSIFIES

Kadath841:21

superscatboyAka "how to divvy up weed without scales".

supersoldier7738Just cut it into equal pieces of 12 and everyone take 4 each

Preston GrangerJust cut it well and don't complain. Solved

BlueFireSo, let's say Charlie takes the "Dud" piece, then, Bob, seeing the trimmed and untrimmed slices as being equal, takes the untrimmed piece, would that not make Alice unhappy due to getting a piece with some cake trimmed off? Or is that in the rules, Bob must take the piece he trimmed if it is available?

Cranston SnordThe cake is a lie.

Lillie GoodmanWhy not just cut into 6 then have 2 slices