## How To Split A Cake Fairly Using Math

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How can 2 people split up a cake, knowing that each person wants to get a larger piece than the other? What about 3 people, or even N people? This is an example of a fair division problem from game theory. There are many cake-cutting algorithms to produce a fair solution mathematically. In this video I describe the “I cut, you choose” method and the “last diminisher method.”

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## Comments

Michael Wong says:

Thats not a pie its a cake﻿

Babbaj3212 says:

i cut my cake concentrically﻿

Feral Device says:

Last person gets a pile of crumbs.﻿

ahmad zainal says:

Could you do one on cutting the cheese?﻿

Ace Diamond says:

[Point 1] Why not (with Blue, Red, Green) just have blue cut a slice, then give red the option to take that slice, or give it to blue.  Then, of course the other of red/blue who didn't get the slice, does the 2-person procedure with green on the remainder of the cake?  It would work just the same, right?  Only thing I can think of is that you're letting more people optionally cut it, just to pare it down to a perfect third, in case the first guy didn't do well enough at cutting an accurate third; but it would seem that we're assuming perfect cutters, or else the 2-person method isn't quite fair.  Besides, if it's just about getting more accuracy, why not say that green can cut it too if he likes, and pass it back to blue, looping around to the beginning and continuing ad infinitum until it's perfect?  I may be missing something, but I don't see why you couldn't just go down the list of people in order, 1-on-1 matchup of cut+(accept/defer).  [Point 2] Blue and red could form a written pact.  Blue cuts a tiny sliver out of the cake, but insists that the giant portion is the "piece" he actually cut.  Red says, "Hell no, I don't want that giant piece, you keep it blue."  Red and green split the sliver, then Blue and Red split the giant piece per contractual obligation.  Blue and red each end up with essentially 50% of the cake, green with essentially 0%.﻿

Felix Bade says:

A simpler n people solution: one person cuts the cake into n pieces. The cutter chooses last. Thus the cutter wants to make the smallest piece as big as possible eg. all pieces the same size.﻿

Cam Whitling says:

TL;DR
Divide cake so everyone gets 1/n amount of cake (n = number of people)﻿

kirkelicious says:

Substitute "cake" with "weed" and you have a practical application.﻿

darkgtprince says:

so basically if you have n people, you cut the cake into 1/n pieces to share evenly﻿

Harrison Harris says:

Adding the "I cut you choose" just complicates the last step, last diminisher works for 2 people as well.﻿