Cake Cutting Math Problem

Let 1 divide cake into three equal pieces.

Cake cutting math problem. The problem has found its way into recreational mathematics under the name chore division problem a2. A cake is sliced roughly in half the largest piece being chosen each time the other pieces discarded. This is a strange world of never ending chess games empires on the moon furious fireflies and of course disputes over how best to cut a cake. You have a rectangular cake and two friends.

This problem can be solved with arbitrary number of children using the algorithm for finding maximum matching in a bipartite graph. Please list all the pieces you will be satisfied. Here are twenty more curious puzzles and fantastical mathematical stories from one of the world s most popular and accessible writers on mathematics. The problem involves a heterogeneous resource such as a cake with different toppings that is assumed to be divisible it is possible to cut arbitrarily small pieces of it without destroying their value.

The first person wants to cut the cake so as to maximize his share min x 1 x. Cake cutting is a metaphor for a wide range of real world problems that involve dividing some continuous object whether it s cake or say a tract of. The maximum value of min x 1 x for x between 0 and 1 occurs when x 0 5 which means 1 x is also 0 5. The mathematics of cake cutting.

Suppose number of children is n. Recently 2000 there has been quite a bit of interest in fair division and cake cutting. This problem is the piece of cake problem from elements of information theory for which there are many solutions available. Cake cutting is a metaphor for a wide range of real world problems that involve dividing some continuous object whether it s cake or say a tract of land among people who value its features differently one person yearning for chocolate frosting for example while another has his eye on the buttercream flowers.

The solution below is from this course. Fair cake cutting is a kind of fair division problem. Ask others the following. If you want to slice a cake into 7 or 9 or n slices divide the perimeter of the square cake into 7 or 9 or n equal lengths.

The resource has to be divided among several partners who have different preferences over different parts of the cake i e some. The man who loved circles objectivity. Cutting the cake algorithm is the following. So the first player will cut the cake into 2 equal slices and the i cut you choose method produces a fair division of the cake.