# Cake-cutting problem: How to fairly divide a cake - Lycée Notre Dame du Grandchamp (Versailles)

Établissement
Lycée Notre Dame du Grandchamp (Versailles)
Année
2023-2024
Résumé
Suppose you want to divide a cake, with uneven distributions, between two people in a way that makes both of them satisfied, i.e., both of them believe that they have a better or equally good piece as the other one. Such a solution is called an envy-free solution. This is a classical problem whose solution is given by the ‘you cut, I choose’ approach. This means that one of the players cuts the cake into two pieces, and the other one chooses which one to pick for themselves. Since the first player knows that if they cut the cake into unequal pieces then the other player can just pick the better piece, the best strategy for the first player is to cut the cake into equally valued pieces. So the first player would be equally happy independent of the piece they get. The second player then just chooses the piece which makes them more happy, and we get an envy-free solution. How can one generalize this approach to divide a cake between 3 players?
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