How to cut a cake fairly using a minimal number of cuts

Abstract

What is the minimum number of cuts needed to divide a cake among n players so that each player receives at least 1 n of the whole cake? The simple “one cuts - the other chooses” shows that one cut suffices for 2 players. It was previously known that 3 players require 3 cuts and 4 players require 4 cuts with only upper bounds available for n> 4. Algorithms using 6 cuts for 5 players and 8 cuts for 6 players are discussed, which lower the previously known upper bounds. Moreover, it is shown that 6 cuts is the best possible for 5 players.