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

✍ Scribed by William A. Webb

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 528 KB
• Volume: 74
• Category: Article
• ISSN: 0166-218X
• DOI: 10.1016/s0166-218x(96)00032-7

✦ Synopsis

What is the minimum number of cuts needed to divide a cake among IZ players so that each player receives at least l/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.