Three Persons, Two Cuts: A New Cake-Cutting Algorithm

Steven J. Brams, Peter S. Landweber

    Research output: Contribution to journalArticlepeer-review


    Summary: We describe a 3-person, 2-cut envy-free cake-cutting algorithm, inspired by a continuous moving-knife procedure, that does not require that the players continuously move knifes across the cake. By having the players submit their value functions over the cake to a referee—rather than move knives according to these functions—the referee can ensure that the division is not only envy-free but also maximin. In addition, the referee can use the value functions to find a maximally equitable division, whereby the players receive equally valued shares that are maximal, but this allocation may not be envy-free.

    Original languageEnglish (US)
    Pages (from-to)110-122
    Number of pages13
    JournalMathematics Magazine
    Issue number2
    StatePublished - 2022

    ASJC Scopus subject areas

    • General Mathematics


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