## Abstract

In general, moving-knife schemes seem to be easier to come by than pure existence results (like Neyman's [N] theorem) but harder to come by than discrete algorithms (like the Dubins-Spanier [DS] last-diminisher method). For envy-free allocations for four or more people, however, the order of difficulty might actually be reversed. Neyman's existence proof (for any n) goes back to 1946, the discovery of a discrete algorithm for all n ≥ 4 is quite recent [BT1, BT2, BT3], and a moving-knife solution for n = 4 was found only as this article was being prepared (see [BTZ]). We are left with this unanswered question: Is there a moving-knife scheme that yields an envyfree division for five (or more) players?

Original language | English (US) |
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Pages (from-to) | 30-35 |

Number of pages | 6 |

Journal | The Mathematical Intelligencer |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1995 |

## ASJC Scopus subject areas

- Mathematics(all)
- History and Philosophy of Science