Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A moving-knife solution to the four-person
envy-free cake-division problem

Authors: Steven J. Brams, Alan D. Taylor and William S. Zwicker
Journal: Proc. Amer. Math. Soc. 125 (1997), 547-554
MSC (1991): Primary 90D10; Secondary 62C20
MathSciNet review: 1353378
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players.

References [Enhancements On Off] (What's this?)

  • [A] A. K. Austin, ``Sharing a cake'', Mathematical Gazette 6, no. 437 (October 1982), 212-215.
  • [BT 1] S. J. Brams and A. D. Taylor, ``An envy-free cake-division protocol'', American Mathematical Monthly 102, no. 1 (January 1995), 9-18. CMP 95:09
  • [BT 2] S. J. Brams and A. D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge, UK: Cambridge University Press (1996). CMP 96:10
  • [BT 3] Steven J. Brams and Alan D. Taylor, On envy-free cake division, J. Combin. Theory Ser. A 70 (1995), no. 1, 170–173. MR 1324009,
  • [BTZ] S. J. Brams, A. D. Taylor, and W. S. Zwicker, ``Old and new moving-knife schemes'', Mathematical Intelligencer 17, no. 4 (Fall, 1995). CMP 96:05
  • [N] J. Neyman, ``Un theoreme d'existe'', C. R. Acad. Sci. Paris 222 (1946), 843-845. MR 7:457h
  • [S] H. Steinhaus, ``The problem of fair division'', Econometrica 16, no. 1 (January 1948), 101-104.
  • [St] Walter Stromquist, How to cut a cake fairly, Amer. Math. Monthly 87 (1980), no. 8, 640–644. MR 600922,
  • [W] W. Webb, ``But he got a bigger piece than I did'', preprint, n.d.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 90D10, 62C20

Retrieve articles in all journals with MSC (1991): 90D10, 62C20

Additional Information

Steven J. Brams
Affiliation: Department of Politics, New York University, New York, New York 10003

Alan D. Taylor
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308

William S. Zwicker

Received by editor(s): December 20, 1994
Received by editor(s) in revised form: August 29, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society