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The Fair pie-cutting procedure provides a simpler solution to the same problem, using only 3 rotating knives, when the cake is a 1-dimensional circle ("pie"), The Robertson–Webb rotating-knife procedure provides an even simpler solution, using only 1 rotating knife, when the cake is 2-dimensional. Moving-knife procedure
The Levmore–Cook moving-knives procedure is a procedure for envy-free cake-cutting among three partners. It is named after Saul X. Levmore and Elizabeth Early Cook who presented it in 1981. [1] [2] It assumes that the cake is two-dimensional. It requires a referee, two knives and four cuts, so some partners may receive disconnected pieces.
The simplest example is a moving-knife equivalent of the "I cut, you choose" scheme, first described by A.K.Austin as a prelude to his own procedure: [2] One player moves the knife across the cake, conventionally from left to right. The cake is cut when either player calls "stop", when he or she perceives the knife to be at the 50-50 point.
The Stromquist moving-knives procedure uses four simultaneously-moving knives - one moved by a referee and another one for each agent. Barbanel–Brams moving-knives procedure uses two simultaneously-moving knives. The Robertson–Webb rotating-knife procedure can be used when the cake is two-dimensional, and uses only a single moving-knife.
Pages in category "Cake-cutting" The following 40 pages are in this category, out of 40 total. ... Barbanel–Brams moving-knives procedure; Robertson–Webb rotating ...
Alice places one knife on the left of the cake and a second parallel to it on the right where she judges it splits the cake in two. Alice moves both knives to the right in a way that the part between the two knives always contains half of the cake's value in her eyes (while the physical distance between the knives may change). George says "stop!"