Scientists prove: banitsa can not be divided equally

Not a host has encountered a problem how to divide banitsa, cake, cake or other round culinary delicacy among its guests, so no angry. Three researchers were about to offer a satisfactory solution, since their colleagues nearly 30 years on the job unsuccessfully think.

It turns out that the subject has long occupied researchers. The first publications are from 1980 and the American mathematician Walter Stromkuist, but he does not propose a specific algorithm, how to do this. This shortcoming of proving Stromkuist „drive today to be the case began two scientists from the Department of Management Science from Stanford University in the U.S. and their colleagues from the Department of Computer Science of the University of Hong Kong.

Their algorithm, developed on 26 pages and izobilstvasht of complex formulas and drawings, allowing banitsa be fairly divided into three relatively equal parts, with only two cut. Article the researchers have not yet been published, but can be found on the website arXiv.org.

The problem of fair division of banitsa comes from there that if you have N people, each has different requirements for their piece – some like jewels, others more or filling glaze etc. Despite the serious work on the case three mathematicians recognize that failure to deal fully with the task.

They shall be counted towards the so-called. PPAD problems of the theory of games in which no game in how a few players with a single decision by them to win more without change in the position of other players.

Such tasks are known as the calculations of the Nash equilibrium and of mathematics named John Nash. The name of the scientist became widely known after the public release of a background screen film „Beautiful Mind“ in 2002 in which the winner of the „Oscar“ was Russell Crowe in the role of Nash.

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