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For two agents with additive valuations, the answer is yes: we can round a connected envy-free cake-cutting (e.g., found by divide and choose). For n {\displaystyle n} agents with additive valuations, we can find an "EF minus 2" allocation by rounding a connected envy-free cake-cutting, and there also exists an EF2 allocation (proof using a ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. . That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth ...
17 indivisible camels. The 17-animal inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.) which must be divided in some stated proportion among a number of beneficiaries.
A genetic algorithm was used to search for the best division candidates: out of the 1024 possible divisions, a subset of 20 divisions was shown to the players, and they were asked to grade their satisfaction about the candidate division on a scale ranging from 0 (not satisfied at all) to 1 (fully satisfied). Then, for each subject, a new ...
Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to ...
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