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The hospitals/residents problem with couples allows the set of residents to include couples who must be assigned together, either to the same hospital or to a specific pair of hospitals chosen by the couple (e.g., a married couple want to ensure that they will stay together and not be stuck in programs that are far away from each other).
Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics, particularly the twelvefold way and combinations without replacement. It can also be used to analyze coincidences that happen in lottery drawings, such as repeated numbers appearing across different draws. [1
A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. [3] The stable matching problem has also been called the stable marriage problem, using a metaphor of marriage between men and women, and many sources describe the Gale–Shapley algorithm in terms of marriage proposals. However ...
In any stable table, if every reduced list contains exactly one individual, then pairing each individual with the single person on their list gives a stable matching. If the stable roommates problem instance has a stable matching, then there is a stable matching contained in any one of the stable tables.
A six-number lottery game is a form of lottery in which six numbers are drawn from a larger pool (for example, 6 out of 44). Winning the top prize, usually a progressive jackpot , requires a player to match all six regular numbers drawn; the order in which they are drawn is irrelevant.
Match 5: Match all five numbers to win $1 million. The odds of winning are one in 12,607,306. ... Mega Millions is a lottery draw game that occurs twice a week on Tuesdays and Fridays. Players ...
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis is a book on matching markets in economics and game theory, particularly concentrating on the stable marriage problem. It was written by Alvin E. Roth and Marilda Sotomayor , with a preface by Robert Aumann , [ 1 ] [ 2 ] and published in 1990 by the Cambridge University Press ...
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an assignment problem (also called house-allocation problem or one-sided matching ), there are m objects and they have to be allocated among n agents, such that each agent receives at most one object.