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A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. [1] [verification needed] [clarification needed] Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes. Generally, mathematical games need not be conceptually intricate to involve deeper ...
In the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a knife .
N, A cuts from the cake an arbitrary part. B has now the right, but is not obliged, to diminish the slice cut off. Whatever he does, C has the right (without obligation) to diminish still the already diminished (or not diminished) slice, and so on up to N. The rule obliges the "last diminisher" to take as his part the slice he was the last to ...
A 2-spot game of Sprouts. The game ends when the first player is unable to draw a connecting line between the only two free points, marked in green. The game is played by two players, [2] starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to ...
Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource ("the cake") and two partners who have different preferences over parts of the cake (both want as much of it as possible).
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 ...
The transformations of the 15 puzzle form a groupoid (not a group, as not all moves can be composed); [12] [13] [14] this groupoid acts on configurations.. Because the combinations of the 15 puzzle can be generated by 3-cycles, it can be proved that the 15 puzzle can be represented by the alternating group. [15]
The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards dealt and the first player that can achieve the number 24 exactly using only allowed operations (addition, subtraction, multiplication, division, and parentheses) wins the hand.