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Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance.
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques.
The Rubik's Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 German Game of the Year special award for Best Puzzle. As of January 2024, around 500 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Yahtzee is a dice game made by Milton Bradley. It was first marketed under the name of Yahtzee by game entrepreneur Edwin S. Lowe in 1956. The game is a development of earlier dice games such as Poker Dice, Yacht and Generala. It is also similar to Yatzy, which is popular in Scandinavia.
The 15 puzzle is a sliding puzzle. It has 15 square tiles numbered 1 to 15 in a frame that is 4 tile positions high and 4 tile positions wide, with one unoccupied position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the puzzle is to place the tiles in numerical order.
Pig is a simple dice game first described in print by John Scarne in 1945. Players take turns to roll a single dice as many times as they wish, adding all roll results to a running total, but losing their gained score for the turn if they roll a 1.
Liar's dice is a class of dice games for two or more players requiring the ability to deceive and to detect an opponent's deception. In "single hand" liar's dice games, each player has a set of dice, all players roll once, and the bids relate to the dice each player can see plus all the concealed dice. In "common hand" games, there is one set of dice which is passed from player to player. The bids relate to the dice as they are in front of the bidder after selected dice have been re-rolled. Originating during the 15th century, the game subsequently spread to Latin American and European countries. In 1993, a variant, Call My Bluff, won the Spiel des Jahres.
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.
Cee-lo is a gambling game played with three six-sided dice. There is not one standard set of rules, but there are some constants that hold true to all sets of rules. The name comes from the Chinese Sì-Wŭ-Liù (四五六), meaning "four-five-six". In America it is also called "See-Low," "Four-Five-Six," "The Three Dice Game," "Roll-off!," and by several alternative spellings, as well as simply "Dice." In China it is also called "Sān Liù Bàozi" (三六豹子), or "Three-Six Leopards". In Japan, it is known as "Chinchiro" (チンチロ) or "Chinchirorin" (チンチロリン).
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number of outcomes all equally likely to happen."
Don't Go to Jail is a 1991 Parker Brothers dice game for two or more players inspired by Monopoly. The game is played by rolling ten dice and attempting to roll matches to score points.
A set of dice is intransitive if it contains X>2 dice, X1, X2, and X3... with the property that X1 rolls higher than X2 more than half the time, and X2 rolls higher than X3 etc... more than half the time, but where it is not true that X1 rolls higher than Xn more than half the time. In other words, a set of dice is intransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive. More simply, X1 normally beats X2, X2 normally beats X3, but X1 does not normally beat Xn.
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the fewest possible moves. The allusion to the deity is based on the notion that an omniscient being would know an optimal step from any given configuration.
Dice notation is a system to represent different combinations of dice in wargames and tabletop role-playing games using simple algebra-like notation such as d8+2.
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
Horsengoggle is a method of selecting a random person from a group. Unlike some other methods, such as rock paper scissors, one of the features of horsengoggle is that there is always a winner; it is impossible to tie.
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners. At first glance, the situation appears hopeless, but a clever strategy offers the prisoners a realistic chance of survival.
In mathematics, leximin order is a total preorder on finite-dimensional vectors. A more accurate, but less common term is leximin preorder. The leximin order is particularly important in social choice theory and fair division.
Fair allocation of items and money is a class of fair item allocation problems in which, during the allocation process, it is possible to give or take money from some of the participants. Without money, it may be impossible to allocate indivisible items fairly. For example, if there is one item and two people, and the item must be given entirely to one of them, the allocation will be unfair towards the other one. Monetary payments make it possible to attain fairness, as explained below.
References
- 1 2 3 4 5 Harshbarger, Eric (2015). "Go First Dice" . Retrieved 9 Oct 2019.
- ↑ Bellos, Alex (18 Sep 2012). "Puzzler develops game-changing Go First dice". The Guardian . Retrieved 9 Oct 2019.
- ↑ https://intapi.sciendo.com/pdf/10.2478/rmm-2023-0004
- ↑ "significant_solutions", Go First Dice Wiki, archived from the original on 2023-10-02
