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Treblecross
Treblecross is a degenerate tic-tac toe variant. The game is an octal game The octal games are a class of two-player games that involve removing tokens (game pieces or stones) from heaps of tokens. They have been studied in combinatorial game theory as a generalization of Nim, Kayles, and similar games. Revised and reprin ..., played on a one-dimensional board and both players play using the same piece (an X or a black chip). Each player on their turn plays a piece in an unoccupied space. The game is won if a player on their turn makes a line of three pieces (Xs or black chips) in a row. Gameplay The game begins with all the 1×''n'' spaces empty. Each player plays an X on the one-dimensional board in an empty cell. The game is won when a player makes a row of three Xs. See also * References {{Tic-Tac-Toe Tic-tac-toe variants ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treblecross
Treblecross is a degenerate tic-tac toe variant. The game is an octal game The octal games are a class of two-player games that involve removing tokens (game pieces or stones) from heaps of tokens. They have been studied in combinatorial game theory as a generalization of Nim, Kayles, and similar games. Revised and reprin ..., played on a one-dimensional board and both players play using the same piece (an X or a black chip). Each player on their turn plays a piece in an unoccupied space. The game is won if a player on their turn makes a line of three pieces (Xs or black chips) in a row. Gameplay The game begins with all the 1×''n'' spaces empty. Each player plays an X on the one-dimensional board in an empty cell. The game is won when a player makes a row of three Xs. See also * References {{Tic-Tac-Toe Tic-tac-toe variants ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe Variants
Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an ''m''×''n'' board until one of them gets ''k'' in a row. Harary's generalized tic-tac-toe is an even broader generalization. The game can also be generalized as a nd game. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertices. Many board games share the element of trying to be the first to get ''n''-in-a-row, including three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo. Variants of tic-tac-toe date back several millennia. Historic An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three; thus, they had to move them around to empty spaces to keep playing. The game's grid ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case. The definitions of many classes of composite or structured objects often implicitly include inequalities. For example, the angles and the side lengths of a triangle are supposed to be positive. The limiting cases, where one or several of these inequalities become equalities, are degeneracies. In the case of triangles, one has a ''degenerate triangle'' if at least one side length or angle is zero. Equivalently, it becomes a "line segment". Often, the degenerate cases are the exceptional cases where changes to the usual dimension or the cardinality of the object (or of some part of it) occur. For example, a triangle is an object of dimension two, and a degenerate triangle is contained in a line, which makes its dimension one. This is similar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octal Game
The octal games are a class of two-player games that involve removing tokens (game pieces or stones) from heaps of tokens. They have been studied in combinatorial game theory as a generalization of Nim, Kayles, and similar games. Revised and reprinted as Octal games are impartial meaning that every move available to one player is also available to the other player. They differ from each other in the numbers of tokens that may be removed in a single move, and (depending on this number) whether it is allowed to remove an entire heap, reduce the size of a heap, or split a heap into two heaps. These rule variations may be described compactly by a coding system using octal numerals. Game specification An octal game is played with tokens divided into heaps. Two players take turns moving until no moves are possible. Every move consists of selecting just one of the heaps, and either * removing all of the tokens in the heap, leaving no heap, * removing some but not all of the tokens, le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
