Practical four-dimensional tic-tac-toe

Details Practical four-dimensional tic-tac-toe Practical four-dimensional tic-tac-toe

1999-03-01

2001-07-03

Layno, Benjamin H. (Department: 3711)

Amusement devices: games

Board games, pieces, or boards therefor

Alignment games

C273S264000

Reexamination Certificate

active

06254098

ABSTRACT:

FIELD OF THE INVENTION
A layout and a method of play which are practically useful for playing tic-tac-toe (TTT) in four dimensions are disclosed. The layout consists of an array of tiles, each tile containing a 5×5 array of substantially square cells, where the tiles are arrayed in a 5×5 pattern. For ease of visual interpretation, the tiles should be separated by approximately the width of a cell. The layout may be implemented physically or electronically. The rules are analogous to classical TTT; two variants are described.
BACKGROUND
The ordinary two-dimensional (2D) game of tic-tac-toe (TTT), having 3×3 cells, is well known. It is suitable for play by children, but there are relatively few strategies, and most players with experience achieve the theoretically-predicted draw.
TTT has been implemented in three dimensions (3D) by vertical stacking of boards, each of 3×3 or 4×4 cells, and respectively 3 or 4 high. The 3×3×3 version is a trivial win for the first player to move in a two-player game (two-player games are assumed herein unless otherwise stated.) The more complex 4×4×4 3-D game has been predicted to be a win for the first player, although the strategy is less directly obvious from the 2D 3×3 game than is the strategy for the 3×3×3. Vertically stacked games in both formats have been sold from time to time, but have not been commercially successful on a continuing basis. This may be because they are physically complex, taking up space and being prone to breakage; or because they are not satisfyingly complex in terms of strategy. In either case, no following has developed (compare Monopoly®—or even Othello™).
There do not appear to be examples of the proposed board structure or layout in the art, and in particular in U.S. Class 273/271 (“Tic-Tac-Toe games”). Compton (U.S. 4,371,169) proposed “imaginary multilevel tic-tac-toe”. In FIG. 7 of Compton, a 1-dimensional array of 3×3 boards is shown; in FIG. 9, a crossed arrangement of 3×3 boards is illustrated; and in FIG. 2A, the 3×3 boards are arranged circularly. Boyer et al (U.S. 4,131,282) illustrate a 3×3 array of tiles each tile having a 3×3 array of cells (a “3×3:3×3” array), and propose a n×n:n×n array where n is an integer. However, the proposed rules of play in Boyer et al involve a multiplicity of colors and do not correspond to classical TTT, or to the rules proposed here.
SUMMARY OF THE INVENTION
A method for playing tic-tac-toe (TTT), also known as “naughts and crosses”, in four dimensions (4D) is disclosed, in which the game board consists of a 5×5 array of tiles, each tile of which is composed of a 5×5 array of cells. This is illustrated in FIG.
1
. The rules of play are analogous to those in three dimensional TTT. Each player has a particular mark, or type or color of piece. Each plays one mark or piece in turn; played pieces are not moved or removed. The winner is the first player to complete a row of five pieces or marks (“pieces”), where the concept of “row” includes both a conventional two-dimensional (2D) TTT row—horizontal, vertical or diagonal within a single tile—and the equivalent when a “super-row” of five tiles is projected onto a horizontal plane. A super-row is a row of tiles, where the allowed twelve patterns are the same as in conventional TTT if the tiles are considered as cells—i.e., the five (5) horizontal rows, the five (5) vertical rows, and the two (2) diagonals. At least two variants of the conventional rules for TTT are possible on such a game board.


REFERENCES:
patent: 3749401 (1973-07-01), Hayko
patent: 4131282 (1978-12-01), Boyer et al.
patent: 4275442 (1981-06-01), Underwood et al.
patent: 4371169 (1983-02-01), Compton
patent: 4884819 (1989-12-01), Lambert

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