## ::Qubic

### ::concepts

Qubic::solved    Position::board    Points::games    Allis::parker    Category::lines    Winning::brothers

{{#invoke:Hatnote|hatnote}}

Qubic is the brand name of a four-in-a-row game played in a 4×4×4 matrix sold by Parker Brothers starting in 1953.<ref>United States Patent and Trademark Office</ref> The original box, and the 1972 reissue, described the game as "Parker Brothers 3D Tic Tac Toe Game". Players take turn placing pieces to get four in a row horizontally or diagonally on a single boardâ€”or vertically in a column or diagonal line across four boards.

The four boards were made of clear plastic (in a simple square design in the original release and in a funkier design for the 1972 reissue) with circular playing pieces that resembled small poker chips in red, blue, and yellow; each player used a single color. Markers could be placed in any unoccupied position, rather than stacked in a pile on a square as in Score Four. The game is no longer manufactured.

Either two or three players could participate in a game. In two-person play, the first player will win if there are two optimal players. There are 76 winning lines. The 16 positions lying at the 4 space diagonals (8 corners and 8 internal positions) are equivalent and each involved in 7 winning lines; the other 48 positions (24 face positions and 24 edge positions) are also equivalent, each being involved in four winning lines. (The equivalence of a corner and an internal position is via an inversion; likewise for a face and an edge position.) The game was weakly solved by Eugene Mahalko in 1976, Oren Patashnik in 1980 and then solved again by Victor Allis using proof-number search.

A plotter based 3D computer game was written by Arthur Hu and Carl Hu in 1975 on a HP 9830 in Lindbergh High School. It used four stacked trapezoids. It was later ported to the HP 2647 demo tape with a graphical interface, using a simple mathematical transform to solve for 3D input position. It also was included in the Microsoft Windows Entertainment Pack in the 1990s as part of TicTactics.

Qubic sections