158:; likewise for face and edge cells. The group of automorphisms of the game contains 192 automorphisms. It is made up of combinations of the usual rotations and reflections that reorient or reflect the cube, plus two that scramble the order of cells on each line. If a line comprises cells A, B, C and D in that order, one of these exchanges inner cells for outer ones (such as B, A, D, C) for all lines of the cube, and the other exchanges cells of either the inner or the outer cells (A, C, B, D or equivalently D, B, C, A) for all lines of the cube. Combinations of these basic automorphisms generate the entire group of 192 as shown by R. Silver in 1967.
855:
147:
boards. There are eight vertically-oriented planes parallel to the sides of the boards, each of these adding two more diagonals (the horizontal and vertical lines of these planes have already been counted). Finally, there are two vertically-oriented planes that include the diagonal lines of the 4x4 boards, and each of these contributes two more diagonal lines—each of these including two corners and two internal cells.
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On the 4×4×4 board, there are 76 winning lines. On each of the four 4×4 boards, or horizontal planes, there are four columns, four rows, and two diagonals, accounting for 40 lines. There are 16 vertical lines, each ascending from a cell on the bottom board through the corresponding cells on the other
101:
In the original issue, the bottom level board was opaque plastic, and the upper three clear, all of simple square design. The 1972 reissue used four clear plastic boards with rounded corners. Whereas pencil and paper play almost always involves just two players, Parker
Brothers' rules said that up to
47:
but is played in a cubical array of cells, usually 4×4×4. Players take turns placing their markers in blank cells in the array. The first player to achieve four of their own markers in a row wins. The winning row can be horizontal, vertical, or diagonal on a single board as in regular tic-tac-toe, or
176:
that consumed 1500 hours of computer time. The strategy comprised move choices for 2929 difficult "strategic" positions, plus assurances that all other positions that could arise could be easily won with a sequence entirely made up of forcing moves. It was further asserted that the strategy had been
132:
The 3×3×3 version of the game cannot end in a draw and is easily won by the first player unless a rule is adopted that prevents the first player from taking the center cell on his first step. In that case, the game is easily won by the second player. By banning the use of the center cell altogether,
85:
Gobblets
Gobbler and Otrio, use marker sizes (small, medium, large) as the replacement of the third element. Players can 'steal' the opponent spot by placing larger marker at the top of the opponent smaller marker or just simply competing with overlapping spot.
319:
150:
The 16 cells lying on these latter four lines (that is, the eight corner cells and eight internal cells) are each included in seven different winning lines; the other 48 cells (24 face cells and 24 edge cells) are each included in four winning lines.
137:
in the choosing of the side the player must use, the game becomes fair and winnable by all players but is subject to chance. By making the choice of the player piece (× or ⚬) subject to chance, the game becomes fair and winnable by all players.
279:, text terminals, or similar interaction: the human player would enter moves numerically (for example, using "4 2 3" for fourth level, second row, third column) and the program would respond similarly, as graphics displays were uncommon.
354:. It uses the standard joystick controller. It can be played by two players against each other, or one player can play against the program on one of eight different difficulty settings. The product code for the Atari game was CX-2618.
165:, meaning that the existence of a winning strategy was proven but without actually presenting such a strategy, by Eugene Mahalko in 1976. He proved that in two-person play, the first player will win if there are two optimal players.
289:
William Daly Jr. wrote and described a Qubic-playing program as part of his Master's program at the
Massachusetts Institute of Technology. The program was written in assembler language for the
51:
As with traditional tic-tac-toe, several commercial sets of apparatus have been sold for the game, and it may also be played with pencil and paper with a hand-drawn board.
653:
70:, the game may be played with pencil and paper. A game board can easily be drawn by hand, with players using the usual "naughts and crosses" to mark their moves.
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computer. It included lookahead to 12 moves and kept a history of previous games with each opponent, modifying its strategy according to their past behavior.
115:
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independently verified. As computer storage became cheaper and the internet made it possible, these positions and moves were made available online.
98:, starting in 1964. It was reissued in 1972 with a more modern design. Both versions described the game as "Parker Brothers 3D Tic Tac Toe Game".
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77:) sold a series of "Paper Games", including "3 Dimensional Tic Tac Toe". Buyers received a pad of 50 sheets with preprinted game boards.
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Several computer programs that play the game against a human opponent have been written. The earliest of these used console lights and
560:
304:. Its strategy involved looking for combinations of one or two free cells shared among two or three rows with particular contents.
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the game is easily won by the first player. By including a 3rd player, the perfect game will be played out to a draw. By including
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strategy was developed and published. However, the strategy is too complicated for most human players to memorize and apply.
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McFeetors, P. Janelle; Palfy, Kylie (May 1, 2017). "We're in Math Class
Playing Games, Not Playing Games in Math Class".
361:
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988:
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462:
Kubota, Runa; Troillet, Lucien; Matsuzaki, Kiminori (December 2022). "Three Player Otrio will be
Strongly Solved".
909:
1057:
678:
L .V. Allis & P. N. A. Schoo (1992). "Qubic solved again". In H. J. van den Herik & L. V. Allis (eds.).
168:
A more complete analysis, including the announcement of a complete first-player-win strategy, was published by
173:
102:
three players could play. The circular playing pieces resembled small poker chips in red, blue, and yellow.
854:
756:
551:
Golomb, Solomon W.; Hales, Alfred W. (August 2002). "Hypercube Tic-Tac-Toe". In
Nowakowski, Richard (ed.).
43:, is an abstract strategy board game, generally for two players. It is similar in concept to traditional
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was written by Robert K. Louden and presented, with an extensive description of its design, in his book
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978:
555:. Mathematical Sciences Research Institute Publications. Vol. 42. Cambridge University Press.
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464:
2022 International
Conference on Technologies and Applications of Artificial Intelligence (TAAI)
94:"Qubic" is the brand name of equipment for the 4×4×4 game that was manufactured and marketed by
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576:
R. Silver (March 1967). "The group of automorphisms of the game of 3-dimensional ticktacktoe".
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315:. Ahl said the program "showed up", author unknown, on a G.E. timesharing system in 1968.
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Three-dimensional tic-tac-toe on a 4x4x4 board (optionally 3x3x3) was included in the
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Heuristic
Programming in Artificial Intelligence 3: The Third Computer Olympiad
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838:. The San Bernardino County Sun (San Bernardino, California). August 5, 1981
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The corner cells and the internal cells are actually equivalent via an
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Oren
Patashnik (September 1980). "Qubic: 4 x 4 x 4 Tic-Tac-Toe".
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vertically in a column, or a diagonal line through four boards.
898:
782:"3-D Tic-Tac-Toe Release Information for Atari 2600 - GameFAQs"
894:
286:
used front panel switches and lights for the user interface.
713:
Robert K. Louden (1967). "Integer manipulation in FORTRAN".
74:
332:
released a 4x4x4 graphical version of the game for the
21:"Qubic" redirects here. For the cosmology project, see
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A program library named Qubist, and front-end for the
307:
A Qubic program in a DEC dialect of BASIC appeared in
368:. In 2010, Microsoft made the game available on its
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584:(3). Mathematical Association of America: 247–254.
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745:. Digital Equipment Corporation. pp. 175–177.
682:. Ellis Horwood, Chichester, UK. pp. 192–204.
504:"Trademark Status & Document Retrieval (TSDR)"
344:, who went on to greater fame as the creator of
54:The game has been analyzed mathematically and a
702:(M.Sc.). Massachusetts Institute of Technology.
517:Freeman, Jon; Jackson, John (August 6, 1979).
910:
613:A Possible Win Strategy for the Game of Qubic
385:window library are a project on SourceForge.
8:
506:. United States Patent and Trademark Office.
519:"The Playboy winner's guide to board games"
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903:
895:
207:
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696:Computer Strategies for the Game of Qubic
693:William George Daly Jr. (February 1961).
615:(M.Sc. thesis). Brigham Young University.
437:Mathematics Teaching in the Middle School
116:The Playboy Winner's Guide to Board Games
413:
32:3-D Tic-Tac-Toe played with glass beads
73:In the 1970s, 3M Games (a division of
796:"AtariAge - Programmers - Carol Shaw"
7:
340:in 1978. The program was written by
105:The game is no longer manufactured.
717:. Prentice-Hall. pp. 179–204.
540:Tic-tac-toe game on the cube 3×3×3
449:10.5951/mathteacmiddscho.22.9.0534
14:
871:. SourceForge. December 12, 2018.
715:Programming the IBM 1130 and 1800
302:Programming the IBM 1130 and 1800
1053:Harary's generalized tic-tac-toe
1007:
853:
757:"Atari 2600 VCS 3-D Tic-Tac-Toe"
39:, also known by the trade name
822:"3-D Tic-Tac-Toe at MobyGames"
521:. Chicago : Playboy Press
1:
1187:Three-dimensional board games
529:– via Internet Archive.
422:"Gaming Unplugged Since 2000"
180:The game was solved again by
472:10.1109/TAAI57707.2022.00015
364:in the 1990s under the name
1218:
1063:Strategy-stealing argument
611:Eugene D. Mahalko (1976).
362:Windows Entertainment Pack
282:A program written for the
172:in 1980. Patashnik used a
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1005:
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739:101 BASIC Computer Games
309:101 BASIC Computer Games
192:Computer implementations
1172:Abstract strategy games
553:More Games of No Chance
174:computer-assisted proof
1192:Paper-and-pencil games
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81:Marker sizes variation
33:
16:Abstract strategy game
1182:Parker Brothers games
1073:Paper-and-pencil game
736:David H. Ahl (1975).
338:Atari 8-bit computers
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296:An implementation in
123:Gameplay and analysis
66:Like traditional 3×3
31:
1197:Tic-tac-toe variants
1058:Hales–Jewett theorem
994:Ultimate tic-tac-toe
869:"Qubist source code"
802:on November 30, 2016
628:Mathematics Magazine
979:Quantum tic-tac-toe
578:Amer. Math. Monthly
402:Quarto (board game)
186:proof-number search
161:3D tic-tac-toe was
1116:Three men's morris
654:"qubic.dictionary"
466:. pp. 30–35.
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1089:Nine men's morris
481:979-8-3503-9950-9
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142:4×4×4, two-player
128:3×3×3, two-player
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1202:Solved games
1131:Connect Four
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1098:Tic-Stac-Toe
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846:– via
840:. Retrieved
836:"(Atari Ad)"
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804:. Retrieved
800:the original
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229:Publisher(s)
217:Developer(s)
182:Victor Allis
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1177:Tic-tac-toe
1146:Toss Across
1068:Futile game
957:Treblecross
926:Tic-tac-toe
806:February 8,
761:Atari Mania
658:Google Docs
260:Atari 8-bit
251:Platform(s)
222:Atari, Inc.
68:tic-tac-toe
45:tic-tac-toe
1166:Categories
1121:Nine Holes
1094:Score Four
723:B0006BRBTQ
408:References
397:Score four
366:TicTactics
351:River Raid
346:Activision
342:Carol Shaw
334:Atari 2600
256:Atari 2600
244:Carol Shaw
233:Atari Inc.
842:August 6,
766:August 6,
663:August 6,
525:August 6,
490:257408458
378:console.
371:Game Room
359:Microsoft
1136:Connect6
934:Variants
391:See also
376:Xbox 360
277:switches
1151:Pentago
1104:Gobblet
952:Notakto
640:2689613
598:2316015
298:Fortran
284:IBM 650
266:Release
109:Reviews
90:"Qubic"
1110:Quarto
947:Gomoku
721:
638:
596:
559:
488:
478:
184:using
1035:-game
984:Renju
974:Pente
886:Qubic
743:(PDF)
700:(PDF)
636:JSTOR
594:JSTOR
486:S2CID
383:GTK 2
330:Atari
41:Qubic
1126:Achi
1043:game
844:2014
808:2016
768:2023
719:ASIN
665:2023
557:ISBN
527:2023
476:ISBN
291:TX-0
269:1978
1141:OXO
989:SOS
888:at
586:doi
468:doi
445:doi
348:'s
311:by
1168::
759:.
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632:53
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592:.
582:74
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484:.
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441:22
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258:,
188:.
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447::
25:.
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