169:; 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.
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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.
157:
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
112:
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
58:
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
187:
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
143:
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,
330:
96:
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.
161:
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.
148:
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.
290:, 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.
365:. 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.
176:, 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.
300:
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
220:
62:
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.
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81:, 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.
188:
independently verified. As computer storage became cheaper and the internet made it possible, these positions and moves were made available online.
109:, 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".
705:
126:
806:
88:) sold a series of "Paper Games", including "3 Dimensional Tic Tac Toe". Buyers received a pad of 50 sheets with preprinted game boards.
286:
Several computer programs that play the game against a human opponent have been written. The earliest of these used console lights and
315:. Its strategy involved looking for combinations of one or two free cells shared among two or three rows with particular contents.
144:
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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446:
McFeetors, P. Janelle; Palfy, Kylie (May 1, 2017). "We're in Math Class
Playing Games, Not Playing Games in Math Class".
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571:
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473:
Kubota, Runa; Troillet, Lucien; Matsuzaki, Kiminori (December 2022). "Three Player Otrio will be
Strongly Solved".
1202:
689:
L .V. Allis & P. N. A. Schoo (1992). "Qubic solved again". In H. J. van den Herik & L. V. Allis (eds.).
1192:
179:
A more complete analysis, including the announcement of a complete first-player-win strategy, was published by
1207:
113:
three players could play. The circular playing pieces resembled small poker chips in red, blue, and yellow.
767:
562:
Golomb, Solomon W.; Hales, Alfred W. (August 2002). "Hypercube Tic-Tac-Toe". In
Nowakowski, Richard (ed.).
372:
999:
54:, is an abstract strategy board game, generally for two players. It is similar in concept to traditional
311:
was written by Robert K. Louden and presented, with an extensive description of its design, in his book
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920:
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566:. Mathematical Sciences Research Institute Publications. Vol. 42. Cambridge University Press.
184:
792:
475:
2022 International
Conference on Technologies and Applications of Artificial Intelligence (TAAI)
105:"Qubic" is the brand name of equipment for the 4×4×4 game that was manufactured and marketed by
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R. Silver (March 1967). "The group of automorphisms of the game of 3-dimensional ticktacktoe".
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326:. 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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849:. 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.
957:
793:"3-D Tic-Tac-Toe Release Information for Atari 2600 - GameFAQs"
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used front panel switches and lights for the user interface.
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Robert K. Louden (1967). "Integer manipulation in FORTRAN".
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released a 4x4x4 graphical version of the game for the
85:
32:"Qubic" redirects here. For the cosmology project, see
392:
A program library named Qubist, and front-end for the
318:
A Qubic program in a DEC dialect of BASIC appeared in
379:. In 2010, Microsoft made the game available on its
595:(3). Mathematical Association of America: 247–254.
756:. Digital Equipment Corporation. pp. 175–177.
693:. Ellis Horwood, Chichester, UK. pp. 192–204.
515:"Trademark Status & Document Retrieval (TSDR)"
621:
1174:
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355:, who went on to greater fame as the creator of
65:The game has been analyzed mathematically and a
713:(M.Sc.). Massachusetts Institute of Technology.
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528:Freeman, Jon; Jackson, John (August 6, 1979).
527:
445:
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624:A Possible Win Strategy for the Game of Qubic
396:window library are a project on SourceForge.
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517:. United States Patent and Trademark Office.
561:
530:"The Playboy winner's guide to board games"
202:
928:
914:
218:
707:Computer Strategies for the Game of Qubic
704:William George Daly Jr. (February 1961).
626:(M.Sc. thesis). Brigham Young University.
586:
448:Mathematics Teaching in the Middle School
127:The Playboy Winner's Guide to Board Games
91:
328:
133:
38:
43:3-D Tic-Tac-Toe played with glass beads
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84:In the 1970s, 3M Games (a division of
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807:"AtariAge - Programmers - Carol Shaw"
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351:in 1978. The program was written by
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116:The game is no longer manufactured.
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728:. Prentice-Hall. pp. 179–204.
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24:
551:Tic-tac-toe game on the cube 3×3×3
460:10.5951/mathteacmiddscho.22.9.0534
25:
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882:. SourceForge. December 12, 2018.
726:Programming the IBM 1130 and 1800
313:Programming the IBM 1130 and 1800
1064:Harary's generalized tic-tac-toe
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768:"Atari 2600 VCS 3-D Tic-Tac-Toe"
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50:, also known by the trade name
833:"3-D Tic-Tac-Toe at MobyGames"
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532:. Chicago : Playboy Press
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1198:Three-dimensional board games
540:– via Internet Archive.
433:"Gaming Unplugged Since 2000"
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191:The game was solved again by
483:10.1109/TAAI57707.2022.00015
375:in the 1990s under the name
7:
401:
10:
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1074:Strategy-stealing argument
622:Eugene D. Mahalko (1976).
373:Windows Entertainment Pack
293:A program written for the
183:in 1980. Patashnik used a
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320:101 BASIC Computer Games
203:Computer implementations
1183:Abstract strategy games
564:More Games of No Chance
185:computer-assisted proof
1203:Paper-and-pencil games
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92:Marker sizes variation
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27:Abstract strategy game
1193:Parker Brothers games
1084:Paper-and-pencil game
747:David H. Ahl (1975).
349:Atari 8-bit computers
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307:An implementation in
134:Gameplay and analysis
77:Like traditional 3×3
42:
1208:Tic-tac-toe variants
1069:Hales–Jewett theorem
1005:Ultimate tic-tac-toe
880:"Qubist source code"
813:on November 30, 2016
639:Mathematics Magazine
990:Quantum tic-tac-toe
589:Amer. Math. Monthly
413:Quarto (board game)
197:proof-number search
172:3D tic-tac-toe was
1127:Three men's morris
665:"qubic.dictionary"
477:. pp. 30–35.
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1100:Nine men's morris
492:979-8-3503-9950-9
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153:4×4×4, two-player
139:3×3×3, two-player
16:(Redirected from
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1028:Related concepts
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1142:Connect Four
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1109:Tic-Stac-Toe
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857:– via
851:. Retrieved
847:"(Atari Ad)"
841:
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815:. Retrieved
811:the original
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228:Developer(s)
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1188:Tic-tac-toe
1157:Toss Across
1079:Futile game
968:Treblecross
937:Tic-tac-toe
817:February 8,
772:Atari Mania
669:Google Docs
271:Atari 8-bit
262:Platform(s)
233:Atari, Inc.
79:tic-tac-toe
56:tic-tac-toe
1177:Categories
1132:Nine Holes
1105:Score Four
734:B0006BRBTQ
419:References
408:Score four
377:TicTactics
362:River Raid
357:Activision
353:Carol Shaw
345:Atari 2600
267:Atari 2600
255:Carol Shaw
244:Atari Inc.
853:August 6,
777:August 6,
674:August 6,
536:August 6,
501:257408458
389:console.
382:Game Room
370:Microsoft
1147:Connect6
945:Variants
402:See also
387:Xbox 360
288:switches
1162:Pentago
1115:Gobblet
963:Notakto
651:2689613
609:2316015
309:Fortran
295:IBM 650
277:Release
120:Reviews
101:"Qubic"
1121:Quarto
958:Gomoku
732:
649:
607:
570:
499:
489:
195:using
1046:-game
995:Renju
985:Pente
897:Qubic
754:(PDF)
711:(PDF)
647:JSTOR
605:JSTOR
497:S2CID
394:GTK 2
341:Atari
52:Qubic
18:Qubic
1137:Achi
1054:game
855:2014
819:2016
779:2023
730:ASIN
676:2023
568:ISBN
538:2023
487:ISBN
302:TX-0
280:1978
1152:OXO
1000:SOS
899:at
597:doi
479:doi
456:doi
359:'s
322:by
1179::
770:.
667:.
643:53
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452:22
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