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pedestals of matching color until one player connects the two opposite sides of the board marked in the player's color. A variant of the game is described in the instructions: each player gets a limited number of bridges, say 10. If neither player has won when all the bridges are placed, a player in his turn, may reposition one of his bridges until a winner results. The game is long out of production.
163:
190:
under the name Bridg-It. The game consisted of a plastic board with two interleaved 5x6 rectangular grids of pedestals (one set yellow, the other red), two sets of 20 each red and yellow plastic bridges, and matching pegs to mount them on. Players alternate placing a bridge across any two adjacent
182:
Oct. 1958, two grids of differently-colored dots are overlaid at an offset. One player links orthogonally adjacent dots on one grid, and the other player uses the other. One player attempts to link the top of their grid to the bottom, while the other tries to link their left side to the right. The
232:
An extension of Gale, called Qua, is played by three players on a 3D game board cube composed of a grid of N cells. N is an odd number equal to the number of cells along the edges of the game board cube. The initial Qua Cube game board layout and rules are described at its Board Game Geek entry.
229:". Players alternate drawing in a vertical or horizontal line connecting any two adjacent dots. When a line completes a square, the player initials the square. After all the lines have been filled in, the player who has taken the most squares is the winner.
221:
is played on a grid of hexagons, and has 6-connectivity. Generalized Hex is played on a graph, just like the
Shannon game, but instead of coloring the edges, in Hex the players color the vertices. These games have completely different structure and properties.
39:. One player has the goal of connecting two distinguished vertices by a path of edges of their color. The other player aims to prevent this by using their color instead (or, equivalently, by erasing edges). The game is commonly played on a
107:, Short wins. The game always terminates after a finite number of moves, and one of the two players has to win. Either Short, Cut, or the player moving first is guaranteed the existence of a winning strategy on any given graph.
91:, and alternate moves. On Cut's turn, Cut deletes from the graph a non-colored edge of their choice. On Short's turn, Short colors any edge still in the graph. If Cut manages to turn the graph into one where
558:
Cláudio, A. P.; Fonseca, S.; Sequeira, L.; Silva, I. P. (2015). "Shannon switching game and directed variants". In
Bourguignon, J.-P.; Jeltsch, R.; Pinto, A.A.; Viana, M. (eds.).
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of the starting graph. The problem of testing for the existence of two disjoint trees, each connecting the distinguished vertices, can be represented as a
183:
game is equivalent to the
Shannon switching game played on a rectangular grid. No draw can result; the first player can always win with correct play.
118:
games are a duality; that is, the game can be restated so that both players have the same goal: to secure a certain edge set with distinguished edge
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Dynamic, Games and
Science: International Conference and Advanced School Planet Earth, DGS II, Portugal, August 28–September 6, 2013
225:
Another connectivity game played with paper and pencil on a rectangular array of dots (or graph paper) is the children's game of "
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35:, the "father of information theory", some time before 1951. Two players take turns coloring the edges of an arbitrary
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including the two distinguished vertices, as well as two disjoint subsets of the remaining unchosen edges supported on
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problem, which can be solved in polynomial time. Alternatively, it is possible to solve the same problem using
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289:, such that either of the two subsets (together with already chosen edges) would connect all vertices in
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have been described for theoretical purposes; but no corresponding commercial games have been published.
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An explicit solution for the undirected switching game was found in 1964 for any such game using
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83:. Each edge of the graph can be either colored or removed. The two players are called
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43:; this special case of the game was independently invented by American mathematician
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are no longer connected, Cut wins. If Short manages to create a colored path from
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Player Cut took 3 turns (dotted edges), player Short took 4 turns (green edges).
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The Second
Scientific American Book of Mathematical Puzzles and Diversions
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630:
Mansfield, Richard (1996). "Strategies for the
Shannon switching game".
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A commercial board game implementing the scheme was marketed in 1960 by
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445:
Hayward, Ryan B.; van
Rijswijck, Jack (2006). "Hex and combinatorics".
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171:
44:
40:
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hard, optimal moves for the undirected switching game can be found in
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28:
484:"An implemented graph algorithm for winning Shannon Switching Games"
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can make a move that results in a position with this property, then
214:, in which the winning patterns for the Maker are connecting paths.
562:. CIM Series in Mathematical Sciences. Springer. pp. 187–199.
402:
Lehman, Alfred (1964). "A solution of the
Shannon switching game".
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should aim for a position in which there exists a set of vertices
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199:
662:"A Combinatorial Problem Which is Complete in Polynomial Space"
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The
Shannon switching game can be seen as a special case of a
404:
Journal of the
Society for Industrial and Applied Mathematics
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can win regardless of what the other player does; otherwise,
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makes up a cutset, the minimal set of edges that connect two
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per move. After removing from the graph the edges chosen by
162:
557:
364:, a different and harder connection game on the square grid
753:, a Java implementation of the Shannon switching game
703:
Reisch, Stefan (1981). "Hex ist PSPACE-vollständig".
529:(1986). "Directed switching on graphs and matroids".
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146:Versions of the Shannon switching game played on a
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130:, while Cut tries to secure an edge set that with
324:Unlike some other connection games, which can be
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170:In this game invented by American mathematician
122:. Short tries to secure the edge set that with
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194:An electronic implementation of the Game of
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388:. NY: Simon and Schuster. pp. 86–87.
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31:mathematician and electrical engineer
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47:in the late 1950s and is known as
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632:The American Mathematical Monthly
217:A weakly-related connection game
16:Pencil and paper connection game
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532:Journal of Combinatorial Theory
71:The game is played on a finite
644:10.1080/00029890.1996.12004732
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27:for two players, invented by
568:10.1007/978-3-319-16118-1_10
545:10.1016/0095-8956(86)90083-3
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340:, the resulting graph is a
206:Relationship to other games
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461:10.1016/j.disc.2006.01.029
489:Communications of the ACM
482:Stephen M. Chase (1972).
237:Computational complexity
75:with two special nodes,
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777:Abstract strategy games
525:Hamidoune, Yahya Ould;
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772:Paper-and-pencil games
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21:Shannon switching game
681:10.1145/321978.321989
503:10.1145/361284.361293
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166:A win for red in Gale
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455:(19–20): 2515–2528.
448:Discrete Mathematics
346:matroid partitioning
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198:is available in the
527:Las Vergnas, Michel
188:Hassenfeld Brothers
180:Scientific American
719:10.1007/BF00288964
667:Journal of the ACM
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212:Maker-Breaker game
200:Ludii Games Portal
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577:978-3-319-16117-4
302:{\displaystyle S}
282:{\displaystyle S}
262:{\displaystyle S}
174:and described in
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382:Gardner, M.
126:makes up a
761:Categories
751:Graph Game
616:2020-08-28
369:References
172:David Gale
45:David Gale
321:can win.
136:subgraphs
658:Even, S.
591:Bridg-it
512:21110956
384:(1961).
356:See also
245:theory.
142:Variants
53:Bridg-It
29:American
735:9125259
727:0599616
690:8845949
469:2261917
432:0173250
424:2946344
243:matroid
150:and an
128:circuit
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326:PSPACE
731:S2CID
686:S2CID
607:"Qua"
508:S2CID
420:JSTOR
362:TwixT
342:minor
338:Short
315:Short
311:Short
309:. If
247:Short
112:Short
85:Short
73:graph
59:Rules
37:graph
23:is a
572:ISBN
196:Gale
158:Gale
114:and
110:The
95:and
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79:and
49:Gale
19:The
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640:doi
636:103
593:at
564:doi
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412:doi
334:Cut
319:Cut
219:Hex
116:Cut
103:to
89:Cut
51:or
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297:S
277:S
257:S
132:e
124:e
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105:B
101:A
97:B
93:A
81:B
77:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
