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117:, who published a treatise on edge-colouring of a variety of shapes in 1921. This particular puzzle uses 24 tiles consisting of all permutations of 3 colors for the edges of a square. The tiles must be arranged into a 6×4 rectangular area such that all edges match and, furthermore, only one color is used for the outside edge of the rectangle.
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TetraVex is a computer game that presents the player with a square grid and a collection of tiles, by default nine square tiles for a 3×3 grid. Each tile has four single-digit numbers, one on each edge. The objective of the game is to place the tiles into the grid in the proper position, completing
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3D edge-matching puzzles are not currently under direct U.S. patent protection, since the 1892 patent by E. L. Thurston has expired. Current examples of commercial puzzles include the
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418:. Within each serpentile, the edges are paired, thus restricting the set of tiles in such a way that no edge color occurs an odd number of times within the hexagon.
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board game employs edge matching to constrain where its square tiles may be placed. The original game has three types of edges: fields, roads and cities.
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this puzzle as quickly as possible. The tiles cannot be rotated, and two can be placed next to each other only if the numbers on adjacent edges match.
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This puzzle can be extended to tiles with permutations of 4 colors, arranged in 10×7. In either case, the squares are a subset of the
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164:. It was named by Scott Ferguson, the development lead and an architect of the first version of Visual Basic, who wrote it for
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whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match.
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MacMahon
Squares, along with variations on the idea, was commercialized as Multimatch.
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pieces have distinguished edges to require that the edges of adjacent pieces match.
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526:"Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity"
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729:(5). Information Processing Letters, Volume 99, Issue 5, Pages 171–174: 171–174.
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759:(2020). Survey: Sixty years of Douglas Rachford. Cambridge University Press.
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TetraVex was inspired by "the problem of tiling the plane" as described by
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in 1892. Current examples of commercial edge-matching puzzles include the
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numbers along the edges that can be chosen arbitrarily. Hence there are
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436:. A 3D edge-matching puzzle is such a puzzle that is not flat in
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A solution to MacMahon
Squares with the largest single-color area
595:. Gerstein - University of Toronto. Cambridge, University Press.
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The first edge-matching puzzles were patented in the U.S. by
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Deciding if a TetraVex puzzle has a solution is in general
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TetraVex is also available as an open source game in the
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Takenaga, Yasuhiko; Walsh, Toby (15 September 2006).
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The possible number of TetraVex can be counted. On a
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444:a three-dimensional area such as the surface of a
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241:horizontal and vertical pairs that must match and
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471:Part of a Carcassonne game showing matching edges
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631:Wade Philpott (credited). Kadon Enterprises.
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790:"Kadon Enterprises, More About Edgematching"
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432:Mathematically, edge-matching puzzles are
387:. Its computational approach involves the
113:puzzle suggested by British mathematician
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577:Sphere Packing, Lewis Caroll and Reversi
410:are the hexagonal tiles used in various
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109:MacMahon Squares is the name given to a
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646:Energize Education Through Open Source
428:Three-dimensional edge-matching puzzle
61:Edge-matching puzzles are known to be
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770:"Rob's puzzle page: Pattern Puzzles"
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812:Erich's Matching Puzzles Collection
848:. You can help Knowledge (XXG) by
605:Steckles, Katie. Blackboard Bold:
589:MacMahon, Percy Alexander (1921).
552:"Rob's puzzle page: Edge Matching"
414:such as Psyche-Paths, Kaliko, and
328:{\displaystyle 2n(n-1)+4n=2n(n+1)}
25:
54:an area with (typically regular)
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156:Volume 1: Fundamental Algorithms
161:The Art of Computer Programming
158:, the first book in his series
723:Information Processing Letters
463:Incorporation of edge matching
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644:Whittum, Christopher (2013).
579:. Cambridge University Press.
373:{\displaystyle 10^{2n(n+1)}}
166:Windows Entertainment Pack 3
672:"The Birth of Visual Basic"
335:choices of 10 digits, i.e.
199:{\displaystyle n\times {}n}
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635:. Retrieved 12 April 2021.
622:. Retrieved 12 April 2021.
609:. Retrieved 10 March 2021.
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389:Douglas-Rachford algorithm
735:10.1016/j.ipl.2006.04.010
719:"TetraVex is NP-complete"
592:New mathematical pastimes
403:A single-cross serpentile
575:Gardner, Martin (2009).
412:abstract strategy games
844:-related article is a
659:Moving to Ubuntu Linux
657:Gagné, Marcel (2006).
618:Guy. Cube Root of 31.
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234:{\displaystyle n(n-1)}
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34:A partially completed
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900:NP-complete problems
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44:edge-matching puzzle
38:edge-matching puzzle
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693:"License - README"
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446:regular polyhedron
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257:{\displaystyle 4n}
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92:Notable variations
82:Eternity II puzzle
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817:Rob's puzzle page
699:. gnome.org. 2011
522:Martin L. Demaine
380:possible boards.
111:recreational math
16:(Redirected from
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554:. Archived from
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422:Three dimensions
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140:GNOME Tetravex
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115:Percy MacMahon
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78:E. L. Thurston
67:jigsaw puzzles
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48:tiling puzzle
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27:Tiling puzzle
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850:expanding it
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793:. Retrieved
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152:Donald Knuth
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43:
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697:gnome-games
477:Carcassonne
408:Serpentiles
385:NP-complete
173:GNOME Games
63:NP-complete
36:Eternity II
889:Categories
795:2009-06-22
775:2009-06-22
703:2012-10-02
678:2010-05-11
633:Multimatch
620:Wang Tiles
562:2007-08-12
534:2007-08-12
505:References
122:Wang tiles
50:involving
457:Dodek Duo
450:polygonal
284:−
223:−
189:×
71:polyomino
648:. pg 32.
483:See also
395:Hexagons
131:TetraVex
56:polygons
18:Tetravex
743:7228681
416:Tantrix
86:Tantrix
741:
442:tiling
52:tiling
840:This
739:S2CID
529:(PDF)
846:stub
475:The
69:and
731:doi
42:An
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727:99
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543:^
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
