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Tile-laying puzzles (in German, "Legespiel") of both the edge-matching and polyform varieties have been explored and produced by Kate Jones at Kadon, and you can read a lot of interesting material at the Kadon site - see Edgematching Colors and Shapes, and More About Edgematching. You can see some original designs by Yukio Hirose here.Take a look at George Hart's article "A Color-Matching Dissection of the Rhombic Enneacontahedron." Also see Peter Esser's page. Jacques suggests the following seven categories: Jacques also defines a classification scheme by which one can identify the puzzles abstractly and find isomorphisms (i.e. Jacques' conclusions, based on computer analysis, regarding the best approach to solving these puzzles agree with my empirical findings - in general, fix the tile in the middle and work around it.A good tile to choose for this middle position is the tile with the most possible matches.As discussed in my polyforms section, the only regular polygons which can be used to completely tile the plane are the equilateral triangle, the square, and the hexagon. It is described on page 36 of Slocum and Botermans' "Puzzles Old & New." The goal is to form a 3x3 grid such that at the points where the quarter-circles on the corners of the tiles meet (either four or two), there are always different colors on each of the meeting quarter-circles.edges or corners) match (or complement, or dismatch) those at corresponding points on abutting pieces" or "the heights (or numeric values) of aligned pieces total a specific constant" or "defined sets of faces have all distinct (or equal) features." Sometimes, as in the case of matchstick puzzles or the "Eight Queens" puzzle, the individual pieces are indistinguishable, but their arrangement in a particular pattern is paramount.
Edge-Matching puzzles usually consist of a set of tiles whose edges have various distinct patterns, symbols, or colors.It is evident in Haubrich's Compendium that these shapes comprise the majority of tile shapes used in existing edgematching puzzles. Grandpa's head must always be upright on every card, so the cards cannot be rotated.Rectangles have also been used, as have octagons (allowing empty areas). Jacques says this is the first example of a corner dismatching puzzle. The Besco Soap Puzzle - from the Beaver Soap Company of Dayton Ohio.I've organized my example puzzles by tile shape: The Thurston design was used by Calumet ca. In the Calumet Puzzle, one must match not just the proper color edges, but also the corresponding top and bottom halves of the baking powder cans. Form a 3x3 grid such that there are four different colors in each circle at the corners, and two different colors in each half-circle.I solved the Calumet puzzle using a variant of my Drive Ya Nuts technique. There must also be a different color at each of the four corners of the grid.