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This page collects matching puzzles consisting of triamond (the trapezoid consisting of 3 regular triangles) tiles.
The object of this puzzle is to put 32 triamond tiles shown in the picture above together to form regular hexagon of edge length 4 units with joining all lines on the tiles to be straight. The tiles are not reversible.
The pattern construction is similar to Diamond Match (lines): The patterns collects all possible coloring of 5 straight lines on the triamond by 2 colors (in the picture, one color is transparent), where the lines are parallel to the edges with crossing mid points of unit edegs.
This puzzle is terribly difficult. However, since I could solve it without computers, you may have a chance.
(Jan. 17, 2005)
Similar to Triamond Match (lines), put 32 triamond tiles shown in the picture above together to form regular hexagon of edge length 4 units with joining all lines on the tiles to be straight. The pattern construction is the same with the previous puzzle except lines are shifted to left or right instead of coloring.
This puzzle is also terribly difficult, but a solution exists.
(Jan. 17, 2005)
The patterns of this puzzle reuses the patterns of Triamond Match (lines), where 8 symmetric patterns are removed and the remaining patterns are drawn on both faces of tiles with pairing mirror images. Thus, 12 triamond tiles are made. The object is to put 12 tiles to form regular triangle of edge length 6 units with joining all lines on the tiles to be straight. This puzzle may be easier than Triamond Match (lines), but still hard to solve.
(Jan. 22, 2005)
(Unsolved) As similar construction of Triamond Match (lines mini), the 12 tiles of this puzzle are made from patterns of Triamond Match (lines #2).
(Jan. 22, 2005)
The object of this puzzle is to put 18 triamond tiles shown in the above picture together to form regular hexagon of edge length 3 units with matching the pattern. The tiles are not reversible. This puzzle is similar to 16L in a certain sense; the whole pattern can be abstracted to a periodic pattern symmetric with rotation of angle 120 degree centered at any point of the triangular lattice. These symmetric points can be classified into 3 kinds corresponding to 3 colors as in the picture. The tiles collects all 18 possible patterns obtained from clipping out from the periodic pattern along lines passing any symmetric point to its nearest ones of the same kind.
The periodic pattern in the picture also has a symmetry of reflection with axes connecting between any two nearest points of the triangular lattice, which is not necessary for this puzzle.
(May. 11, 2005)
The above picture is an alternative design which uses only 2 colors. (Recollect M. C. Escher?) The abstract structure of the periodic pattern is almost the same as the previous one but reflection symmetry is removed. However, the resulting puzzle is isomorphic.
(May. 13, 2005)
The periodic pattern is isomorphic to the 3 colored design of 18 Triamonds #1 but the rotation symmetric points is positioned at the center of regular triangles consisting the tiles.
(May. 11, 2005)
The above picture is an alternative design which uses only 2 colors. The pattern and so the resulting puzzle is isomorphic to the 3 colored one. In this design, the coloring is not essential; only the border lines between colored regions matter.
(May. 13, 2005)
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