Put domino tiles together to form a certain shape with matching patterns on them.
(terms) for the domino tiles used in this page, the term vertex means not only the corner points but also the midpoints of the longer sides of the rectangle, and the term edge means the sides of unit length joining adjacent vertices; thus there exists 6 edges for each tile.
Put 18 tiles shown in the picture above together to form 6 x 6 square with connecting lines. The lines may break off at the circumference of the 6 x 6 square. There can be 9 patterns for connecting a line from a midpoint of an edge to a midpoint of another edge of domino tile. And also 9 patterns available for connecting midpoints of 4 different edges of a domino tile with lines corssing each other.
The folowing additional conditions can be given. Note that the third condition satisfies the second condition.
Put 18 tiles shown in the picture above together to form 6 x 6 square with connecting lines. The lines may break off at the circumference of the 6 x 6 square. Each tile pattern consists of two fundamental square patterns shown in the above figure, where one for one of a pttern indicated by orange framed box and one for one of a pttern indicated by blue framed box (these are mirror images of orange framed patterns), with lines not breaking off at the joint in the tile.
Like the previous Domino Match (spiral loop), the folowing additional conditions can be given. Though it is pretty hard to solve without such conditions.
This puzzle is a variation of the previous Domino Match (path #1), where the fundamental patterns are changed. The patterns consists of pairing of a square patterns one for chosen from the group at left of the above figure and one for chosen from the right group. Note that the 3rd condition is impossible for one loop, because there exists only 6 tiles that can be used for corners of 6 x 6 square, but only 3 tiles can be used to satisfy parity matchng.
Put 18 tiles shown in the picture above together to form 6 x 6 square with connecting white lines without branches. The lines may break off at the circumference of the 6 x 6 square. The tiles patterns are selected such like as a beam of light passing through the tile's area entered at midpoint of an edge with incident angle 45 degree, reflects inside the area on tile's edges and exiting at midpoint of another edge.
There exists a solution to make all white lines to be loops.
The next design is essentially the same as "reflections" but the matching condition is bit loose. Each tile on the figure below corresponds to the tile at the same position in the picuture of "reflections" above. With this correspondence, any solution of "reflections" satisfies this puzzle but the opposite is not always true (compare with the tile marked with green frame for both figure).
Put 18 tiles shown in the figure above together to form 6 x 6 square with matching patterns. The selection is similar to the "reflections" that black / white vertices corrsponds to 45 / -45 dgree of slant of "black segments" on the vertices of tiles in "reflections". Or one can think of it patterns are selected from possible patterns of black/white vertices such that tile's area is divided to 3 regions if adjacent black vertices are joined as shown in this design.
There exists a solution such that opposite edges of circumference also match.
Put 18 tiles shown in the figure above together to form 6 x 6 square, making diagonal lattice patterns with matchng colors. The patterns collects all possible paintings of the diagonal lattice with 3 colors so that any 2 adjacent squares have different colors. This design is somewhat similar to diamond match (hex), and has similar feeleing of solving experience. It is harder than it looks like.
Put 18 tiles shown in the figure above together to form 6 x 6 square with matchng lines and their colors. The patterns are collection of all possible drawings of one black and one white lines intersecting and connecting midpoints of tile's 4 different edges. This puzzle is very hard.
Put 18 tiles shown in the figure above together to form 6 x 6 square with matchng lines and their colors. The tiles are reversible. The pattern on the back face is the mirror image of the fornt face. There are only 2 colors are shown. Tha last one color is transparent. The patterns are collection of all possible coloring by 3 colors of certain fundamental line pattern (and its mirrored pattern) consists of 3 parallel lines connecting mid points of tile's edges. This puzzle is also very hard.
The next is a design similar to the previous one that fundamental line pattern is changed. Also, the tiles are reversible and the pattern on the back face is the mirror image of the fornt face. Note that unlike the previous one, number of patterns is 27 (9 of them are symmetric and the rest 18 patterns consists of 9 pair of mirrors.)
This puzzle is not so hard as the previous one. The following additional condition can be given.
There exists a solution satisfaying 2nd thru 4th conditions. Note: It seems impossible to make two colored line segments all to be a part of a loop or loops (black/white lines do not break off at circumference).
(insolved) The next is a design like a mixture of the previous two puzzles. Also, the tiles are reversible and the pattern on the back face is the mirror image of the fornt face.
The pattrens are collection of possible combinations of the following 3 fundamental patterns of square with matching line colors (each of square patterns consists of 2 arcs of 2 colors). Very hard (is it possible?)
Put 18 tiles shown in the figure above together to form 6 x 6 square, making square lattice patterns with matchng colors. the tiles are reversible and the pattern on the back face is the mirror image of the fornt face. Similar to the "diagonal lattice", the patterns collects all possible paintings of the diagonal lattice with 3 colors so that any 2 adjacent squares have different colors. There exists 27 patterns, 9 of them are symmetric and the rest 18 patterns consists of 9 pair of mirrors. Very hard.