Put heagonal tiles together to form certain shapes with matching patterns on them.
Put 12 tiles in the above picture together to form the shape as shown, with matching colors and lines.
The patterns collects all possible drawings of 3 straight lines angled 120 degree each others on a hexagonal tile, perpendicular to an edge of the hexagon where: (1) lines are painted with either black or white for each and are (2) slightly shifted certain length from center of the tile.
This is an equivalent model of the above "Hexa-Match (lines)" (black/white coloring is converted to 1/2 phase shift of waved lines).
Put 12 tiles shown in the above picture together to form the shape as shown, with matching colors and curves to form waved lines.
The patterns ar almost same with Hexa-Match (lines), but instead of using lines shifted from center of the tile, waved lines are used, each connecting from midpoint of an edge to midpoint of the oppsite edge with wave length 2 times distance of the mid points.
Put 12 tiles shown in the picture above together to form the shape as shown, with matching colors and curves to form waved lines. The tiles are reversible and the pattern of the back face is mirror image of the front face.
The patterns are similar to Hexa-Match (waves), but phase of the waves are shifted 1/4 wave length; thus, passing through the center of the tile and every patterns are symmetric with 180 degree rotation. With this design, 24 patterns are possible. While tiles can be flipped, it is harder than the previous 2 puzzles.
The figure below is a mechanical design of the same matching model:
The patterns are similar to Hexa-Match (waves #2), but wave length is halved. The tiles are also reversible, but the pattern of the back face is not mirror image, intead, only colors are swapped. The figure below illustrates the back faces of tiles in the above figure, where tiles are flipped at the same position for each.
Note: There is no solution if front and back face is paired with mirrored image.
This is a variation of Hexa-Match (waves #1). Instead of line coloring, lines are shifted certain length from the center.
This is also a variation of Hexa-Match (waves #1). Instead of line coloring, wave length is doubled. It is a pretty hard puzzle.
Patterns based on combination of Hexa-Match (lines) and Hexa-Match (waves #1) . The matching logic is different from both of them.
Patterns based on combination of Hexa-Match (#2) and Hexa-Match (waves #3) . The tiles are reversible and the pattern of the back face is mirror image of the the front face.
Put 12 tiles shown in the picture above together to form the shape as shown, with matching colors and build lattice of small regular hexagons. The tiles are reversible, but the pattern on the back face is not mirror image of the front face.
The surface of the regular hexagonal tile (including both front and back face) can be covered with 6 smaller regular hexagonal 'sheets' of 1/3 area size (the distance of opposite edges of a sheet equals to the length of an edge of the tile), if folding of sheets is allowed. 3 sheets meet at the center of a face of the tile and the others meet at the center of the back face. If 6 sheets are painted with 4 colors (4 colors must be used) so that adjacent sheets to have that diffrent colors, 12 diffrent patterns (involving both front and back face) are obtained. The picture below shows the view from back side of the tiles in the avove picure.
Put 12 tiles shown in the picture above together to form the shape as shown, with matching arcs.
The patterns are generated by the following rules: (1) The pattern must have black/white pair of arcs with their center points at vertices of the hexagon. (2) The radius of an arc can be longer one or shorter one; where the sum of them equals to the edge length. (3) For each edge, At most one arc can meet.
Put 12 tiles shown in the picture above together to form the shape as shown, with matching the same color of arcs or lines to meet at for each edge.
The patterns are generated from the following rules: (1) The pattern must have black/white pair of arcs lines or an arc and a line, where center point of each arc is at a vertex of the hexagon and each line is perpendicular to an edge of the hexagon. (2) For each edge, at most one arc or line can meet. (3) The meet points at the edges are from certain length (shorter than half of edge length) from adjacent "even" vertices, where a set of 3 vertices not adjacent each other are selected as "even".
If we consider that there exists a 'transparent' arc or line that meets the 2 edges that doesn't meet the other arcs or lines for each tile, the condition (1) can be replaced with the following condition: (1') There exists 3 diffrent colored arcs or straight lines on a tile, and slightly complex visual but somthing 'balanced' design is obtained.
Put 12 tiles shown in the above picture together to form the shape as shown, with matching colors and make triangles on all inner edges. The patterns are generated from the following rules: (1) The 'top' and 'bottom' part of triangular shape appears alternately on the edges. (2) 3 pairs of 'top' with 'bottom' shape are painted with 3 different colors for each.
The matching model of this puzzle is the same as Hexa-Match (arcs and lins) above, though it has completely different visual (assuming the condition (1'), one can consider pairs of top/bottom triangular shape of the same color on two edegs as lines/arcs connecting them).
Put 12 tiles shown in the picture above together to form the shape as shown, with matching colors and connect the boundaries smoothly. The tiles are reversible. The pattern on the back face is mirror image of the front face. The patterns are generated from the following rule: The boundary divides tiles in to two regions painted with different colors for each. Each boundary on a tile starts from a vertex tangent to one of two adjacent edge and ends with a vertex (which can be same as the start point) with tangent to the line connecting the vertex and the center of the tile. This puzzle is unique from normal matching puzzle that positioning of tile matching can vary.
It is impossible to make a loop or loops of boundaries using all tiles though, connecting them into one boundary is possible. The figure demonstrates nearly a solution but is not complete, because one end of the boundary at top right tile break aginst the white region and cannot extent more.
Put 12 tiles shown in the picture above together to form the shape as shown, with matching colors on the tiles. The tiles are reversible (The right picture is a turn over of the left picture).
Put 12 tiles in the figure together to form the shape as shown, with connecting lines to make just one path of a straight line or a reflected line appear at every internal edges. In the figure, only one tile marked with green edge is not match. The tile patterns collects all possible drawings of 6 straight lines each connecting midpoint of tile's 2 edges, parallel to a tile's edge and painted with one of 2 colors (in the figure, one color is transparent), except two mono colored patterns (all 6 lines are the same color). It is easy to construct until 11 tiles but fitting the last one is not easy.
This puzzle is similar to the above "reflections" that the selection is equivalent to it but the pattern's shape are altered from lines to arcs to make matching logic diffrent. This puzzle seems relatively easy than the above "reflections".
Put 12 tiles shown in the figure together to form the shape as shown, with connecting all lines to be straight. The tiles are reversible but not paired with mirror image. The right figure shows the back side of the left figure. The tile at bottom center of the left figure inidcates the fundamental line pattern thar all lines are painetd with black. If they are painted with one of 2 colors, namely black and white, for each line, 24 patterns can be obtained (in the above figure, white lines are obscured by tile's background color). The patterns of front/back face are paired with such that a black line and a white line paired for each line on the front/back face. (One can think of it as if tiles are made with transparent material and tapes of 2 colored faces are sticked on them.)