Custom order for Carl Hoff's "HexPave^{TM}" puzzle set 
The 15 tiles represent all the combinations of a hexagon with side lengths of 1, 2, and 3 units. While there are 19 solutions to fit all 15 into the hexagonal tray, with 16 triangular filler spaces, there are 3051 solutions for fitting 14 tiles (omitting the smallest equilateral hexagon) into the tray with 22 fillers. That is how it is packaged, with the little hexagon parked on the border. Note how no two of the same color share sides. That is a unique solution with the maximum number of separated fillers (only one place has two of them together). No solution exists with all 22 triangles separated.
Your challenge will be to get all 15 snuggled into the tray, and to solve several other amazing tasks in and outside the tray. The colors of the tiles define how the shapes are related by similar combinations of side lengths of 1, 2, and 3. So, for example, 111111, 222222, and 333333 have the same color. Likewise, 122213 and 322231 are similar. Only one tile has 123123 edges and is the oddball single of one color. To order HexPave^{TM} in 11" round black tray and 6 Lucite colors, simply click on the green logo below and it will be added automatically to your order form. The triangular spaces will contain 22 gray fillers. Color mix may vary. An instruction manual is under construction. $65 (plus shipping)

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