# Kate Jones

I have been designing and making combinatorial/mathematical tilings and puzzles for 38 years. Each is an original concept that can form countless artistic/geometrical patterns--pure math as art. I make them in lasercut acrylic and handcrafted wood. They are very challenging and enjoyable to play, and educational even for kids. One of my special interests is to turn any of the 17 classic symmetry groups into polyform puzzles. My flagship is pentominoes and other polyomino and polycube sets. They have inspired the development of many other polyform sets, such as polyhexes, polyiamonds, polyhops, polytans, polyrhombs, polyocts, polyrounds, polybends. We hope someday to involve all 17 forms. I have also developed dozens of edgematching sets.

My 25th anniversary creation: 25 unique curved wedges, each one-fifth of a circle (golden ratio!), analogous to a Penrose kite, have 5 equally spaced ruler marks on their two straight sides. Each tile connects those marks in a different way, yielding all 25 permutations of paths. Match tile paths in groups of 5 to form 5 circles, or 2 circles of 5 and one longer wavy loop of 15 tiles. The largest figure joins all 25 tiles into a single closed loop forming one continuous path. The loop's shape can vary in many ways. I show here the one with largest enclosed area. This artwork replicates one of the solutions with a physical puzzle set (www.gamepuzzles.com/pentuniv.htm#AA). What would a loop with smallest enclosed area look like?

A 2x2 square can be filled with 4 colors in 6 ways. If the square becomes a chevron, the colors can vary their directional placement in 24 ways. Arrange the 24 chevrons unidirectionally in a 4x6 zig-zag panel so no 2x2 areas anywhere (there are 77 of them, including overlaps) have the same color order. This art shows one of those solutions. It is difficult to solve by hand. This image was originally solved with a physical puzzle, lasercut and hand-inlaid (www.gamepuzzles.com/tactile.htm#QU). It is believed not to be a unique solution. The total number of permutations of 2x2s with up to 4 colors is 256, of which 232 contain duplicates. Placing the 24 all-different 4-color tiles in a 4x6 array leaves only 53 areas with duplicate colors.