Special designs: Tri-Chex

 With some or all of the 53 Tri-Chex tiles, a limitless variety of figures can be formed, following the set's color pattern. The main requirement is that no two pieces of the same color may touch each other on sides. Points or vertices of the triangles of the same color may touch, and, of course, all the squares are joined by their corners. EGGS. One of the special features of Tri-Chex is its being filled with "eggs", which are regions containing 4 of each kind of element: 4 squares, 4 triangles of one color, and 4 triangles of the other color. See the first image below. These 12 polygons form an oblong decagon (10 sides) we call an oval, or simply an egg. In the sample figures below, see how many complete eggs they contain. If any part of an egg is missing, it doesn't count. For example, in the figure with the central egg cut out, only 10 eggs remain intact, another 11 having been broken. Eggs overlap, like the long chain of 15 eggs below. Overlaps count as complete eggs as long as each egg has all 12 parts. The Tri-Chex booklet contains many more egg figures, small and large, to explore and solve. SAMPLE FIGURES. Here are some samples of squares, a pyramid, a super-symmetric assembly of the whole set, a 25-egg pyramid, and a "pentomino" model (our logo!) built from 6 eggs. Many sizes of squares and rectangles are listed in the booklet, as well as all 12 pentominoes. In the figures shown here, those with dark outlines mark where the pieces fit; these solutions are not unique. ALPHABET. Building each letter within a 3x3 arrangement of eggs, leaving out pieces as necessary to allow the shape of each letter to emerge, lets us solve the entire alphabet. Here's a sampling of just the first five letters. CONTRARIAN. We wouldn't be puzzle lovers if we didn't think of going against the rules. A contrarian conundrum is to fill the tray with the entire set and make as many solid-color diamonds as possible. That means placing same-color triangles together. Not counting the pieces that contain two opposite-color triangles joined, we're left with only 32 pieces out of the 53 that have singleton triangles available to connect to one of its own color. So, technically, it should be possible to make 16 solid-color diamonds of each color. We show you here a solution with 14 of each color. Be the first to find a new 16/16 solution and win a contrarian award. Email your solution to: kadon@gamepuzzles.com.