Trioker

History

The mathematical foundation for Trioker was laid in 1921 by Percy Alexander MacMahon in his book New Mathematical Pastimes. He demonstrated that when each of the three edges of an equilateral triangle is assigned one of four colors, exactly 24 distinct combinations are possible. MacMahon proposed using these pieces in an edge-matching puzzle on a regular hexagonal board, where colors must match along adjacent edges and at the board's border. The standard notation for these triangular tiles lists each edge in anti-clockwise order, starting from the bottom left edge. Rotating a tile by 120 degrees changes this notation—for instance, a tile noted as 314 becomes 431 and then 143—but the physical tile remains unchanged. To avoid confusion, a consistent notation can be adopted that begins with the lowest-numbered edge and proceeds anti-clockwise, so the tile above would always be written as 143. Orientation can then be indicated separately, such as by noting the clock hour position of the ones digit, so 143.08 represents the orientation [314] and 143.04 represents [431].

Marc Odier adapted MacMahon's concept by moving the markings from the edges to the corners, creating the Trioker tiles. This design was patented and published by Robert Laffont Games in 1969. Alongside the original 24 combinations, Odier added a tile with a wild card value in one corner, marked by a solid square. In 1970, the Belgian magazine Spirou included a supplement in issue 1661 that provided the game pieces and rules, followed by a regular column through the end of that year.

Trioker is similar to Triominoes, which also uses equilateral triangle tiles with corner values. Both games require that adjacent tiles have matching corners. However, Triominoes uses values from zero to five (or more) and imposes an additional rule: values must not decrease when counted clockwise from the lowest value. As a result, the two games share some pieces, but neither is a subset of the other.