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This is a French puzzle (Casse-Tete) called "Le Nombre Treize" - The Number Thirteen.Arrange the tiles in a 3x3 square such that the red figures align vertically and the blue figures align horizontally, and such that the three figures in each of the six rows and six columns add to 13. At the January 2007 Toy Fair, Tomy launched the Eternity II puzzle (Wikipedia entry here) and a contest prize of M USD.The individual pieces can be easily arranged in many different ways that partially satisfy the rule - but overall there is usually only one total arrangement (or a relatively small number among all possible arrangements) that will completely meet the goal.Finding a solution within a huge range of possibilities can be very hard, and this class is often attacked using computers - but beware, the class of edge-matching puzzles is NP-Complete .Arrange the tiles in a 3x3 grid such that the total in each square formed where edges meet totals 10.According to Jacques, this is the first known example of a Heads/Tails puzzle (the two numbers which must add to ten comprising the head and tail).The goal is to arrange the pieces in some simple configuration such that their features respect a given rule (or rules) - form a pattern - occasionally but not typically enforced by mechanical means.

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Jocelyn applied for a patent in Great Britian in 1892 (#3297 - I could not find a copy online - it is reproduced in Haubrich's About,...) in which they describe several triangular tile games and puzzles.

I've organized my example puzzles by tile shape: The Thurston design was used by Calumet ca. In the Calumet Puzzle, one must match not just the proper color edges, but also the corresponding top and bottom halves of the baking powder cans. Form a 3x3 grid such that there are four different colors in each circle at the corners, and two different colors in each half-circle.

I solved the Calumet puzzle using a variant of my Drive Ya Nuts technique. There must also be a different color at each of the four corners of the grid.

You can read more on this topic in Erik and Martin Demaine's 2007 paper Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity ( download a PDF here ).

Edge-Matching puzzles usually consist of a set of tiles whose edges have various distinct patterns, symbols, or colors.

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