Without the constraints that define some of the mathematical tangram patterns, there are a seemingly infinite number of possibilities. Beginning with the first books from China, tangram problems took on these more whimsical shapes, imitating a huge range of objects. Tangram patterns take the form of animals, buildings, household tools, people and vehicles. Even if it takes a little imagination to see the cat peering back at you from that blocky, triangular outline, that's part of the fun.
The only proven strategy for solving tangram problems is trial and error -- rearranging the shapes in multiple combinations until the answer strikes you. But, there are a few tips to solving the puzzles that you'll find in books, and these days, in collections of problems online.
First, it's always easier to begin by identifying any dangling pieces -- the tans whose outlines are either completely exposed, or exposed enough that no other tan could take its place [source: Koller]. Of course, some of the tans are interchangeable. The two triangles can form the same shape as the parallelogram or the square, for example, so that dangling cat's tail might not be as easy to fill in as you think. It's also helpful to make note of any corners that stick out of the figure. An exposed triangular edge would eliminate the square from fitting in that spot, for instance.
The most difficult puzzles to solve are those that have regular edges with no corners or edges exposed [source: Koller]. For example, the convex polygons discussed on the previous page are notoriously tricky to solve. Probably the most difficult problem is forming the perfect square [source: Koller]. Since most sets of tangrams are sold pre-assembled as squares, most tangram players will have to face that particular challenge every time they put their tiles back in the box. Representational figures (animals, buildings, etc.) tend to be easier, since they have more jutting pieces that form ears, legs and chimneys. Read on for more information on tangrams, and to find Web sites where you can make and solve your own problems.