B-Dazzle Scramble Squares

Christmas Day, I woke up to find Mike and Joannie working on a puzzle at the breakfast table. Nine squares, each with either the head or tail of a wolf on each side. The goal was to arrange the nine squares in one 3x3 grid so that the heads and tails matched up. There were four different wolves.
I spent a half hour before breakfast trying to tease it out, to no avail. I always got 8 pieces in place, the but the last piece never fit.
Rich and Carol let me bring it home with me to finish. At Derek's house I spent another hour on it, beginning to develop a system. 9 pieces, each of which can go in 9 positions, and within each of those 9 positions, each piece could be rotated into one of 4 orientations. The number of combinations is staggering: 9! * 4^9 or 95,126,814,720. However, one quickly realizes that the easiest way to solve the puzzle (short of using a computer algorithm) is to start with one piece as the center piece and then work out from there. You can choose any side of the center piece and there will only be several other pieces that connect to it. From there, there are only several pieces that can connect with those two pieces, and you can quickly determine which just don't work. It took me about five or six maddening hours of using that method to finally stumble across the solution, pictured below.
There may be other solutions, though I'm not certain. I know that in order to preserve my sanity I'm not ever going to touch this puzzle again.
Makes a great stocking stuffer, though. The puzzle is deceptively simple, the rules are easy, and you can drive people crazy with it. The puzzles are manufactured by a company called B.dazzle, Inc., and they're called Scramble Squares. You can purchase any of the dozens of variants of the Scramble Squares directly from B.Dazzle online for $9.95 each. There's an online sample puzzle at their website.