Challenge: Scramble Squares

A few years ago, I was sitting in the waiting room of my dentist's office waiting for my kids to finish their appointments.  On the table was a small wooden puzzle containing nine square pieces.  Each piece had half a picture along each edge.  The puzzle was to arrange the pieces into the 3x3 grid so that each edge matched on either side.  The head on one side of the edge matched the tail on the other side and the colors were the same.

Here's a simplified picture of a scrambled puzzle with all the pieces.

When it's solved, the colors all line up and each arrow head is connected to an arrow tail. In the picture above only two edges match up - the blue arrow in the first row and the red arrow in the last column.

I tried solving it but found it amazingly difficult. The receptionist looked over and said "Nobody's ever solved that."  I took that as a challenge.  I went home and wrote a program in Smalltalk to solve the puzzle.  I went back with my solution and amazed them by instantly putting all the pieces in the right places with the right orientations.

So, I challenge you.  Can you solve this puzzle?  Please don't put solutions into the comments - e-mail them to me at david@simberon and I'll announce the winner who solved the puzzle first.  Feel free to write the program in any language.  Next week, I'll post the Smalltalk source for my solution.

Have fun!