You may be interested in the applet I wrote for solving Sudoku.  It's not  
the most effective solver - it was written to demonstrate my evolutionary  
algorithm library rather than to be the best solver.  Because it uses  
evolution it can occasionally get stuck on the last couple of cells (the  
likelihood of this diminishes as the population size increases).  Because  
of this, I doubt it qualifies as "elegant", but it does visualise its  
progress (by colouring cells) and may be a bit different to the other  
programs that you find.

    https://watchmaker.dev.java.net/examples/sudoku.html

(Requires Java 5 or later).

Dan.

What do you mean? A solver wouldn't need much of a GUI, just something
to input the problem, and to display the answer.  Or do you mean
elegant in the execution of the problem solving?

I never wrote a program to solve Sudoku mainly because the challenge
for me is to solve the problem myself.  If I just have to type it into
a screen and press "go", then I might as well get a data entry job
somewhere.

I can imagine though, as a tutorial for Sudoku solving, a program that
allows the user to enter the problem, and then clicks a "Step" button
that solves just one step, and how it got there.