Math Snake Puzzle A colleague recently showed me the following puzzle game and I'm interested in how this can be solved. I thought it would be a good talking point for you guys as well :)

A detailed description of the puzzle is here.  A sequence of 7 cubes may be rotated about the axis.  The puzzle is to rotate them until all 4 equations are correct, such as $2 + 2 / 4 = 1$.  Operators are evaluated left to right.  The faces of the cube presented in the video (not agreeing with the image) are:
The following pictures show the sides...





Question
Other than trial and error, is there an easy way to solve this?

 A: The puzzle in the video only has 1 solution.
$$\begin{array} {|c|c|c|c|c|c|}
\hline
4 & -      & 3 & \times & 3 & = & 3 \\
2 & +      & 2 & \div   & 4 & = & 1 \\
1 & \times & 4 & -      & 2 & = & 2 \\
3 & \div   & 1 & +      & 1 & = & 4 \\
\hline
\end{array}$$
I doubt there is any significantly faster way to solve it than with a computer.  It's only $4^6 \div 4 = 1024$ cases to check.  I doubt there is a faster way than with a computer, since in general there can a large number of solutions.  This is a combinatorial logic problem, so it is NP, and I don't see any obvious way to put it into P.
A: I just realised that I didn't get it, I just thought all the cubes had to show different numbers/symbols.
A solution that uses each number exactly once, and two different operations
$$
\frac{4}{2}+1=3
$$
I found that thinking about what divisions were possible. Obviously we can divide by one, but then we're just left with one operation ($+$, $-$ or $*$) on $\{2, 3, 4\}$, so 9 possibilities, it's not hard to check all of them and conclude that there are no solutions.
If we want the division to give an integer result the only other option is $\frac{4}{2}$, and that gives the solution I've already named.
If we just ignore a remainder from a a division, we get more solutions, like:
$$
\frac{4}{3}+1=2
$$ 
