Simple depth-first search for Instant Insanity

Write a simple depth-first search for Instant Insanity, for puzzles of size 30 cubes. I will post up a 30-cube puzzle as well as one solution for it. You can test your program on this puzzle, although if you hit another solution, you will have to write a short program to verify that what you have found is indeed a solution. The purpose of this exercise is to see how sensitive the time-to-solution is to permutations in the input order of the cubes. You will first have to uniformly randomly permute the cubes. Perform as many random trials as you can, then display your time data in a histogram. Of particular interest would be the shape of the distribution, and the extent of the variation. To get credit for the program I will need a rough English description of your algorithm, as well as pseudocode. Note that I am not asking for a fancy algorithm here, although you are free to put as many bells and whistles in it as you want. I am really mainly interested in how sensitive your program is to changes in the input order, whatever (working) program you have. Now we know that there are 40! input orders-way too many to look at each one. That is why we are doing some random sampling. Depending on the underlying distribution, a fairly good picture of it can be had through sampling, as long as the samples are sufficiently random. And it helps to have a “large” sample. Doing 10, or even 20 runs would be insufficient.