2) My first main failing was not being able to find a chessboad in the house. We claim to be civilized, educated men and yet don't have a chess set? After that, I struggled to find the pattern to the failings - a bunch of sketches on the back of scraps of paper. Only after asking my roomate for a inspiration and he told me to draw in the colors to the chessboard, did things become more clear. Then I played with permutations of the problem to get at some more basic answers.

3) At first I depended on myself and a pencil and a pencil and paper. I moved on to bugging my roomates as they came home.

4+5) I pretty much tried to put as many failed solutions together as possible and try to detect patterns in my failures.

6) A computer report the problem was impossible by doing a brute force test. It couldn't tell me why.

What have I learned? )

1) Own a chess set.

2) Own dominos.

3) Symetry of ignorance is a wonderful thing.

4) Be careful not to step on the power strip of your computer as you finish up your right-up.

5) Always look for patterns in your problems.

6) Change your methods and perspectives if things aren't coming clear.
7) Try reducing the problem. When I played with permutations of this problem, I realized that I would have been able to reach the same conclusion quicker had I reduced the problem. Slowly growing the problem from a 2x2 matrix to a 8x8 (only even numbers) let the fundemental problems be more clear. In a 2x2 or 4x4 exhaustive searches are doable and the results only need to be applied upwards. Of course, this won't always work, but it sure would have been handy this time.