We had 90 minutes to work on this problem and submit a solution. I thought that would be plenty of time, as I had often done harder things in 90 minutes, as had many others in the room. I felt like I was not thinking clearly, and the time went by quickly. I was fortunate to find something that worked, and submitted my solution with a few minutes to spare. We had been told the solutions would be based on elegance.
Elegance is subjective, of course.
I would have preferred to use a constructive solution as they tend to be shorter and faster, but they are also more subtle to construct. That turned out to be the right strategy. Incidentally, I just have to mention that my solution actually produces the picture given to us during the contest, without rotation. Matthew's solution produces an image rotated 90 degrees.