I don't have time to read all the links in this thread but I used to draw mazes all the time in school. My approach was to start with an "in" tube and start bra

I don't have time to read all the links in this thread but I used to draw mazes all the time in school. My approach was to start with an "in" tube and start branching it, so long as I kept one branch open I could split and recombine all the others and know that I still had a valid maze. After I had filled up most of the page I would stop and declare the end position. It might not be clear from my description but I kept adding paths to the maze by doubling back on what was already there and building it out so it looked like a brain. The main point is that I kept one path open, never closing all my paths in a dead end. That way I knew there was a solution but since I did them so fast I wouldn't know the solution myself.