Hello Pierre Charland,

I had spent some time making Tommy's original question into something more definite that could be solved, but I never actually tried to solve it. Thank you for finding and presenting the solution.

It is interesting to see that the number of regions is growing like a polynomial. Without seeing your solution, I might have thought that the number would grow exponentially, because at the beginning each new line cuts all the previous regions, which doubles the number. Of course, when there are already many regions, a new line will only cut a few of then, so the growth is not so fast -- polynomial becomes more plausible then.

Thank you,

Stuart Anderson