Lars' contest

This is a long-term (one month) programming contest. Definitely worth a look. Your job is to find an answer as good as possible to two hard problems.

1. Find zero-one matrices that maximize (determinant / one_count2);
2. Find a linear zero-one system of equations with a single solution such that the closest root to 1 is as close as possible but not quite 1.

The job of finding the zero-one matrix that maximizes the determinant has been a research math problem for over 100 years.