This is very close to the "percolation problem." [0] According to Robert Sedgewick, this particular problem has no known mathematical solution, and the thresho

This is very close to the "percolation problem." [0] According to Robert Sedgewick, this particular problem has no known mathematical solution, and the threshold (for a given N) is only obtained through, e.g. a Monte Carlo simulations where you randomly open sites until the grid percolates (akin to the adding of threads). The whole thing is a good application of the union find algorithm. The threshhold for N > 2 is about 60%. Not sure how that applies to software complexity, but it's interesting to think about. Thanks, Coursera! [0] http://en.wikipedia.org/wiki/Percolation_threshold http://en.wikipedia.org/wiki/Percolation_threshold