see http://www.diophante.fr/problemes-par-themes/jeux-de-plateaux/5430-j164-ratissage-optimal
What is the least number of straight lines you need to draw across a n x n square grid so that every cell in the grid has at least one of the lines passing through its interior ?
It is conjectured that the answer is n - 1 for every n ≥ 3.
One can easliy exhibit a configuration of n - 1 straight lines entirely covering the n x n grid. But it is more difficult to prove that n - 1 is the miniumum number, and that no configuration of n - 2 lines exists.
This program constitutes a brute force exploration of this conjecture. In particular, it shows that the conjecture holds for all 3 ≤ n ≤ 8.
Program's output is shown below :
