Alex wants to cover a 30 by 30 board perfectly with 450 1 by 2 dominos. He also wants to ensure that he can trace a path between any 2 dominos that connect through at most \(N\) dominos. What is the minimum possible value of \(N\) which would allow Alex to form such a configuration?
Details and assumptions
A perfect covering of the board means that each square is covered by exactly 1 domino, and none of the dominos jut out over the board.
\(N\) would be inclusive of both the initial and the final domino.