# Domino covering

Discrete Mathematics Level 5

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.

×