Given a $6\times 6$ chessboard. The chessboard is filled with $18$ dominos (each domino covers $2$ adjacent squares). Prove that one can find a line from the one side of the board to the other side of the board that isn't intersected by one domino.
In the trivial case you have exactly $3$ dominoes lined up in each column or row of the square. Then you'll get $5$ lines verticaly and $2$ lines horizontaly and you're done.
Please give me only a hint on how to proceed proving this generally.