Question 99
Consider tilings of a rectangular $m\times n$ board with $1\times2$ dominoes. Dominoes may be horizontal or vertical, but may not overlap or extend outside the board. Every square must be covered.
a) Prove that every tiling of a $4\times2010$ board has a straight line dividing the board into two pieces, with every domino lying wholly within one piece.
b) Prove that there is a tiling of a $5\times2010$ board with no straight line dividing the board into two pieces with every domino lying wholly within one piece.
a) Prove that every tiling of a $4\times2010$ board has a straight line dividing the board into two pieces, with every domino lying wholly within one piece.
b) Prove that there is a tiling of a $5\times2010$ board with no straight line dividing the board into two pieces with every domino lying wholly within one piece.