Use mathematical induction to show that a rectangular checkerboard with an even number of cells and two squares missing, one white and one black, can be covered by dominoes.

Question

anonymous · Answer

this one is best said in english
base case two square, $n=2$ one white one black, can cover with a domino

anonymous · Answer

now i guess we have to consider the case of an $m\times n$ rectangular checkerboard where $m$ is the width and $n$ is the length.

 we know that the number of square is even, which means either $m$ is even or $n$ is even ( or both)  let us say that $m$ is even 

remove the last two rows, so now you have an $(m-2)\times n $ checkerboard, which has an even number of tiles, and so 
by the induction hypothesis, 
can be covered by dominoes

the last two rows is $2\times n$ and that can clearly be covered by an even number of dominoes either again by induction (so we are using strong induction) or by the obvious fact that you can lay them one across and n up

clean this up and it should work

anonymous · Answer

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