Would it be possible to fill the chessboard with dominoes?

Imagine a standard chessboard, but two squares with the same color are removed from the board. If a domino could take up the room of exactly two squares, would it be possible to fill the chessboard with dominoes so that none overlap or hang off the edge? Explain with logical reasoning.|||Not possible. The standard chess board is 64 squares, 32 black, 32 white. If you take two of one color away, you have 32 black and 30 white or 30 black and 32 white. When you put a domino down, no matter how you place it, you cover one black and one white square. So, assume you take away two white squares at the beginning.


After the first domino, you have 31 black and 29 white left.


After the second domino, you have 30 black and 28 white left.


After the third domino, you have 29 black and 27 white left.





Eventually, you will have covered all the white, and will still have 2 black remaining. No matter how the domino is placed, you cannot cover two black squares with one domino.|||it is only possible if you have 1 of each colour left over.


Any single domino can cover any 2 adjacent tiles, but each pair of adjacent tiles is 1 black and 1 white, so the dominoes are laid down in a -1b -1w format starting with either 32w +30b or 30w+32b in the equation;


30w+32b +x(-b-w) (where x is the number of dominoes)


or


32w+30b +x(-b-w) (where x is the number of dominoes)


is this is to have no overlap and no overhang the equation must be = to 0 where x is a integer (whole number)


as there is no solution that meets these conditions the answer to your questions is :





NO, it is not possible.|||Well there are 28 dominoes, which would take up a maximum of 56 squares. There are 64 squares on the chess board. If you take away two squares you still have 62. So there is no way 28 dominoes can fill 62 squares.