Mathematical Brain Teaser?

Question

It is easy to cover a typical 8x8 chessboard with dominos that cover two squares each. Now suppose you remove two diagonally opposite corner squares from the chessboard. Can you still cover what's left of the board with dominos?

And if you can't, how many would be left?

I mean if you can't cover all the squares, how many uncovered squares left are there?

Answer 1

You cannot. Each domino covers one black square and one white square, so the number of black squares and white squares covered by any arrangement of dominoes is equal. However, the squares in diagonally opposite corners are of the same color, so after removing them there would not be equal numbers of squares in each color, thus the remaining squares could not be covered by any arrangement of dominoes.

After the squares are removed, and as many of the remaining squares covered as possible, there would be two squares remaining, both of the opposite color as the squares you removed.

Answer 2

8 x 8 = 64 sq / 2 = 32 dominos

If you take two away, no you can't cover the board.

If you mean how many dominos would be left, that's 30.

If you mean how many squares would be covered, it's 60. Why?

Uncovered would be 64 total - 60 covered = 4 uncovered

or

2 squares per domino x 2 dominos = 4 squares

Answer 3

No. There would be 2 single (separated) uncovered squares.

Answer 4

Sure you can, just cut the last domino in half.

Answer 5

Not enough if you want to avoid cheating, and your partner has brain cells. Answer...all but the ones you covered.

Answer 6

tricky situation. look into into a search engine. this will help!

Answer 7

WTF you think i am smart????