A Puzzle While Waiting for Al Rodgers

I can't wait for Al tonight. And yes indeed we need to stay focused in these last few critical days/hours of the election season. But micro-breaks are healthy for maintaining focus, especially when they involve using different parts of the brain. The following was an extra credit addendum to my final examination in a sophomore Logic and Philosophy course.

Take an 8x8 chess/checkerboard and imagine being given 32 rectangular dominoes sized and shaped so that they can be placed on the board to cover all 64 squares. Now remove all of the dominoes from the board. Next cut off two opposing corner (diagonally opposed that is) squares from the board (either pair is fine). Also discard one domino.

Your goal now is to cover all 62 remaining squares with the remaining 31 dominoes. Show how you would do that or if you think it cannot be done, clearly prove it.

If you've seen this before, don't be a spoiler and blurt the answer out below. I guess the best way to handle that is to post "Answer" or "Possible Answer" in your subject heading and offer your idea in the body of your comment. This puzzle has an interesting, elegant solution.

P.S. Thanks to Melvin below for the nice visual aid. I'm too much of a newb to know how to include it myself just yet.