Martin Gardner - The Mutilated Chessboard

Martin Gardner was a mathematician known for what is called recreational mathematics, puzzles, magic, and being cranky about pseudoscience.

His extensive writing about gematria…sorry.  Being invested in real math he wanted nothing to do with gematria.  Math and puzzles and in general Gardner’s world was filled with actual solutions to the questions.  Gematria, being the reigning champion of fake math and forcing the wrong answer to be viewed as correct is diametrically opposed to this.

My poor parents had their hands full with me as try as he might to hide them, Dad’s collection of chess books and Martin Gardner books as well as similar fare fascinated me.  Again with the facetiousness, they were just lying around on his desktop and on the bookshelf.

One of Gardner’s notable puzzles is the Mutilated Chessboard puzzle.

The challenge is this:  Take an ordinary chessboard, cut off two diagonally opposite corner squares.  Then get yourself some dominos, big enough to cover two squares at a time.  And answer this question, “Is it possible to cover the remaining 62 squares with 31 dominos?

The long answer, by trial and error, is to physically place dominos around and keep retrying until you get frustrated and bored and never get it to happen.  Which doesn’t prove you can’t, but intuitively you get a good idea that it’s not possible.  While you’re doing that you may get some critical thinking boosting and figure out the real answer.  A math based answer.  Or you flip the pages to the solutions section and read it and then it sinks in why the answer is NO.  You can’t do it.

The actual solution - each domino must cover exactly one light colored square and one dark colored square.  The corners you chopped off must be the same color.  So there’s 32 of one color and 30 of the other remaining, which can’t possible be handled by your 31 of each color dominos.

Or you can do a gematria style solution which is based on fake math and bullshit.  Gematria is all about convincing people to break the rules and that’s supposed to be a good thing.  Like Kirk reprogramming the computer simulation and being rewarded, the most ridiculous method of outstupiding your rival decoders is rewarded with the most attention.  So let’s run through some gematria style break the rules solutions.

1). 31x2=62.  End of story.  Yes it can be done.

2).  THIRTY AND ONE = 63 in both reduction ciphers, so that makes it doubly magically.  The corners cut off are the same color and are the same, so 64-1=63.  Bonus points for phraseshopping in the AND in THIRTY ONE.  Yes it can be done.

3).  The chessboard represents the eternal struggle between light and dark, good and evil.  Which are opposite sides of the same coin.  All the squares are the same color.  Yes it can be done.

4).  Chess is beyond my target audience.  That’s a checkerboard.  Checkers only cover one space at a time, fuck the dominos.  Yes it can be done.  Bonus points for getting away with not being challenged that chess pieces also occupy just one square.

5).  CHESSBOARD = 444 in the Satanic cipher.  Triple digits are cool.  The Satanic cipher is cool.  The Antichrist is coming, so that’s cool.  Yes it can be done.

6).  Cut one domino in half.  Yes it can be done.

7).  Cut all the dominos in half.  Yes it can be done.

8).  Cut all the squares off the board.  Let’s save time on a number nine and just cut all the dominos in half as well as cutting up the board.  Yes it can be done.

That could go on awhile because the gematria style solutions are only bound by imagination.  The only common factor is that deliberately getting the wrong solution and that making you a better person for being wrong has been achieved.  Appropriately, gematria does a lot of cutting in the process.  Large numbers are reviled.  They are chopped down into tiny bits with dropping digits and prime number lists all the time.  Which somehow makes getting the wrong answer much cooler.