The 65th square

The secret of Grandmaster play is to make use of the hidden 65th square on the chess board. I'm sure you've all had the experience of having a piece come at you, apparently out of nowhere, to take one of your army. That piece came from the 65th square.

I can't show you the square, because it's not on the usual 8x8 grid system, but I can show you that it is there. Watch...

Take a 8x8 chessboard (64 squares, right?), and divide it up in a special way:

                 5             3  



8
8x8=64 3




5                                                                                                                                                

 
             3              5  

These can be rearranged to make a rectangle. 

               5                  3                  5  



5
5x13=65 5


 
                           8                    5  

But of course, the 5x13 rectangle has 65 squares. I'm not sure which one is the extra square...

(Post inspired by Ivor Annetts, but puzzle devised by Sam Loyd, I believe.)

Chess Quotes

"In order to improve your game, you must study the endgame before everything else, for whereas the the endings can be studied and mastered by themselves, the middle game and the opening must be studied in relation to the endgame."
— Jose Raul Capablanca, World Champion 1921-1927

  [More endgame quotes?]