You may enjoy this. It was published in I.A. Horowitz and P.L. Rothenberg, The Complete Book of Chess, Collier Books, 1963. Chapter 14, "Chessboard Recreations." However, its chess trappings are just for show: no knowledge of the game is required. Warning: it is tedious reading!
- - - - - -
What, a blank Chessboard? That is right. What is more, it is the only prop you need for what is the greatest puzzle ever conceived by man. You need no knowledge of Chess, checkers or any other game or stunt on the Chessboard to appreciate the wholesomeness and beauty of this poser. But you do have to muster that little bit of common sense and elementary reasoning which is often the key to ostensible mysteries. In short, finding the answer is most gratifying; failing to find it exacts a gasp at the fiendish simplicity of this gem. Observe.
Two men sit at a perfectly constructed Chessboard, each square of which is, to the nth fraction of an inch, exactly like any other. Each man has an unlimited number of Pawns at his disposal, each of which is also perfectly constructed, so that the diameter of the base of any one Pawn does not vary, by so much as the nth fraction of an inch, from any other. Each of the two men, in turn, places a Pawn – always in upright position – anywhere on the surface of the Chessboard. In the center of a chosen square, or at the edge, or at the line of intersection between one square and the one contiguous to it, or, actually, at the very edge of the board with but part of the base of the Pawn resting on the board.
Now then, it is stipulated that he who succeeds in placing the last Pawn on the board, with no space whatever left for his opponent to place an additional Pawn, is declared the winner. Who wins? The man who is first to place a Pawn on the board, or his opponent?
In the interest of guarding against captious stratagems, we add that the base of the Pawn is not larger than the surface of the entire chessboard. This would be a bit too inanely simple. It may be reasonably assumed that the base of the Pawn is much smaller than the are of each square.
- - - - - -
Can either side force a win? Okay, does the first player always win, or the second?
I'll invite speculation before revealing their answer, which is interesting, though I'm not sure that I agree with it.