This column will appear on April 2, 2016. Yesterday was April 1, or "April Fool's Day," the traditional date for all sorts of stunts and jokes. Do keep this in mind as we explore the "impossible" on a checkerboard.

In fact, today's problem is more in the nature of a "thought" problem. We know it's possible to construct positions that can't arise on the checkerboard. Here's one taken from "Impossible Settings" in Ben Boland's book, Famous Positions in the Game of Checkers.

BLACK

WHITE
White to Play and Win
W:W10,31:B1,3.

There are only four pieces in this position, but we'd like to challenge you to find the minimal position that can't possibly arise in play that follows the rules. Can you find an impossible setting with fewer than four pieces?

Click on Read More when you're done fooling with this and possibly wish to see the answer.

Solution

The following position is the smallest position that can never be achieved in actual play:

BLACK

WHITE
Either to Play!

Yes, an empty board contains zero checkers, and you can't get any smaller than that! There's obviously no way it can actually happen, short of dumping the last lone checker on the floor, which we wouldn't call a legal move.

And just for completeness, you'll find that if you play out Ben Boland's impossible 4-checker position, White will win by First Position.

Was this a suitable April Fool teaser? We hope you found it more amusing than annoying!