While we enjoy and appreciate both applied and abstract math, it can certainly be challenging at times, and we'll wager the young man above finds the going more than hard enough.

Today's position in our ongoing Checker School series is definitely hard enough, or, as it is attributed to old-time checkerist E. M. Harden, we can say it is Harden-nuff.

E. M. HARDEN
BLACK

WHITE
White to Play, Black Draws

W:W31,27,25,21,20,19:B14,13,12,11,10,5.

The position looks simple but in fact an unwary White or Black player can go wrong, and both sides must make a "star" move to save the draw; the terms could equally well have been "White to Play and Draw."

Don't "harden" your heart against this problem; it's instructive and intriguing. When you've worked harden-nuff on it, click on Read More to see the solution, a sample game, and complete explanatory notes.

Solution

Solution and lettered notes are from Ben Boland's Famous Positions in the Game of Checkers. Numbered notes are by the editor, using the KingsRow computer engine and 10-piece endgame database.

20-16*---1, 11-20, 25-22, 12-16*---A,2, 19-12, 20-24---B, 27-20, 10-15, 12-8, 14-18---C. Drawn

Game: 11-15, 23-19, 8-11, 22-17, 4-8, 25-22, 15-18, 22-15, 11-18, 17-13, 9-14, 29-25, 10-15, 19-10, 6-15, 26-23, 8-11---D, 23-19 (30-26, 11-16, etc. Draws), 7-10, 30-26, 2-6---E, 24-20, 15-24, 28-19, 11-15, 13-9, 6-13, 26-22, 15-24, 22-6, 1-10, 32-28, 3-7, 28-19, 7-11. Forms above position--- American Draughts Player, End Game No. 10, E. M. Harden corrects first edition.

A---10-15, 19-10, 12-16, 10-6, 16-19, 6-2, 19-24, 2-6, 24-28, 27-23, etc. White Wins.

B---W. Stuart, Game 1446, Draughts World, Oct. 1902, Plays: 10-15, 27-23, 20-24, 12-8, 24-28, 8-3, 28-32, 3-7, 32-28, 7-11, 15-19, 23-16. White Wins. See Note D.

C---A probable continuation: 8-3, 18-25, 3-7, 25-30, 7-10, 15-18, 10-15, 18-22, 15-18, 30-25, 18-23, 5-9, etc. Drawn.

D---Another Route: 7-11 (Losing Move), 30-26, 2-6, 26-22, 3-7, 23-19, 7-10, 13-9, 6-13, 24-20, 15-24, 22-6, 1-10, 28-19, 11-15, 32-28, 15-24, 28-19, 8-11. Forms above position. W. Stuart.

E---In Janvier's corrections to A. D. P., F. G. Fisk wins with 5-9.

1---This move looks strange, but it is the only move to draw for White. Consider one alternative line: 25-22 11-15 27-24 14-18 Black Wins.

2---5-9 31-26 10-15 19x10 12-16 26-23 White Wins.

Note the resemblance to Wyllie's Position, Page 161.