In our elementary calculus classes, we all learned the right-hand rule, as demonstrated in the photo above, for finding a vector cross product. It's just a bit of simple mental gymnastics. (And, no doubt, we all learned that old, tired joke, "What do you get when you cross an elephant with a grape?")

Checkers, of course, provides its own excellent form of mental gymnastics, and no calculus classes, be they basic or advanced, are required. Today's problem in our continuing Checker School series will give us a good workout with a practical ending. The position is attributed to a Mr. D. Gourlay, and while it may be old, it is far from tired.

D. GOURLAY
WHITE

BLACK
Black to Play and Draw

B:WK27,25,21,9:BK30,K15,13.

Black is a man down; obtaining a draw is going to require some real thought. Exercise your mind, find the saving moves, and then exercise your mouse finger by clicking on Read More to see the solution.

Solution

The solution, sample game, lettered notes, and Boston Globe citation are taken from Ben Boland's Famous Positions in the Game of Checkers.

15-18---A, 9-5, 30-26, 5-1, 26-31, 27-24, 31-26, 24-19, 26-31, 19-16, 31-26, 16-11, 26-23, 11-7, 23-26, 1-5, 26-23---B, 7-2, 23-26. Drawn---3.

Game: 11-15, 21-17, 9-13, 25-21, 8-11, 17-14, 10-17, 21-14, 6-10, 22-17, 13-22, 26-17, 15-18, 29-25, 18-22, 25-18, 10-15, 24-19, 15-22, 27-24, 2-6, 32-27, 6-9, 24-20, 9-18, 23-14, 5-9, 14-5, 11-15, 19-10, 7-21, 28-24, 22-25, 24-19, 25-29, 27-23, 29-25, 31-26, 25-29, 19-15, 29-25, 23-18, 25-29, 18-14, 4-8, 15-10, 29-25, 14-9, 8-11, 9-6, 11-15, 6-2, 15-19, 10-6, 1-10, 2-7, 10-14, 7-11, 14-17, 11-15, 25-22, 15-24, 22-31, 5-1, 17-22, 1-6, 22-25, 6-10, 25-29, 10-14, 29-25, 14-18, 3-8, 18-15---C, 25-22, 24-19, 22-17, 19-24, 17-14, 24-19, 14-9, 15-10, 31-27, 19-15, 27-32, 10-7. Forms a variation of the above position, colors reversed, men on 21 and 30 surplus. Wm. Souter.

A---White's last move was 24-27; 9-6 would have won: 9-6, 15-18, 6-2, 30-26, 24-19, 26-31, 19-16, 31-26, 16-11, 26-23, 2-7, 23-19, 7-3, 19-23, 3-8, 23-19, 8-12, 19-23, 12-16, 23-26, 16-19, 26-31, 19-15, 18-23, 11-7, 31-27, 7-10, 27-31, 10-6, 31-27, 6-9, 27-31, 15-10, 23-18, 10-14, 18-23, 25-22---1. White Wins.

B---26-22, 21-17, 22-29, 17-14---2. White Wins. This variation was overlooked in F. Wright - W. Warburton, No. 16 Problemist's Guide.

C---Now No. 57, I. D. M. This corrects Wyllie's Switcher Book, Var. 99, at 28th move where 24-19 is played. E. Clark in Game No. 64, Sept. 1891, I. D. M. shows 24-19 to be a Black Win---4.

1---White finally will get a man through and win: 31-27 22-18 23-19 14-10 27-23 18-15 23-18 15-11 etc.---Ed.

2---29-25 7-10 25-21-10-15 13-17 15-19 17-22 19-23 22-25 23-26 25-29 26-30 29-25 14-18 25-29 18-22 White Wins. Who says checkers is easy?---Ed.

3---There is just no way for White to push a man through. A fascinating position---Ed.

4---Computer analysis with KingsRow shows 24-19 to indeed be a draw as originally postulated---Ed.

The above game is No. 94, International Draughts Magazine, Vol. 3, Nov. 1891. This position is No. 51, Gould's Problem Book.

GOOD MENTAL GYMNASTICS

Problem-solving is said to be one of the most useful mental drills for obtaining proficiency in actual games. It educates the brain for the concentration of thought, and for forming combinations many moves deep. Moreover, the practice gained in studying intricate positions --- no matter how unnatural such constructions may be --- is invaluable as a training for the higher draughts faculties. Problems should be solved from the diagram. If from the board, no pieces should be moved until the position is thoroughly mastered. ---Boston Globe

Oh, the punch line to the joke, "What do you get when you cross an elephant with a grape?" The answer, of course, is "elephant grape sine theta." Vector cross products, remember?