The concept of negative numbers is said to be due to the Hindu mathematician Brahmagupta, who defined them around the year 600 A.D; but the idea is even older, dating back at least to the Greek mathematician Diophantus, around 250 A.D., who wrote about "forthcomings" and "wantings" to represent the modern idea of positive and negative numbers.

An ancient idea indeed, although most historians believe the foundations of our game of checkers go back even further!

And this brings us to the point of today's Checker School session: a situation which as been referred to as Negative Second Position. No doubt you're familiar with the basics of the Second Position ending (it's been covered in a previous Checker School lesson); today's position changes, or perhaps negates, the value of a few of the pieces, changing White to Black, King to man, and vice-versa. If that's confusing, a look at the diagrammed position, attributed to W. Strickland, will clear it all up.

W. Strickland
WHITE

BLACK
Black to Play and Win

B:WK28,13,12:BK15,5,3.

Can you negate the difficulty of this problem and find the win? A negative attitude will never do! Think positively, find the answer, and then be certain to click on Read More to see the solution, a sample game, and detailed notes.

Solution

15-11, 28-32, 3-7, 32-27, 7-10, 27-31, 10-15, 31-27, 15-19, 27-32, 19-24, 32-28, 24-27, 28-24, 27-31, 24-28, 31-27, 28-32, 27-23, 32-28, 23-19, 28-32, 19-15, 32-27, 15-10, 27-23, 10-6, 23-18, 5-9, 18-22, 9-14, 22-25, 14-18, 25-21, 18-23, 21-17, 23-26, 17-14, 26-30, 14-9, 6-10, 9-5, 30-26---F, 5-1, 26-22, 13-9, 11-7. Black Wins---1.

The solution, sample game, and lettered notes come from Ben Boland's Famous Positions in the Game of Checkers.

Game: 10-15, 21-17, 11-16, 17-14, 9-18, 23-14, 8-11, 22-17, 4-8, 25-21, 15-18, 29-25, 16-20, 24-19, 11-15, 19-10, 6-15, 14-10, 7-14, 17-10, 2-7, 10-6, 1-10, 27-24, 20-27, 32-14, 10-17, 21-14, 12-16---A, 25-22, 16-19, 31-27, 7-10, 14-7, 3-10, 22-17, 5-9, 17-13, 8-11, 13-6, 19-23, 27-18, 15-31, 6-2, 11-16, 2-7, 10-14, 7-11, 16-20, 11-15, 31-27, 15-10---B, 14-17, 10-14, 17-21, 14-18, 27-31, 18-23---C, 31-26, 23-27, 26-22, 27-31---D, 22-18, 31-26, 18-15, 26-23, 15-10, 23-18, 10-6, 18-22, 6-10, 30-26, 10-15, 26-23, 15-10---E, 3, 23-18, 10-6, 18-14. Forms above position, colors reversed at 9th move.

A---Now No. 1461 in the Draughts Review, by N. T. Byars.

B---Now into Dr. T. J. Brown, No. 121 Liverpool Weekly Mercury, Apr. 30, 1892; Black---1,3, King 18 and White---21, 28, King 2. Black Plays, White Draws; 18-14, 28-24, 14-9, 21-17, 1-5, 17-13, 9-14, 24-19, 14-18, 2-6, 18-23, now the same. E. Clark in the May 20th Issue pointed out "Strickland's Second Position" Win.

C---18-15, 31-27, is No. 270 by W. J. Wood, Morris-Systems Checkerist. Alfred Jordan in his American Checker Player, Apr. 1913, Page 53, says, "This looks like an easy win by 18-23 but I have been unable to find a win by any move at all---2."

D---Dr. Brown here plays 28-24 to a draw as does Wood. M. C. Hammer in M. S. Checkerist for May 1925, thought he corrected Wood with this move.

E---In the July 1925 issue of M. S. Checkerist, Wood shows 15-11, colors reversed to draw. This was also pointed out by J. M. Cramer in Roseville Citizen, Dec. 1, 1932, to correct above game.

F---A. Jordan in his A. C. P. Apr. 1913, wins easier by: 10-14, 13-9, 11-7, 9-6, 7-2, 6-1, 30-26, 12-8, 26-23. Black Wins.

1---The man on 9 will soon be lost---Ed.

2---Computer analysis confirms that there is indeed no win to be found---Ed.

3---Indeed, this is the losing move while 15-11 would have saved the day---Ed.

The above position is No. 203 in the American Checker Review, Vol. 2, 1889, where it in turn was taken from the Leeds Mercury. The position has often been set at an earlier stage, the Black King on 15 to a man on 7, and the White King on 28 to a man.

The above game is No. 1530, Draughts Review, Vol. 7, July 1931, by N. T. Byars. Wm. Donaghy in Roseville Citizen, Nov.17, 1932, republishes the game as No. 3355, and at Note D plays 27-31 to correct Byars 28-24, which in turn is Dr. Brown's, see Note B and D. Byars terms this position "Negative Second Position.''

Editor's Note: Additional computer analysis and verification by Ed Gilbert's King's Row with 10-piece endgame database.