We're certain you'll be interested to know that 1004 is the Heptanacci number for n=12.

And that the "1004 Penthouse" is a popular economy lodging spot in Patagonia.

And that in the year 1004, Henry II of Germany became Holy Roman Emperor and a long war started almost at once.

In the world of checkers, though, there is problem number 1004 in Gould's Problem Book, and rather than further considering mathematical series, Argentine hostels, or medieval wars, we'd like to turn our attention instead to Ben Boland's detailed study of this difficult and controversial problem and its variants, which he in turn attributes to a William M. Courtney. As a lesson in our Checker School series, this one is long and demanding, but very much worth the effort.

Below we present six positions. It will take you some time to work through them all. When you've done so--- and no slacking, now!--- you can click on Read More to see the solutions, detailed notes and explanations, and numerous additional variations. Don't expect to finish up in an hour, or even a day; there's a lot of material here. We've quoted directly from Ben Boland's Famous Positions in the Game of Checkers.

A position by T. B. Murphy as No. 1004, Gould's Problem Book, Page 353, with solution on Page 367. A note on Page 375 says: "A very fine problem; the advantage of the Bridge and the King on 18---2 are sufficient to balance the inequality of pieces."

1---The position was originally, and incorrectly, published as "White Plays to Win"---Ed.

2---An evident misprint; the King obviously is on 19, not 18---Ed.

Solutions

Diagram No. 1: 13-9---1, 19-16---v14, 9-6, 16-19, 6-2, 19-16, 2-6, 16-19, 6-9---v13, 19-16, 9-13, 16-19, 7-2, 19-15, 13-17, 15-8, 17-14---v9, 8-11, 14-18, 1-5---v5, 10-6---4, 3-8, 6-1, 8-12, 1-6, 11-16, 18-15---v3, 16-20, 15-19, 20-16, 19-24, 16-20, 24-27---v2, 12-16, 6-10, 16-19---A, 27-32---v1, 19-24---B, 32-28, 24-27, 28-32, 27-31, 10-15, 20-24, 2-6, 31-26, 15-18---C, 26-31, 18-23---D, 24-28, 23-19---E, 31-26, 6-10, 5-9. Drawn.

A---Murphy left it here as drawn in Gould's Problem Book.

B---The continuation is by J. K. Lyons, solution to No. xxi in Horsfall's Problem Book. Variation 1 off Trunk; 20-24 loses and forms No. xxii by H. Morrall in Horsfall's Problem Book; 20-24, 10-14, 19-23, 14-18, 24-27---F, 18-22, 27-31, 22-25, 31-26, 2-6, 26-31, 6-10, 5-9, 10-6, 9-13, 6-10, 31-26, 10-15, 26-31, 15-11, 31-27, 11-16, 27-24, 16-20, 24-27, 25-30, 13-17, 30-25, 17-21, 25-30---G. White Wins.

C---6-10, 26-23. Drawn.

D---18-22, 24-19, 6-10, 19-23, 10-14, 23-26. Drawn.

E---6-10, 31-27. Drawn.

F---23-26, 18-23, 26-30, 32-28. White Wins.

G---Curious that a Bridge Position on one side runs into a Bridge Ending on the opposite side.

1---Computer databases today can give definitive answers in many endgame positions. This position is a database draw. KingsRow's line of play is 13-9 19-23 9-5 23-19 7-2 19-15 11-7 15x6 2x9 3x10 9-6 10-15 6-2 Drawn. Of course the computer goes straight to the optimal moves; consideration of the many possible variant lines of play is the subject of this study---Ed..

In March, 1923, American Checker Monthly, Page 75, the 1004 was republished as No. 29 and credited to Joe Collins with terms, white plays to win. A note added that it was Milwaukee Sentinel No. 24. The position also appeared as No. 123, by T. B. Murphy, in Wendemuth's Companion. The Collin's solution follows the Murphy solution for 32 moves then varies with 24-28 for a white win, where the latter plays 24-27 for a draw:

Variation 2 off Trunk; 24-28, 20-16---C, 2-7, 16-11, 7-16, 12-19, 6-10, 19-23---B, 28-24, 23-26, 10-14, 26-31---A, 14-18, 5-9, 18-23, 9-13, 24-20, 13-17, 23-27. White Wins. J. Collins.

A---26-30, 24-19, 30-26, 14-18. White Wins.

B---5-9, 10-15, 19-23, 28-24. White Wins.

C---12-16, 2-7, 16-19, 7-11, 19-23, 11-15, 23-27, 28-32, 27-31, 15-19. White Wins.

After Sentinel published this Collins solution to its No. 24, it recorded an interesting history of the problem from which we learn that No. 1004 was first published by Peter Thirkell, in Newcastle Chronicle in 1892 as a White Win. The Murphy solution for a draw to correct Thirkell's win was in the Draughts World, 1893, and later as No. 1004 in Gould's Problem Book. In 1909 Allen Hynd republished 1004 in Birmingham Post with the same line of play shown by Collins.

Play for a win was also demonstrated by Problem No. 45, in the North Rose Advocate, August 19, 1914, and have no information that the play has been corrected, leaving a question as to the terms of No. 1004.

From the Draughts World Gem No. 789, May, 1910, it appears that a great controversy raged over the terms to the above problem.

Variation 3 off Trunk; 6-10, 16-19, 18-15, 19-24, 2-6, 12-16, 15-11, 24-20. Drawn.

Variation 4 off Trunk; 2-6, 11-7, 18-14, 7-2, 6-9, 2-7, 9-13, 7-2, 13-17, then 2-7, 10-6, 7-10. Drawn.

Variation 5 off Trunk; 11-16, 18-23---v8, 3-8, 10-7, 8-11---v7, 7-3, 11-15, 3-7, 15-19, 23-27---A, 16-20, 7-11, 19-24, 27-32, 24-28, 2-7---v6, 1-5, 7-10,5-9, 11-15, 9-13, 10-14, 20-24, 15-18, 24-19, 18-22, etc. Drawn. McGill.

A--7-11, 16-7, 23-16, 7-10, 2-6, 10-14, 6-2, 14-10. Drawn. Hynd.

Variation 6 off 5; If 11-15, 20-24, 15-18, 24-20, 18-14, 1-5, 2-6, now same as No. 5932 in the Roseville Citizen, May 4, 1939, Forms Diagram No. 4, after first move.

Variation 7 off 5; 8-12, 23-27, 16-19---A, 7-3, 12-16, 3-7, 16-20, 7-10, 19-24, 27-23, 24-28, 10-15, 28-24, 23-19, 24-28, 15-18. White Wins by first position, Graham.

A---16-20, 7-3; 12-16, 27-23, 16-19, 23-16, 20-11, 3-7, 11-8, 2-6. White Wins. Graham.

Variation 8 off 5; 2-7---A, 3-8---B, 18-15---D, 8-12, 7-2, 16-20, 15-19, 20-16, 19-24, 16-20, 24-27, 12-16, 2-7, 16-19, 27-32, 20-24, 7-11, 19-23, 11-15, 24-27. Drawn. Hynd.

A---18-15, 16-11. Drawn.

B---1-5, 18-14---C, 3-8, 7-3, 8-11, 3-8, 11-15, 10-6. Drawn. McGill.

C---18-15, 5-9, 15-11, 16-19, 11-15, 19-23, 7-11, 9-13, 10-6, 13-17. Drawn. McGill.

D---7-3, 8-12,3-8; 16-19, 18-15, 19-16, 8-3, 16-20, 15-19. Drawn. Hynd.

Variation 9 off Trunk; 17-22 would be Diagram No. 2.

Diagram No. 2; 17-22, 8-11, 22-26, 1-5---11, 10-6, 3-8, 26-31, 8-12-v10, 31-27, 11-16, 2-7, 5-9, 6-2, 16-19, 7-10, 9-13, 2-7, 13-17, 7-11, 17-22, 11-16. White Wins. Morrall.

Variation 10 off Diagram No.2; 11-16, 2-7, 8-11, 7-10, 16-19, 31-27, 5-9, 6-2, 9-13, 2-7, 11-15, 10-14, 19-16, 7-10, 16-19, 27-23, etc. White Wins. Morrall.

Variation 11 off Diagram No. 2; 11-16---12, 2-7, 3-8, 7-3, 8-11, 26-23, 11-15, 3-7, 16-12, 23-27, 12-16, 27-31, 1-5, 10-6,. 15-18, 31-26, 16-19, 7-10, 5-9. Drawn.

Variation 12 off 11; 3-8, 10-7, 11-16, 7-3, 8-12/3-8, 16-20, 8-11, 20-24, 26-31. White Wins.

Variation 13 off Trunk; 7-2, 19-16, 11-7, 1-5, 6-1, 16-11, 1-6, 11-16, 6-9. Drawn.

Variation 14 off Trunk; 19-15---A, 9-6, 15-8, 6-2, 8-4, 7-11, 3-8, 11-16, T-5, 2-6, 8-12, 16-11. White Wins.

A---1-5, etc. White Wins.

Then No. 1004 reappeared about 1910 in "Notable Problems" by J. K: Lyons in Dunne's English Column, credited to Herbert Morrall, who corrects Murphy's draw and shows a White Win as in Variation 9, Diagram No. 2.

Diagram No. 3; See Diagram No. 2 and Variation 11.

Then No. 1004 appeared as No. 907, Glasgow Mail. Graham offered a prize. A. McGill sent play for both a draw and a win and got the prize. It varied a little from the Collins play. In Manchester Times, No. 1004 was No. 1470, and there Hynd showed a draw and corrected the Morrall play in Var. 9 above, and Diagram No. 3.

Diagram No. 4; 1-6, 20-16, 6-10, 16-11, 14-17, 11-16, 10-15, 16-20, 17-22, 5-9, 22-26, 9-13, 26-31, 13-17---A, 31-27, 17-22, 15-19, 22-25, 19-24, 20-16, 24-19, 16-23, 27-18, 25-30, 18-22. White Wins. Vair.

A---But F. Dalumi claims above position to be only a draw. At "A" play 20-24 instead of 13-17 and White cannot exchange in time to block the other Black King---1.

1---It appears Mr. Dalumi was correct. The computer scores Diagram No. 4 as a database draw, and agrees with Mr. Dalumi's correction at Note A. Interestingly, the computer's calculated line of play is rather different from the published line.

A Double Corner Game by Jackson—M'Ateer, from Eureka Checker Player 1920, published in Glasgow Herald.

Game: 9-14, 22-18, 5-9, 25-22, 11-16, 29-25, 8-11, 24-19, 10-15, 19-10, 6-15, 27-24, 16-19, 23-16, 12-19, 31-27, 14-23, 27-18, 19-23, 26-10, 7-23, 21-17, 4-8, 24-19, 9-13, 17-14, 11-15, 19-10, 2-6, 28-24, 6-15, 14-10, 8-12, 25-21, 12-16, 24-20, 16-19, 21-17, 19-24, 20-16, 24-27, 16-11, 15-18---A, 22-15, 13-22, 11-7, 1-6, 10-1, 3-19, 1-6. Forms Diagram No. 5.

This is now a prize problem as No. 15 in Eureka Checker Player, in 1920.

A---As originally played Jackson went 27-31 here and the game was drawn. Afterwards M'Ateer played 15-18 to a Black Win. The problem (is) No. 15, Diagram No. 5 above.

Fausto Dalumi offered this position as a correction of Searight's No. 51 in Hill's Manual. The original position has the White King on Square 1 and the terms are White (1-6) to draw, which forms Diagram No. 5.

Diagram No. 5; 27-31, 6-10, 19-24, 10-15---A, 31-26, 15-19, 24-27, 19-24, 27-31, 32-28---B, and the play goes on for many more moves, but is finally abandoned as drawn.

J. Jack received the Dalumi prize for play on the contingent that Gould's No. 1004 is a sound draw.

A---If 10-14, 31-26, Forms No. 1004, colors reversed.

B---This is now Diagram No. 6, as No. 45, Eureka Checker Player, by Fausto Dalumi. It seems to be a close relative of No. 1004, colors reversed.

Diagram No. 6; 22-25, 30-21, 26-22, 24-20, 31-27, 20-16---B, 23-26, 16-19, 26-30, 19-16, 30-26, 16-19, 22-18, 21-17, 27-23, 19-16, 26-31, 16-20, 31-27, 20-16, 27-32, 17-13---A, 18-14, 28-24, 32-27, 24-20, 27-24, 16-12, 23-19, 20-16, 19-15, 12-8, 24-19, 16-11, 15-10, 8-3, 19-15, 3-8, 10-6, 11-7, 6-1, 7-3, 15-11, 8-15, 14-9. Black Wins. F. Dalumi (J. Jack).

A---16-20, 23-19, 20-24, 19-15, 17-13, 18-14, 24-20, 32-27, 20-16, 15-10, 16-20, 14-9, 13-6, 10-1. Black Wins.

B---28-24, 22-18, 24-19, 23-26, 19-16, 26-31, 16-11, 27-24. Black Wins by First Position.

"It is true that I corrected Searight's solution, but there is a possibility that the original terms of the position are right; by varying at an earlier stage of the solution we have a position that contains the possibility of a draw. I say possibility, not certainty." Fausto Dalumi, Aug. 30, 1938.

It seems that the Double Corner Game here Jackson - M'Ateer, runs up to the Searight (Diagram No. 5) position. It may be added that M'Ateer showed the first win for the position and should get credit; and that Searight's play is a correction of M'Ateer.

It appears that the Searight solution may vary and run into the Murphy (Diagram No. 1) or Gould's Problem Book, No. 1004 solution, colors reversed, but it does not appear that No. 1004 may be run into the Searight (5) or the Dalumi (6) positions, with or without colors reversed, although the Dalumi and Searight positions are offshoots of the Murphy Problem.

There has been enough controversy and play published about No. 1004 and the various settings to fill a good book, and yet the result is so indefinite and complicated that no real fundamental theory has been set down by which a definite solution could be used under all circumstances. For practical purposes, however, the Gould Problem Book solution is, perhaps, as safe as any so far advanced.

If we are to credit the appearance of the position by priority of discovery and publication, this record shows that it first belonged to Peter Thirkell (1892) as a White Win, and still should be his although corrected and recorrected by such eminent players as Murphy, Collins, Hynd, Lyons, Morrall, Graham, McGill, Searight, Dalumi, Jack, and perhaps many others.

Editor's Note: As discussed above, the infamous checker problem No. 1004 is indeed a database draw. That is not to say that it is an easy draw, but the "truth" about the position is, in our age of powerful computers, quite clear.