V
PROBLEMS
To offer an exhaustive treatise on the manifold varieties of Chess problems is not within the scope of this book. The intention of the author is merely to make it quite clear to the reader that the Chess problem, apart from the moves of the men, has no relation to the game and to illustrate the vast difference between PROBLEM combinations and positions and GAME combinations and positions by a few typical examples from the works of master composers.
The mating methods and mating positions in the actual game very rarely embody an element of surprise. They are all known from previous experience and the question is merely whether the player concerned is familiar with them. With the problem it is altogether different. Here the mate must be accomplished in a certain number of moves from a given position in some ingenious way which is not known from game practice, or, if the mating METHOD is not extraordinary, the mating POSITION must be surprising and unlooked for.
Moreover, a number of laws must be obeyed in problem composition, which by the general consent of problemists, or rather by natural evolution of a more refined taste, have become the standards by which the merits of a problem are judged.
There is first of all the law of economy in material which demands that the idea of the problem should be expressed with the least possible number of men, and that no pieces should be added for the mere sake of increasing the number of variations. Then, of course, a problem should have only one solution. A position which has more than one key move is not considered a problem, because the main point at issue in a problem is not the NUMBER of moves in which the mate is accomplished but the METHOD in which it is accomplished, and of two possible solutions one will always be prettier so that the existence of the other must necessarily appear a blemish.
A very important law is that the first move of White (who by general consent has always the attack) must not deprive the black King of a flight square, as this would be too brutal, too obvious a procedure. The more possibilities of defense are left to Black the more surprising is the solution and the finer is the problem.
Many problem solvers are under the false impression that the first move in a problem must not be a check. This argument is valid only when by the check the number of defensive moves is limited, but this is not necessarily the case, as can be seen for instance in problem No. 2, in which Black has to move his King anyway, there being no other black piece on the board.
The position of Diagram 76 is an example of how a problem should NOT be constructed. There is a tremendous number of pieces on the board which have nothing to do with the idea of the problem. The latter is one of the most primitive ideas used in problem composition and has been expressed by many composers in charming forms, so that there was no need for the above monstrous addition to the problem literature. The key move is Q-h7 so as to pin the Rook f5 in case Black plays K-d3 and to enable the mate (2) Rxf3. However, if Black replies (1) …, P-d3 or Bxe1, neither the Queen nor the Rook f4 are necessary, but the mate is accomplished by some of the other white pieces which are lavishly distributed over the board.
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8 | | | | | | | | ^Q |
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7 | | | | | | | | |
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6 | ^Kt| | | | #P | | | |
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5 | | | ^P | | ^P | #R | | |
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4 | ^B | | #P | #P | | ^R | | |
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3 | #P | | #K | | | #P | ^Kt| |
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2 | ^P | | | #B | | ^P | | |
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1 | ^K | #Kt| | ^R | ^B | | | |
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a b c d e f g h
DIAGRAM 76.—Mate in Two Moves
A striking contrast will be found in the following problem which is based on the same idea but in which all unnecessary material is dispensed with.
The key move is B-c1, in order to mate with the Queen on b3 in case Black takes the Rook a3. If Black moves the Rook, White mates by Qxb6, and if the Pawn b6 advances (2) Qxe7 is mate.
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8 | | ^K | | | | | | |
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7 | | | | | #P | ^B | | |
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6 | | #P | | | #Q | | | |
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5 | | | | | ^P | | | |
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4 | | #K | | | | | | |
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3 | ^R | | | | ^B | | | |
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2 | | #R | | | | | | |
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1 | | | | | | | | |
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a b c d e f g h
DIAGRAM 77.—Problem No. 1.
Mate In Two Moves.
In problem No. 2 the mating maneuver does not involve a special trick; the idea of the composer was merely to arrive at an extraordinary mating position, and he added considerably to the value of the problem by producing the same mating position in several variations. The key move is B-b3+. Black has three moves in reply. If K-e4, White mates by (2) Q-f2, K-d3; (3) Q-f3. If K- c6, the mate is accomplished by (2) B-b4, K-b5; (3) Q-b7; and if K-d6, White answers (2) B-c4, K-c6; (3) Q-c7 mate.
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8 | | | | ^K | | | | |
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7 | ^Q | | | | | | | |
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6 | | | | | | | | |
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5 | | | | #K | | | | |
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4 | | | | | | | | |
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3 | | | ^B | | | | | |
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2 | | | | | | | | |
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1 | | | | ^B | | | | |
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a b c d e f g h
DIAGRAM 78.—Problem No. 2.
Mate In Three Moves.
A favorite trick with composers is to provide a stalemate which they relieve by obstructing the way of one of the pieces involved in the stalemate. The move which is thereby allowed Black's King exposes him to a discovered mate. The key move of problem No.3 is P-g8 (becomes Knight). After P-b5 Black is stalemate, but White relieves the stalemate by (2) Kt-e7, allowing Black to take the Knight on b4, and then mates by Kt-c6.
In trying to solve a problem it is a good method to examine Black's moves first. Often it will be found that whatever Black moves White can mate in reply so that all that is necessary is to find a first move for White, which leaves the position unchanged as far as the different mating threats are concerned. If Black has one or more moves at his disposal in reply to which there is no mate, the way is indicated in which to provide for these defenses.
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8 | | | | | | ^B | | |
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7 | | | | | | | ^P | |
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6 | | #P | | | | | | |
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5 | | | | | | | | |
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4 | | ^Kt| | | | | | |
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3 | #K | ^P | | | | | | |
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2 | | | ^K | | | | | |
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1 | | | | | | | | |
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DIAGRAM 79.—Problem No. 3.
Mate In Three Moves.
In problem No. 4 for instance, it is evident that Black has to keep the two squares b8 and b4 guarded on which the Knight a6 threatens mate. Of course, Black can take the Bishop f5, relieving the mating threat but White can move the Bishop to some other square in the diagonal h3-c8. Still, Black would have the defense Q-f8. This suggests as White's first move B-c8, interrupting the line from f8 to b8.
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8 | | | | | | | | |
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7 | ^K | ^Kt| | | | | | |
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6 | ^Kt| ^P | #K | | | | | |
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5 | | #P | | #P | | ^B | | |
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4 | | #P | | | | #Q | | |
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3 | | ^P | | | | | | |
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2 | | | | | | | | |
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1 | | | | | | | | |
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DIAGRAM 80.—Problem No. 4.
Mate In Two Moves
The only square for Black's Queen from which to guard both b4 and b8 is then d6; but there the Queen blocks a flight square of the King, freeing the Knight b7 and enabling the mate Kt-a5.
The most difficult problems, of course, are those in which no mate is threatened in the initial position and in which Black can apparently foil all attempts to build a mating net. An example is the following position which illustrates the so-called "Roman idea."
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8 | | | | | | | | |
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7 | | ^Kt| | | #B | | | |
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6 | | | | | | | | |
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5 | | ^B | | | | | | |
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4 | ^K | | | ^P | | | | |
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3 | | | #K | | ^P | | | |
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2 | | | | | | ^Q | | |
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1 | | | | | | | | |
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a b c d e f g h
DIAGRAM 81.—Problem No. 5.
Mate In Four Moves.
Black's King is stalemate so that any check with the Knight would settle him. However, Black's Bishop guards the squares c5 and d6 from which the Knight could threaten a mate, and if White makes a waiting move with the Queen in the second rank to force Black's Bishop from his defensive position, Black replies B-g5 and takes the Pawn e3 on the following move, relieving the stalemate. The same maneuver would foil White's attempt to checkmate by (1) Q- e2, (2) B-d3 and (3) Q-c2, and the position really does not betray any other mating possibility.
The key of this exceptionally fine and difficult problem is (1) Kt-d6, forcing Bxd6. The idea of this sacrifice is to change the line of defense of the black Bishop from the diagonal h4-d8 to the diagonal h2-b8, so that he is compelled to defend the threat Q-e2, etc., indicated above by moving to f4, that is to a square on which he can be taken. After (2) Q-e2, B-f4; (3) Pxf4 the stalemate is relieved and Black can take the Pawn d4. But a most surprising mate is now possible, which could not possibly have been foreseen in the original position, namely: (4) Q-e5.
Problems in which no definite number of moves are stipulated for the mate are usually called STUDIES or ENDINGS. They are nothing but game positions in which a maneuver forces the win that is so well hidden that it would probably not be found by a player in an actual game. The following two positions are examples of this class of compositions.
The first move is evident. White must play (1) P-c7, as otherwise Black retreats with the Rook in the d-file and occupies the c- file so that he can be sacrificed at any time for White's dangerous Pawn.
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8 | | | | | | | | |
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7 | | | | | | | | |
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6 | | ^K | ^P | | | | | |
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5 | | | | #R | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | |
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2 | | | | | | | | |
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1 | #K | | | | | | | |
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DIAGRAM 82.—WHITE TO PLAY AND WIN.
After (1) …, R-d6+ White can neither go to b7 on account of R- d7 nor can he play K-c6 or c5 on account of R-d1 followed by R-c1 whereby Black would draw. The only way to win is: (2) K-b5, R- d5+; (3) K-b4, R-d4+; (4) K-b3, R-d3+; (5) K-c2. At last White has succeeded in guarding his rear, and it seems as if Black could not any longer prevent the Pawn from Queening. However, Black plays (5) …, R-d4 and if White queens the Pawn he gives check on C4 forcing Qxc4 which would stalemate the King.
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8 | | | | | | | ^K | |
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7 | | | | | | | ^P | |
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6 | | | #B | ^B | | | | |
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5 | | | | | | | | |
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4 | | | | | | | | |
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3 | | | | | | | | |
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2 | | | ^Kt| | | #P | | #P |
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1 | | | | #K | | | | |
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a b c d e f g h
DIAGRAM 83.—White to Move and Draw.
This is the point where the problem-trick enters the game. White does not promote the Pawn to a Queen but to a Rook, avoiding the stalemate and threatening mate on a8. Black's only defense is R- a4 and now White wins by (7) K-b3 attacking the Rook and threatening mate on c1 at the same time.
In the position of Diagram 83 Black threatens to queen either of his Pawns. White can play (1) Kt-e3+ K-e2; (2) Bxh2, but after Kxe3 there seems to be no way of stopping the Pawn f2.
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8 | #K | #B | | ^Q | | | | |
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7 | | #P | | | | | | |
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6 | #P | ^P | | | | | | |
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5 | ^P | | ^Kt| | | | | |
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4 | | ^P | | ^Kt| | | | |
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3 | | | | | #K | | | |
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2 | | | | | | | | |
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1 | | | | | | | | |
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DIAGRAM 84.—Sui-Mate in Six Moves
Again an ingenious trick is available which leads to an unexpected finish. White plays (3) K-h8 threatening to Queen his Pawn and forcing B-d5. Then he gives up his Pawn by (4) P-g8 (Queen) and after Bxg8 he saves the game by (5) B-g1 !! If Black takes the Bishop promoting the Pawn to a Queen or a Rook White is stalemate. Otherwise the draw is forced by either Kxg8 or Bxf2.
It remains to explain the meaning of the so- called sui-mates. A sui-mate is a problem in which White has to play so as to force Black to checkmate him (White) in a certain number of moves. One of the most beautiful examples in the literature is the above six mover, the solution of which runs as follows: (1) Kt-b5, Pxb5; (2) Kt-a6, Pxa6. One should not think that White can force Black to checkmate in four more moves; but: (3) K-d4, K-b7; (4) Q-d5+, K-c8; (5) P-b7+, K-c7; (6) K-c5 and Black has no other move except B-a7, checkmating White.
PART II
THE GAME OF CHECKERS
I
THE RULES OF THE GAME
The game of Checkers (English: Draughts) is played on the 32 black or white squares of the Chess board by two opponents, each of whom has twelve men of the same kind. The object of the game is to capture all opposing men or to block them so that they cannot move.
The original position of board and men is shown in Diagram 85. It will be seen that the board is placed in such a way that the players have a vacant square at their lower right hand corner. This corner is called the DOUBLE CORNER because two men are located in its immediate neighborhood while the left hand corner, the SINGLE CORNER, is occupied by only one man.
The squares of the Checker board are usually described by numbers as shown in Diagram 86. This is a rather crude method when compared with the simple notation by means of a system of coordinates as used in Chess, but as it is universally employed in Checker books and Checker columns in daily papers it will be adhered to in the following explanation of the game.
The black men are placed on the squares 1 to 12, the white men on the squares 21 to 32. The first move must invariably be made by the player of the black men.
32 31 30
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| | o | | o | | o | | o | 29
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28 | o | | o | | o | | o | |
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| | o | | o | | o | | o | 21
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20 | | | | | | | | |
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| | | | | | | | | 13
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12 | * | | * | | * | | * | |
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| | * | | * | | * | | * | 5
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4 | * | | * | | * | | * | |
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3 2 1
DIAGRAM 85.
The move of the Checker men is a diagonal step forward, one square at a time. If a hostile man is in his way and if the square beyond the hostile man is vacant, he must capture him by jumping over him on to the vacant square, and he must continue capturing from the square on which he lands as long as this is possible according to the above rule. Captured men are removed from the board.
WHITE
+———————————————————-+ | | 32 | | 31 | | 30 | | 29 | |———————————————————-| | 28 | | 27 | | 26 | | 25 | | |———————————————————-| | | 24 | | 23 | | 22 | | 21 | |———————————————————-| | 20 | | 19 | | 18 | | 17 | | |———————————————————-| | | 16 | | 15 | | 14 | | 13 | |———————————————————-| | 12 | | 11 | | 10 | | 9 | | |———————————————————-| | | 8 | | 7 | | 6 | | 5 | |———————————————————-| | 4 | | 3 | | 2 | | 1 | | +———————————————————-+
BLACK
DIAGRAM 86.
If a man reaches the opposite edge of the board he automatically becomes a King and must be "crowned" by the opponent, who must place another man on top of him. A King may move and capture backward as well as forward. A man, who reaches the "King row" in capturing, cannot, however, continue capturing on the same move with the newly made King.
The position of Diagram 87 may serve to illustrate the above rules. White, on the move, plays 14-9. Black must capture this man with the man on 5 who jumps on to 14.
32 31 30
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| | | | | | o | | | 29
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28 | * | | | | o | | | |
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| | | | o | | o | | * | 21
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20 | | | | | | | | |
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| | | | * | | o | | o | 13
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12 | | | * | | | | | |
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| | * | | * | | | | * | 5
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4 | | | | | | | | |
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3 2 1
DIAGRAM 87.
White then sacrifices another man by 23-18 forcing Black to reply 14-23. Now White captures the three men on 23, 15 and 7 with his man on 26, and Black, before making his next move, must crown White's man who has just reached the King's row. He will naturally move his man 8, as otherwise White would capture him with the King on 3.
If a player overlooks the possibility of a capture his opponent has the right to remove the man who should have made the capture, from the board. This procedure is called "huffing" and does not constitute a play. Instead of huffing a player may ask the opponent to retract his move and to make the capture.
When neither player can force a win the game is considered a draw. When one side appears to be stronger and refuses to accept a draw offered the player of the weaker side can require the win to be demonstrated within 40 moves; otherwise the game is drawn.