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Start Solving Now: Part I Print E-mail
By Gary Kevin Ware   
August 22, 2008
Part I: Mates in Two and Problem Anatomy
Solve et Coagula

Before delving into my column, I'd like to point out a mistake in the CLO preview of this article in the August Chess Life Magazine: The first position in this article by Otto Wurzburg, was incorrectly captioned as a mate in three. I submitted the problem as a mate in two, and the mistake probably came about due to fact-checking of the problem during the editorial process. The program that comes with chessbase, Fritz, does not always search for the fastest mate so if you plug a mate in two into Fritz, it will often tell you it's a mate in three. There is a way to change the settings so Fritz finds the quickest mate, but I don't recommend you use any computer programs at all to solve with you, as it defeats the purpose of chess problems. Speaking of which, I would like to revive the Solving Ladder. There is some missing data, and I would like to get some feedback from solvers as to the fairest way to proceed. You can contact me at [email protected] .

You may be wondering why a Latin phrase used in alchemy is the subtitle of an article on solving chess problems. Aside from the fact that I like puns, we are going to learn how to 'Solve', (dissolve, break up and analyze) and 'Coagulate', (curdle, bring together and synthesize) chess problems. Or, in other words, after breaking down a chess problem into all of its individual components, we will bring together everything that we have learned in the process to find the 'key' that will 'unlock' the entire problem. I will be writing, based not only on my own personal experience as an Expert Solver, but I will be 'distilling', another alchemical term, the wisdom of such composers as Sam Loyd, Brian Harley, Kenneth S. Howard, John Nunn and others.

In a composed chess problem, White plays first, makes the key move, and forces checkmate in the stipulated number of moves. Another key, overlooked by the composer, is called a 'cook'. Eugene B. Cook (1830-1915) had an outstanding reputation as a solver and for his ability to detect any flaw in a composition. While the origin of the term 'cook' is unknown, it has been suggested that it may have come from Cook's remarkable accuracy as an analyst. A problem is also unsound if it is found to have no solution, with some unexpected Black defense defeating the composer's intended key. It is also unsound if the initial position is one, which would be impossible to reach in actual play.

The two main types of problems are the Block and the Threat. A Block is a position in which the Key is a waiting move; it waits for Black to make a move allowing checkmate. In a Threat problem, the Key threatens a definite mate, which can only be refuted by allowing different mates.

Waiting move problems are further divided into incomplete and complete block positions. In the initial position of an Incomplete Block problem, mates are set for some of black's possible moves, but not all of them. So to solve an incomplete block, a key must be found that provides mates for those moves of black for which mates are not already arranged. In a Complete Block problem, there is a mate already provided for any move that black can make. So if White can make a first move that will not disturb any of the mates, "lose a move", the problem is solved.

However, few problems are constructed with such pure waiting move keys, as they can be solved too readily by merely examining each possible white move until one is found that does not affect any of the set mates. In most complete block problems, the key usually changes one or more set mates, and such problems are called mutates, a term coined by Brian Harley, author of Mate In Two Moves: The Two Move Chess Problem Made Easy and Mate In Three Moves: A Treatise on the Three-Move Chess Problem. When the key move allows Black to make defensive moves that lead to more mating positions than those in the initial setting, it is an 'added mate' problem. There are also Complete Block positions, which cannot be solved by a waiting-move key, and so White must make a keymove that threatens mate directly and such a problem is called a block-threat.

The first problem that we will look at is by Otto Wurzburg and the first problem that I recall solving. I will give a detailed analysis of my thought processes in solving it.

Otto Wurzburg The Atlanta Journal September 29, 1939
White to Mate in Two

Especially, in a mate in two problem, the first thing to look at is the 'set' position. That means that we pretend that it is Black to move first and see if every move is set with mate. The Black King has no flight squares, which makes things even easier. 1...Rxg8 is met by 2 Rxg8#. Other moves of the Black Rook are met by QxR mate. Any move of the Black knight unguards e2 and allows 2 Ne2#. Any move of the h7 pawn unguards the Rook and allows 2 Qxg6#. The move 1...h3 is a self-block. Whenever you see a move that takes away a potential flight square for the Black King, one should be alert for the possibility of either freeing up a piece that was previously guarding that square or in this case, blocking said piece with 2 Nf5#. 1...f3 is met by 2 Rxf3#. So all Black moves are set with mate and so we have a Complete Block problem. Now is there any way to make a waiting move to maintain the set mates? We don't want to move our knight at d4 as we want it to mate at e2 if the Black knight at c3 moves. Our knight at h2 has the function of over-protecting f3 if our knight at d4 moves. If our Bishop were to move to e7, for instance, Black could play 1...e6 and we don't have a mate next move. We want to keep our Queen at g8 to pin the Rook. We've seen that if 1...Rxg8, 2 Rxg8 is mate and so if the Rook moved along the back rank, that mate would still be set. But that would eliminate our set 2 Rxf3# after 1...f3. So we are going to have a changed mate or mutate. It looks like 1...f3 is our only problem and so how else can White mate if 1...f3 with the Rook moved along the back rank? 1...f3 gives the Black King f4 as a flight square and so 2 Nf5 does not mate. The only other possibility is Qb8 and the only way to effect that is with our key 1 Ra8, a clearance move.

Our next problem is also by Otto Wurzburg.

Otto Wurzburg American Chess Bulletin September-October, 1939, White to Mate in Two

There is a mate set for every black move except 1...Rg1 and so this is an Incomplete Block position. The key must provide a mate to follow this move, without disturbing other mating arrangements. 1 Ra2 qualifies, since after 1...Rg1, White now mates by 2 Rd2. The key unpins the black pawn, permitting black to play 1...c4, but then White mates by 2 Ra5. This is termed an added mate and the move of the rook back to its original square is called a switchback.

I said that a Complete Block position, in which there is a 'waiting move key' that does not disturb any of the 'set mates', would be too easy to solve. Let's see if that's true.

Kenneth S. Howard American Chess Bulletin July-August, 1925 , White to Mate in Two

In the Enjoyment of Chess Problems, by Kenneth S. Howard, he writes, "Since to solve a pure waiting move problem, it is merely necessary to find a move that does not alter the existing mating arrangements in any way, even a solver of limited experience can readily discover the key by the routine process of examining in turn each possible black move, noting the mate provided for it, and then by elimination determining what particular white move will not affect any mating provisions." The set mates include 1...Qxb8 2 Qc6#, 1...e3 2 Bf3#, 1...b2 2 Qa2#, 1...e8N moves 2 Q(x)d6#, 1...f8N moves 2 Q or B(x)e6#. Our bishop at b8 plays no active part in any of these variations and we want to leave everything else as it is. 1 Bxa7 is defeated by 1...Qc8, 1 Bd6 by 1...Ne6. 1 Bc7 allows 1...Qc8 but now because of the bishop on c7, she no longer guards c6 and so 2 Qc6 is checkmate.

Now, we will look at what is probably the first block-threat problem ever published.

Sam Loyd American Chess Nuts 1868,
White to Mate in Two

This is one of the most famous problems in the history of composition. 

Sam Loyd, "I will here allude to the feature of purposely posing a problem so as to deceive the solver as to the style to which it belongs and show that, while some real waiting positions are arranged so as to conceal the fact, it is also possible to give the deceptive look of a waiting problem to one that is not. Here, where Black's pieces are all locked so that there is a mate ready for every move and the only difficulty seems to lie in finding how to lose a move; it being unnecessary to remark that this apparent waiting condition is here introduced merely as a deceptive trick and takes no part in the solution, which is effected by a direct threat."

The change from a block, or complete waiting position, to a threat solution has a value greater than that attributed to it by Loyd as a means of deceiving the solver. It is the only legitimate way in which the problemist can compose two separate problems on one diagram. Initially, there is a two-mover to be examined, variations noted, tries investigated. All that is missing is a waiting key-move. Then suddenly comes the realization of the presence of a second problem, with its threat, and variations, and other details. Loyd, "Many would try 1 g4 and thus give it up as solved, or think I had slipped up in not seeing the defense of 1...hxg3 e.p."

1 Na3 threat 2 Qa7#
      1...Rxa3 2 Nb2#
      1...Kxa3 2 Qa5(7)#
      1...b2   2 Qb4#
      1...Nb4  2 Qxb4#

In a threat problem, the keymove sets up a definite threat of mate, either by the man that makes the keymove or by another one.

Kenneth S. Howard American Chess Bulletin November-December, 1939
 White to Mate in Two

Howard writes, "The solver will see that the only likely first move is 1 Bg5, threatening 2 Bh6#. There is nothing of interest in this and the threat is employed merely to force the thematic black defenses, 1...e6 and 1...e5, which produce the strategic play of the problem. A large percentage of threat problems have keys of this kind, whose only function is to bring black's thematic defenses into action. The two pawn moves permit the white queen safely to unpin the black one, and to deliver two long-range mates. This maneuver constitutes the Gamage theme, named after a famous problem by Frederick Gamage. This problem was constructed to show the theme in the lightest possible setting."
1 Bg5 e6 2 Qa8#
      e5 2 Qa3#

  The analysis of this next problem, by Comins Mansfield, comes from Brian Harley, in 101 Chess Problems For Beginners.

Comins Mansfield The Observer 1952
White to Mate in Two

"Before dealing with this problem, I will go into the witness box and state my own general process of solving. A glance at the composer's name may give an indication of the problem's style and whether it is worth solving. Then, can the Black King move? Then, can the Key make or maintain a Block? Negative evidence is presented by any Black unit, which cannot be prevented from moving, and in so doing will refuse to yield White a mate. Finally, I guess the theme, and test appropriate Keys. Now to this problem. A suspicion should soon arise that the position is already, or may be made, a block; the indications lie in the restriction of the Black forces, only the Knights and a Pawn being movable. Try out these moves: (a) if Black's Knight/b7 moves, White replies 2 Nb6#; (b) if Black's Pawn moves, White replies 2 Qxd6#; (c) if Black's other Knight moves, White replies 2 Ne5#. The theme is now apparent, for (a) and (b) constitute the familiar (to me) Half-Pin theme (happily so named by Mansfield). In this theme, a move by each in turn of two Black units, in line with their King, leaves the other pinned, allowing a Pin-Mate; the crucial line is called a half-pin line. The solver should now attempt Keys which will not disturb the thematic machinery; he will soon reject moves by the White Queen, Queen Rook, Bishop and Knights. A plausible try is 1 Rb8, but it is defeated by 1...Nd8, giving Black's King a flight-square, or Flight. There is nothing left but 1 Kb8, surprisingly allowing Black to check. While the mates are unchanged, this feature adds spice to the defense. In particular, the variation 1...N/b7 moves with discovered check allowing 2 Nb6# by interposition, shows a Cross-Check, a more artistic maneuver than the blunt 2 Qxd6# after 1...P/c7 moves.

In How To Solve Chess Problems by Kenneth S. Howard, Howard says, "In endeavoring to solve a problem, the solver may first examine its mechanical construction, or he may immediately seek to discover the theme the composer made the problem to illustrate. In actual practice, the expert solver may utilize either method, or a combination of both, depending upon the appearance of the position. The first method may be termed Constructive Solving, and the second Thematic Solving. An examination of the mechanism of a position often will disclose some constructional weakness, and in many instances such a defect will give a broad clue to the key. An example of a constructional defect is a white piece so obviously out of play in the initial position that the solver will see at once that in order to bring the piece into action, it must make the keymove. This is solving from the observance of Constructive Weakness." Here is an example of solving from constructive weakness.

Walter Jacobs, American Chess Bulletin November-December, 1941
White to Mate in Two

Ordinarily, the first thing an experienced solver notes in examining a position is whether the black king has a flight square. Whenever there is a flight square, it is highly desirable to have a mate set if the king moves onto it. Otherwise, it is an unprovided flight, which is considered as a constructive defect. When a solver finds an unprovided flight, he should look for a keymove that will produce mate when the black king occupies the flight square. In the present problem, the Black King can move to e5 without White being able to make a mating reply. So the key 1 c6, threatens 2 Rb5# and now if 1...Ke5, 2 Rc5#. The meritorious features of a problem may so outweigh a constructional weakness that it becomes negligible, except as a guide to the solution. Here, the key had the offsetting merit of permitting the white king to be checked.
1 c6 Rdd3+ 2 Rb6#
     Rxd1+ 2 Re3#
     Rxb3  2 Qh5#

A Black check for which no mate is provided is regarded as a still greater constructional weakness than is an unprovided flight-capture, yet unprovided checks are occasionally found in a problem with sufficient compensating features so that the position may even win a prize, as in this example by Frederick Gamage.

Frederick Gamage First Prize Cross-Check Section, Fourth Tourney C.C.L.A. 1939,
White to Mate in Two

Mates are set for 1...Qe4+ (2 Bxe4#) and 1...Qg1+ (2 Bf1#) and for the discovered checks from the black bishop except for 1...Bd5+. The solver will see that besides discovering check from the rook, this move cuts off the white queen's guard on c6.  He next will note that the white bishop on a3 is out of play. So he may try 1 b5, which guards c6, puts the bishop in play, threatens mate by 2 Nb7, and provides a mate for 1...Bd5+ (2 Ne4#). The constructional weakness of the unprovided check is more than offset by the four distinct cross-check variations.
1 b5 Bd5+ 2 Ne4#
     Bf5+ 2 Be4#
     Qg1+ 2 Bf1#
     Bg4+ 2 Be2#

This next problem is by Alexander Kish, who composed some of his best problems while incarcerated in an institution for the criminally insane.

Alexander Kish First Prize American Chess Bulletin Pawn-One-Two Tourney 1936
 White to Mate in Two

The white bishop at g6 cannot help in the attack until the diagonal is cleared by the removal of the knight, and then only as an additional guard of b1 and c2. So if the knight is moved, it must set up the mating threat; 1 Nd6, threatening 2 Nc4#. Since this reasoning gives a definite clue to the key, this is an excellent example of a problem most readily solved by noting a constructional weakness. Each of black's two thematic defenses, in addition to directly defending the threat, opens one line of guard and closes another.
1 Nd6 Rc5 2 f4#
      Nb6 2 f3#

We have already seen an example, Brian Harley, of solving a problem thematically, but here is another one, this problem by Frederick Gamage.

Frederick Gamage First Prize Cross-Check Section, Third Tourney C.C.L.A., 1938
White to Mate in Two

In solving thematically, the solver endeavors to determine from his initial examination of the position, the type of thematic play the composer is illustrating. Then he seeks the keymove necessary to make the scheme work. Frequently, this is a readier method of solving than to search for some weakness in construction. In this problem, one of the general themes easiest to recognize from the arrangement of the men is the cross-check. Note the relative positions of the white king and black's bishop on a1. If the knight on d4 was not pinned, it could discover check. So the expert solver will experiment by unpinning the knight by 1 Nc4 or 1 Ne4. Since 1 Nc4 can be met by 1...Rxc4, he will decide on 1 Ne4, which threatens 2 Rf4#. Then he will look for mates following each of the discovered checks from the black knight.
1 Ne4 Nde6+ 2 Nc3#
      Nf5+  2 Nf6#
      Nc6+  2 Nd4#
      Nb5+  2 Nd4#
For our last mate in two problem, we will look at yet another problem by Frederick Gamage.

Frederick Gamage First Prize The Falkirk Herald John Keeble Memorial Tourney 1940,
White to Mate in Two

When a solver sees a direct battery in a two-move problem, he can usually assume that the battery will be used for mating moves. One good way to find the solution is to work out the battery mates. If 1...Rxg4+ 2 Nxg4#; 1...Rxa3 2 Nd3#; 1...Bc4 2 Nf7#; 1...Bd7 2 Nc4#. Now, the solver's task is to find a threatened mate to which these black moves will be defenses. When he finds 1 Qb1, threatening 2 Qc1#, he may be surprised to discover that one of the set mates is changed; 1...Rxa3 2 Ng6#.

The next part will cover mates in three and four and will appear next week. Please contact Gary Kevin Ware at [email protected] with any questions about this article, future articles or reviving the solving ladder .

August - Chess Life Online 2008

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