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Falcon Chess

The following essay was written January 2000 for The Chess Variants Page. The Figures 1 through 23 referred to are from the United States Patent 5690334. The description of the falcon move is actually somewhat simplified from the more detailed description in that patent. Other topics of related chess variants, design considerations, and strategy go beyond the basic ideas in the Falcon Chess patent.

I. GAME RULES

-The Initial Set-up-

Figure 1 illustrates the initial position for Falcon Chess. As shown, one falcon for each player stands, to begin the game, between the queen and a bishop. A second falcon for each player stands between the king and a bishop. An additional pawn is positioned in front of each falcon. The orthodox chess game pieces have placements comparable to the standard game. That is, in order from the corner squares, are rook, knight, and bishop. Pawns are positioned in the second rank.

(While not discussed in the preferred embodiment of Falcon Chess, it is possible to play with fewer pawns, even just the five of the Chinese game. It is also possible to position the pawns initially in the third rank, rather than the second. If a game board of size ten by ten is used, one variation positions the pawns in the third rank initially, allowing for from two to five additional game pieces to be positioned within the second rank. These additional pieces may be weak, pawnlike ones, that is one- or two-square movers. Alternately, the additional pieces may include a novel major fairy chess piece or two, such as the giraffe of Timur's Chess.)

The orthodox chessmen retain their customary moves in Falcon Chess, and orthodox chess rules apply regarding the moves of the standard game pieces, play, capture, check, checkmate, stalemate, and draw.

-The Falcon's Move-

The falcon's novel move is three-square, made of both straight and diagonal steps. The falcon always combines two straight and one diagonal, or else two diagonal and one straight. Figures 2 through 7 (U.S. Patent No. 5690334) show six legal falcon moves. The two straight steps of one square each, or two diagonal steps of one square each, are in the same direction, in any order. A change of direction is by forty-five degrees. Every move has at least one straight step and at least one diagonal step.

Figures 8 through 13 are the other six falcon moves. Compared to Figs. 2-7, Figs. 8-13 are mirror images and have the forty-five angle turns reversed. Where 'S' is straight and 'D' is diagonal, the following list describes each of the twelve falcon moves as three steps of one square each.

                Fig. 2    Fig.  8     S S D
                Fig. 3    Fig.  9     D D S
                Fig. 4    Fig. 10     S D D
                Fig. 5    Fig. 11     D S S
                Fig. 6    Fig. 12     S D S   "split block"
                Fig. 7    Fig. 13     D S D   "split diagonal"

Note that the split block and the split diagonal cases each have two oppositely-oriented forty-five angle changes of direction.

All twelve movement patterns are always available to a player. In practice, the player is guided by the over-all falcon rule of movement, that is, two straight or two diagonal in the same direction, and one of the other, and also forty-five degree angle turn(s), with a total of three squares every move. Figures 14 and 15 illustrate that any one of the movement patterns can reach not just one, but four possible squares.

-The Three-fold Way-

Figures 16 and 16A show that any one square the falcon reaches can actually be attained three different ways. There is always this "three-fold way," following the rule of movement, for the falcon to reach the attainable square. Thus, the falcon has a "triple option" of patterns to move to a square. Three, and only three, of the movement patterns are possible for the falcon to move to any of its squares.

Figure 18 shows the importance of the three-fold way, since the falcon cannot jump. In Fig. 18, all the possible captures for the black falcon are shown by arrows. Like any chess piece, the falcon just moves to a legal square, and captures if possible. Whether one, two, or all three patterns are available does not affect the move itself.

Figure 19 shows that a falcon can reach up to sixteen squres, all marked with an 'F'. Of course, any and all of those squares can be reached three distinct ways. However, for simplicity, only one of the three ways to reach each square is shown in Fig. 19. The sixteen squares are the very squares that neither a queen nor a knight can reach from the same starting square.

-Strategy-

Figure 21 shows the falcon's forking ability, superior to any orthodox game piece. After the black side protects its king from the check, the white falcon can capture the black queen.

Figure 22 shows a position in which the white falcon is unable to move. Because the falcon move is always three squares, no move of only one or only two squares is allowed. In Fig. 22 the black pawns and some of white's own pieces prevent any falcon move at all for the turn. In contrast, a bishop, knight, rook, or queen would be able to capture one of the black pawns. The falcon is unable to do so, and in fact cannot even move from the position shown. This position clarifies the rule for the falcon move, a non-jumping move of a required three squares.

Figure 23 shows that "free castling" in Falcon Chess permits the king to move to any of the squares between itself and a rook in a castling move. The castling move is completed by the placement of the rook over the king to the adjacent square. As in orthodox chess, White starts, and turns alternate until a checkmate, or a draw. Expert players have found that games are decisive with few actual draws.

-Other Embodiments-

The most obvious variant is simply to replace the queen of orthodox game with a falcon. That is, the game is played on an orthodox eight-by-eight game board without a queen. Although the game is playable, one problem is that two natural opening moves of the falcon from the queen's position are to squares that opponent's bishop can threaten from its starting position, that is, a3 and b4, or else a6 and b5.

The next logical expansion utilizing a falcon is to expand to a game board of size nine by nine. In this variation, either the queen is omitted or else only one falcon is utilized. The queen is a good counterveiling power to the falcon, the drawback of the form that utilizes two falcons. If only one falcon is used along with a queen, there are obviously no opportunities for paired same-colored falcon interactions, and games largely devolve to orthodox positioning once a falcon is captured.

The major problem with a nine-by-nine set-up, whether or not two falcons are used, is that the size of board "unbalances" the bishops. That is, bishops cannot start on opposite-colored squares unless they are positioned unsymmetrically. A little experimentation with the nine-spaced back rank shows some alternatives, none of them desirable. One group of alternatives on 9x9 game board positions a falcon in the c-file, from which the falcon cannot move to its ideal flank position, a3, a less satisfactory set-up as experimentation shows.

Trial and error with the alternatives on game boards of sizes ranks 9-files 9, ranks 8-files 9, and ranks 10-files 9 show that the falcon is best utilized as a paired piece, like bishop, knight, rook. In fact, the falcon in our system is the fourth fundamental game piece, heretofor overlooked because the move is perhaps not quite so obvious as those of elemental bishop, knight, rook. The queen remains the most powerful piece and apposite counterveiling power. Once the falcon is introduced, having characteristics appropriately counter the other standard pieces, mere experimentation leads to the best game board sizes and initial positioning. The ten-by-ten, nine-by-ten, and eight-by-ten variants, retaining all the orthodox pieces are the most important ones, and the falcons positioned next to the king and the queen. All the considerations necessitate ten file rows, to optimize this chess re-design.

II. HOW THE FALCON MOVES

Falcon Chess was developed in the mid-nineties. The gameboard size is expanded to eight by ten, with the long dimension being left to right. The game pieces existing in traditional chess are the same and carry over to Falcon Chess, and in addition a new piece, the falcon, is created. The falcons are situated, to begin the game, between bishop and queen on one side, and bishop and king on the other. So, each player has two falcons: two white and two black falcons are added to the traditional chess pieces.

Also, each side gets two additional pawns, situated naturally in front of each falcon. Pawns retain their variety of moves, one or two for the opening, one after the opening, capturing diagonally one square forward, en passant, and promotion. The same goes for retaining the standard moves for rook, knight, bishop, king, queen. The labelling system for the ranks and files is expanded to include the two additional files, i and j. So, there are ranks 1 to 8 and files a to j, to correspond to the system in traditional chess. This system is just a logical extension of existing practice.

How does the falcon move? (Use of the word "step" in the following description always means a one-square advance, either straight or diagonal.) The falcon's basic move definition, in part, is two in a straight direction and one in a diagonal direction, or else two in a diagonal direction and one in a straight direction. The move is always a total of three squares altogether. It is crucial that the three straight and diagonal steps of one square not "double back" upon themselves. That is, falcon cannot pass through or enter a square that touches one it has previously passed through in the move. Both straight and diagonal adjacency are thus prohibited. Stated another way, a change of direction can be only by 45 degrees, never by 90 degrees or 135 degrees: the requirement of 45 degree turn(s) completes the definition of the falcon move.

An important variation of the basic move is thus included as legal. The falcon can split its "two straight" or "two diagonal" move in the following way. First, suppose a move starts in any of the four straight directions, forward, backward, to the right, or to the left. After a diagonal step of one square, falcon can finish the move either with another diagonal step in the same direction, or by returning to its original straight direction in a vector-like continuation. Likewise, when the first step of one square is any of the four diagonal directions, followed by a straight step of one square, falcon can complete the move by either another straight step in the same direction, or by a diagonal step in the original direction. As mentioned, in this three-square move, falcon cannot double back upon itself, assured not to happen by requiring any change of direction to be by 45 degrees and two such changes of direction in same move to be oppositely oriented. The legal moves are demonstrated in the sample moves in the figures.

The variations of the three-square move that have two oppositely-oriented changes of direction are called "split block" and "split diagonal." The basic moves, two straight and one diagonal, or two diagonal and one straight, including forms described in the last paragraph of splitting the block and splitting the diagonal, are heart and crux of how the falcon moves.

Take any one move of the falcon. Falcon can actually engineer any one move by any of three pathways, strictly following the definitions of the legal moves. This aptly-called three-fold way is shown in Figs. 16 and 16A. Of course, since the falcon cannot jump over other pieces, in an actual game, one or two or even all three of these movement patterns may be impossible. The falcon is unique in this respect, unlike say bishop or rook, which can only get to a given square in one way, that is, by one particular pathway, having as they do only one advancement pattern. If the target square is occupied, like other game pieces, falcon moves there only by capturing.

It is entirely up to the player which of the patterns of the move is used on a given turn. The situation is superficially like the choice in moving the knight in either of two ways, straight and diagonal, or diagonal and straight, two ways that the legal moves of the knight may be visualized. However, for falcon moves, it is critical that a move can be accomplished in any of three ways, because in an actual game, either zero or else one or more of the three ways may be possible, because of the positioning of intervening pieces. The basis of the distinction is that falcon cannot jump over other game pieces, as the knight can. In other words, the falcon move may be performed or not, according to whether a pathway is available; and only one pathway is sufficient to validate a move. If other pieces intervene, the move is illegal, just as a bishop or rook cannot pass through or over squares with game pieces upon them to get to a final square. Yet the falcon is unique among chess pieces in being able to execute a move one way that it cannot accomplish another way, so long as it uses one of the legal moves that fall within the over-all definition.

To expand the game board to the eight by ten size, it is necessary to consider a change in the white-black square configuration. One rule of thumb that queens initially stand on their own colors applies. However, from each player's standpoint, the rightmost square in the first file is a black square, so that the kingside rook is initially on that black square for White. (and queenside rook for Black) Moving medially from that rook, the kingside knight for White sits on a white square and the bishop on the next square sits on black. Thus the rightside, that is kingside, falcon for White stands on a white square, and so on with respect to Black's remaining queenside pieces.

Alternately, the obvious variation that does not reverse the colors of the bishops from the orthodox game is just as playable, reversing the above black-white pattern. This latter form of game board was favored seventy-five years ago by the world chess champion Jose Capablanca in his attempts, together with former chess champion Emmanuel Lasker, to expand chess to the eight by ten game board size. The present creation favors the schematic first described above as alternative form, in order to preserve the usual king-queen positioning that players are used to: queens start on own color facing each other.

In the original conception, the castling procedure was the same from the standpoint of the king. The effect is to have castling from either side, kingside or queenside, with the king moving two squares over towards a rook. A variation favored more now, allows the king to move any number of squares towards a rook, historically called "free castling."

III. NEW STRATEGY

The following remarks about strategy apply to all the large game boards, particularly when two falcons are utilized. The ideas apply whichever square pattern is used, and whether "free castling" is used or a modified free castling.

The falcon's opening move, after a move of a pawn, enables it to reach squares a3, a6, j3, or j6. These flank positions are surprisingly beneficial for the falcon to become actively involved in the opening game. The reason is that there the falcon is not easily threatened by pawns or any other piece. Those squares are out of the lines of the bishops importantly on 8x10 game board. Those squares cannot be reached by opponent's knights in two moves on that standard 8x10 board. And from those flanks, the falcon can move directly to either d4 and d5, or to g4 and g5, all of which adjoin the four central squares.

The game board sizes eight by ten and ten by ten retain a total of four central squares, important strategically to control early. However, control of the center is of less importance in Falcon Chess than in orthodox chess. The falcon's value along the flanks and interweaving behind advancing pawns make control of the center somewhat less important in the new game.

There are a far greater number of good opening moves in Falcon Chess than in orthodox chess. Any of the pawns in files c through h are possibilities for playable openings, either one square or two. Very quickly the numbers of combinations of plausible opening scenarios multiply. It is more likely intelligently to develop bishops (or falcons) earlier than knights in the new game, compared to orthodox chess. Alternately, the knight developed early is very threatening against initial positions. For example, pawns at c2, c7, h2, and h7 are initially unprotected and especially vulnerable to knight (and falcon) attacks. Similarly, bishops themselves are unprotected initially and, therefore,vulnerable at their initial positions to falcons especially.

The rooks are also easier to develop early in Falcon Chess than in the standard game. One reason that the rooks can be developed earlier in this new game, if a player chooses, is that the larger board lends itself to free castling, resulting in a rook's moving over to any of three or four squares, not just one particular square, in a castle. Bishops' long diagonal threatens rooks in their initial positions, so that care must be taken to protect the rooks by strategic positioning of knight and pawns.

The larger game boards utilizing ten file rows make it less dangerous to develop early all the major pieces: queen, falcon, rook. The reason partly is that there are more squares they can move to after leaving their initial positions. There is also the possibility of strategic exchanges for lesser value and better positional advantage, for example, losing one's queen for an opponent's falcon. There is wide opportunity in Falcon Chess for queen or falcon sacrifice outright for better position or initiative.

Exchange values of the game pieces remain about the same in Falcon Chess. Quite likely, the pawn is of more relative value than in the orthodox game. Here are estimates of these values from experience of hundreds of games played on the eight by ten game board: queen 9, falcon 7, rook 5, bishop 3, knight 3, pawn 1.2 . Research and time will tell whether the pawn's value increases as observed in this initial re-appraisal.

The falcon's value fluctuates more widely over the course of a game than any orthodox game piece, in terms of actual number of moves played and also in terms of possible over-all positions. The falcon's value tends to decrease in positions where many pieces are crowded together. Toward the end game, the falcon also generally assumes somewhat less value. It is not possible to achieve checkmate with king and one falcon against the enemy king. The situation is akin to the inability of king to mate with only two knights or only one bishop against king. However, the rook and king together of course can checkmate opponent's king. Therefore, the rook becomes generally more valuable than the falcon in the end game. It is important to approach the end game bearing in mind this relative weakness of the falcon. For example, one must have at least king, falcon, and some one other piece to have a chance for checkmate against lone king.

Falcon forks are frequent and exciting prospects in any game. These forks are hard to anticipate and often lead to a trap of opponent's major piece. Not infrequently, falcon forks the king along with some other game piece, or even two of them. Forks are all the more unanticipated because of falcon's interpositional maneuvering among pawns. These forks are sometimes disclosed not even by moving the falcon itself, but some other game piece, especially a pawn.

In the new game, the falcon is the only game piece that turns, or changes direction, in moving. The knight cannot be accurately described as making a change of direction, because of its jumping ability. The falcon's changes of direction are critical because the positioning of intervening pieces of either color may make a given move impossible. The falcon can change direction not just once, but even twice, in its three-step move, according to its rules of movement, the enumerated split block and split diagonal cases.

IV. SYMMETRICAL EXPANSION

A seven-by-seven array of squares, centered about a starting square, is useful to describe the squares the falcon reaches. In any array of squares, there must be an odd number, rather than even number, of squares forming the sides, in order to have one central square for a starting square. These relevant numbers are obviously 3,5,7,9. Note that these numbers are for array sizes to determine game pieces' movements: they are not necessarily associated with game board sizes that themselves may or may not be symmetrical, for example, and for which other logic obtains.

The three-by-three array of squares describes the squares the king reaches from the central square. The five-by-five array of squares includes, surrounding the central square, squares that knight, rook, and bishop reach. Next, the seven-by-seven array adds the squares that the natural continuations of the bishops and the rooks reach along their respective diagonals and ranks-files. In addition, the seven-by-seven array has some squares along its outer perimeter that knight, bishop, and rook cannot reach. The squares are from the starting central square those at the opposite corners of a three-by-four and of a two-by-four rectangle of squares. In describing moves to those "falcon squares," a three-square move to those squares is suitable if only forty-five degree turns, or changes of direction, are permitted. Otherwise, there would be an asymmetry in the ways to reach the "two-four squares" as opposed to the "three-four squares." The result is permitting three ways, and only three ways, to reach those "nonorthodox squares."

The next logical array of squares to design new game pieces within is nine-by-nine. The difficulty is that knight, by a continuation of its move in the same direction, can reach squares on the perimeter of the nine-by-nine array. A decision must be made then whether to allow the knight this continuation, or to design a new piece that reaches those squares. The squares in question are those reached by T.R. Dawson's knightrider by two knight-like movements in a line, namely, those squares at the opposite corner of a 3x5 rectangle. For the remaining squares on the outside perimeter of the nine-by-nine array that the orthodox pieces cannot reach, the logical development is for a new game piece that reaches alternative squares any of four different ways. Experimentation shows that this hypothetical four-square four-way game piece would reach, and thus "fill in" the remaining squares, those on the outside contour of the nine-by-nine array. The nonjumping game piece moves by combinations of straight and diagonal steps, at least one of each, with only forty-five degree angle turns permitted, for a total of four squares and four ways to reach each square. Actual use of such a new game piece probably requires a game board of size ten by twelve or greater. (For example, see Ralph Betza's "Chess on a Really Big Board" on Chess Variant Page.)

There is another consideration regarding the seven-by-seven array and its definition of the falcon move. The reason that a game piece was never developed before that reaches only those squares at the opposite of a two-by-four and of a three-by-four is that only extensions of knight-like moves were considered, that is, only jumping, or leaping, moves. Unfortunately, a piece that can jump,or leap, to the falcon's squares is too dominating, having even more value than queen. Lost is the balance of forces that made the orthodox game endure through the twentieth century.

The three-square movers that have been developed historically are either jumpers or reduced queens. (The latter is a type of "limited orthodox piece.") The important exception is that type that permits an unlimited three-square move, in combinations of straight and diagonal steps and changes of direction of 90 degrees and 135 degrees also permitted. Chiefly, Edgar Rice Burroughs' Jetan in "The Chessmen of Mars" has such an unlimited three-square mover, but the game abandons orthodox chess format because of the great power of this game piece.

V. MORE VARIANTS

-Xiangqi and Shogi-

Information about chess variants comes from many sources, not only patents, but also the books cited in U. S. Patent 5690334: H.J.R. Murray "A History of Chess" 1912, John Gollon "Chess Variations" 1968, David Pritchard "Encyclopedia of Chess Variants" 1994, and also from the website "Chess Variants Page" on the Internet.

Shogi and its variants, played largely in Japan, utilizes two pieces, gold and silver, that are one-square movers. These two pieces can move in directions other than the forward direction of the western pawn. In addition, shogi has a row of pawns that both move and capture in the forward straight direction, unlike the western pawn's forward diagonal capture. Some shogi variants have still more one-step movers that are essentially pawn-like. Also found in shogi variants are two-square movers, which are also pawn-like. In cases where not all directions are permitted, any nonjumping one- or two-square movers from known chess variants, such as the shogi variants, are regarded as pawn-like and, in essense, as pawns with particularized rules of movement.

Falcon Chess pawns do not necessarily have all the western, or orthodox, rules associated with their movements. Instead, in a variation a shogi pawn may be used in Falcon Chess, with the rest of the game remaining the same. Equally, a piece that moves like either gold or silver may be used in place of some or all of the pawns in Falcon Chess. These changes give rise to other embodiments of standard Falcon Chess. Use of a pawn with lateral one-square movement permitted may be most interesting in conjunction with the larger board sizes nine-by-ten and ten-by-ten.

Xiangqi, or Chinese Chess, permits its pawns to gain the ability to move laterally one square only after crossing the middle of the gameboard, so-called river. Xiangqi thus subdivides the gameboard into two halves, and within each half certain nine squares (technically points) are designated as a special area, so-called palace. Two pieces are only permitted movements within the palace, and only one other type of piece of its seven types may not cross the river. Similar subdivisions are possible for some unusual Falcon Chess variant just for a novelty. Such added elements are added game rules are thus subsumed under the Falcon Chess conception for game boards 8x10, 9x10, and 10x10.

Xiangqi has a game piece, the cannon, that captures after leaping over another piece along its path. The rule for the cannon in capturing is a little comparable T.R. Dawson's grasshopper. At least Dawson undoubtedly was aware of the cannon's move when he created the grasshopper. Dawson extended the grasshopper's move to all queen-lines, i.e., straight and diagonal, instead of cannon's only straight moves. From another perspective, the grasshopper becomes somewhat modified as a restricted, or limited, queen. Similarly, special rules for Falcon Chess bishops, rooks, or queen are possible, for a novelty, enabling jumping captures, or capturing after jumping, especially on 10x10.

While Shogi and Xiangqi suggest other pawn-like pieces, the following guidelines cover bishop-like and rook-like pieces. A game piece should be considered a bishop, or bishop-like, if its move offers a choice of one-square, two-square, and three-square movements, at a minimum, in two or more same diagonal directions. Likewise, a game piece should be considered a rook, or rook-like, if its move offers a choice of one-square, two-square, and three-square movements, at a minimum, in two or more same straight directions. Relatedly, a game piece should be considered a queen, or queen-like, if its move offers a choice of one-square and two-square movements in any one of all the same straight and diagonal directions. Such a one or two square mover as described is at the outer reaches of a pawn-like game piece, and more closely resembles a queen-like adaptation. Certainly, when a game piece offers a choice of movement from either one-, or two-, or three-square, in any one of all the same straight and diagonal directions, the game piece is queen-like. But attempts thus to label every game piece is a venture too deep into the jungle of classification.

-Changing Games-

Falcon Chess lends itself also to combination with other chess variants that change the rules of play rather than movements of the pieces in and of themselves. For example, various progressive forms of chess are possible wherein players have at times more than one move per turn. Random opening set-ups are possible, in which the major and minor non-pawn pieces are positioned at differing squares within the first rank. The best source for in-depth references of these classes of progressive chess and random chess is David Pritchard's "Encyclopedia of Chess Variants," including also historical and regional variants. While Falcon Chess has been described in its standard form as including all of the orthodox pieces, it is possible to play a variant of the game eliminating the queen, discussed under "Game Rules" above, or adding some other game piece in its place. By and large, chess variants utilizing a falcon on board sizes eight by eight and smaller are not so interesting. The reason is that on such game boards the natural opening set-ups of pieces in one rank row (excluding pawns) require this elimination altogether of one or more orthodox pieces, in order to include at least one falcon.

It is possible to position only some of the pawns in the third rank in the ten-by-ten gameboard size. The likely candidates are the central pawns in front of falcons, queen, and king. The a, b, c, h, i, and j pawns are then retained in the second rank for their initial positions, making for convenient castling positions and better protection of the king. The advantage of so advancing the central pawns is to enable other game pieces to be added, in conjunction with the larger board size. Additional pieces here are likely to be knight-like or else nonjumping one- or two-square movers. One game piece popular with variant designers is sometimes called a guard, having the choice of movement of one or two squares in any one of all the same straight and diagonal directions. As the earlier remark pointed out, this game piece is probably best characterized as a restricted, or limited, queen.

For all its popularity, chess as game and intellectual enterprise is far from perfect. Sometimes mentioned is the arbitrariness of queen's combining powers of rook and bishop, rather than knight with either of those. Also pertinent is juxtaposition initially of two game pieces with movement capabilities exactly the same, queen and its bishop, since both can move diagonally. Also mentioned is the difficulty developing rook early in the orthodox game. Another criticism is the "hole" in the seven-by-seven array of squares centered about a starting square. Why has no game piece up till now been able to move directly to those "unreachable" squares, at the ends of a 2x4 and 3x4 rectangle, in a nonjumping move? Another defect is the rigidity of the move to castle. Another is that the rule to promote pawn excludes logically rook or bishop as being reasonable choices. Why take a bishop when queen always has its capability? Another is the increasing frequency of draws as players become more highly proficient. The list of drawbacks could be extended into a long chapter.

Falcon Chess addresses and measureably remedies the malaise by the addition of the new game piece and its novel method of moving. As the fourth fundamental game piece, the falcon logically and effectively complements classical rook, knight, and bishop. In emerging new paradigm, falcon can combine coherently with those old, proven game pieces. Caissa, "The Chess", the world's best game devised, may move towards a more complete transformation, proceeding directly, or appearing variously and shifting, whilst established ways of playing go by or come to pass.

VI. MATE IN TWO

[A.]       --  --  --  --  --  --  --  --  --  --
        8                              R   K
           --  --  --  --  --  --  --  --  --  --
        7                              p   p   p
           --  --  --  --  --  --  --  --  --  --
        6
           --  --  --  --  --  --  --  --  --  --      White mates
        5                              WF  Wp  Wp
           --  --  --  --  --  --  --  --  --  --      in two moves
        4                              WN
           --  --  --  --  --  --  --  --  --  --
        3
           --  --  --  --  --  --  --  --  --  --
        2
           --  --  --  --  --  --  --  --  --  --      Solution:
        1          WQ                  WK
           --  --  --  --  --  --  --  --  --  --      1 Qxi7
            a   b   c   d   e   f   g   h   i   j


[B.]       --  --  --  --  --  --  --  --  --  --
        8
           --  --  --  --  --  --  --  --  --  --
        7   p      Wp       R
           --  --  --  --  --  --  --  --  --  --
        6                                      WR
           --  --  --  --  --  --  --  --  --  --      (White Mates
        5   K                                          in One Move) 
           --  --  --  --  --  --  --  --  --  --
        4
           --  --  --  --  --  --  --  --  --  --
        3  Wp  Wp       B   Q
           --  --  --  --  --  --  --  --  --  --
        2                          WK  
           --  --  --  --  --  --  --  --  --  --      Solution:
        1                                              c8, promotes
           --  --  --  --  --  --  --  --  --  --      to falcon
            a   b   c   d   e   f   g   h   i   j 
                  
[C.]         --  --  --  --  --  --  --  --  --  --
           8
             --  --  --  --  --  --  --  --  --  --
           7                              p    
             --  --  --  --  --  --  --  --  --  --     White mates
           6                                  p
             --  --  --  --  --  --  --  --  --  --     in two moves        
           5          K      wp                                                    
             --  --  --  --  --  --  --  --  --  --
           4 Wp
             --  --  --  --  --  --  --  --  --  --
           3         WK
             --  --  --  --  --  --  --  --  --  --
           2             WN
             --  --  --  --  --  --  --  --  --  --      Solution: 
           1             WF
             --  --  --  --  --  --  --  --  --  --      1 Fa3
              a   b   c   d   e   f   g   h   i   j


[D.]         --  --  --  --  --  --  --  --  --  --
           8
             --  --  --  --  --  --  --  --  --  --
           7                      K   p      WN
             --  --  --  --  --  --  --  --  --  --
           6                      p
             --  --  --  --  --  --  --  --  --  --     White mates
           5                  p                        
             --  --  --  --  --  --  --  --  --  --     in two moves
           4         Wp   p  WF      Wp
             --  --  --  --  --  --  --  --  --  --
           3
             --  --  --  --  --  --  --  --  --  --
           2  
             --  --  --  --  --  --  --  --  --  --     Solution:
           1 WR                  WF  WK                 
             --  --  --  --  --  --  --  --  --  --     1 Fxd4
              a   b   c   d   e   f   g   h   i   j

    
    A. Black: Rook h8, King i8; pawns h7, i7, j7
       White: Queen c1, King h1, Knight h4, Falcon h5; pawns i5, j5
       Mate in Two Solution: 1 Qxi7

    B. Black: Rook e7, King a5, Bishop d3, Queen e3; pawn a7
       White: Rook j6, King g2; pawns a3, b3, c7
       (Mate in One) Solution: 1 c8, promotes to falcon

    C. Black: King c5; pawns h7, i6
       White: King c3, Knight d2, Falcon d1; pawns a4, e5
       Mate in Two Solution: 1 Fa3

    D. Black: King e7; pawns c4, d5, e6, f7
       White: King f1, Rook a1, Falcon d4, Falcon e1, Knight h7; 
              pawns b4, f4
       Mate in Two Solution:  1 Fxc4
    
    E. Black: King b6, Knight c6, Bishop c8; pawns a6, c5
       White: King e1, Rook c4, Falcon d6, Falcon e4; pawn a3
       Mate in Two Solution: 1 Rb4

See also


Written by George William Duke. HTML conversion by David Howe.
WWW page created: March 13, 2000. Last modified: 18 August 2001.