EXACT ECHOES

Exact Echoes by G. P. Jelliss

Arrangement of Contents Introduction...... 1 4. 90° Rotations...... 25 1. Identity...... 5 5. 180° Rotations...... 28 2. Unit Translations...... 9 6. Lateral Reflections...... 29 2a. Vertical with pawns...... 9 7. Diagonal Reflections...... 36 2b. Horizontal with pawns...18 8. Transflections...... 41 2c. Pawnless...... 19 9. Multiple Echoes...... 42 3. Longer Translations...... 21 10. Fairy King Compositions...... 48

Introduction Repetition of the same pattern of pieces or moves at a different position on the board or at a different stage in the play, known as an echo, is one of the principal themes to be encountered in chess problems. It is a theme with both artistic and scientific appeal. The first published collection of problems showing echoes, in direct-mate chess problems, was Echo by František Dedrle (published in A. C. White's ‘Christmas Series’ in 1927). An extensive essay on echoes in help-play problems was ‘L'Echo dans le Mat Aidé’ by W. Roese (published in L'Echiquier September-October 1931, pages 1469-1487). One of the artistic and scientific aims with any theme is to show it in its purest, most economical, form. An exact echo occurs when all the pieces in the two formations concerned are in the same positions relative to each other, but possibly in a different position relative to the board. It is the pattern formed by the pieces that is echoed, not the actual pieces. For example, in a problem involving two white knights the two similar men may be interchanged between one formation and its echo. Similarly, in a pattern with pawns, their direction of movement may be different from one formation to the other. An echo is an overall visual or geometrical effect, and is independent of the underlying dynamics of move-power by which it may be accomplished. This document contains a collection of chess compositions that show exact echoes. The problems are classified according to the type of echo, and listed in each section according to the problem stipulation and the forces used, which may include fairy pieces. The idea for this study originated in the successful ‘Exact Echoes Tourney’ which was announced in Chessics issue 15 in 1983, entries being published in issues 17 to 21 and the award in issue 23 in 1985. Composers were asked to send in not only their original compositions but also outstanding examples of their previous work, or the work of others that they considered should not be missed, with a view to publishing a booklet on the subject. Thanks are due to Eugene Albert, Erich Bartel, Andrew Kalotay, Russell E.Rice, and Michael McDowell for providing examples, the latter especially of direct mates. However, this project was never completed, partly because of Eugene Albert’s more ambitious Encyclopedia of Ideal Mate Chess Problems, which was proposed around the same time, and would contain much of the same material. Twenty-five years on I can now publish the collection in electronic form (as a web page and as a PDF), but I have not so far attempted to bring the collection up to date to cover work done in the intervening years.

Echoed Play The emphasis here will be on exactly echoed formations (by which we mean an arrangement of pieces fixed relative to each other but not relative to the board). It is also possible to show echoed moves or play, but this is not studied here.

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EXACT ECHOES

The following curious example, which will serve to show exactly echoed play, was provided by Michael McDowell. I give diagrams of both parts of the twin for clarity. ------A. Benedek ¶H542 The Problemist v/1977 w______ww______w [wdwdwdwd][wdwGwdwd] [dwdw0wgw][Iwdw0pdw] [w0pdwdwd][wdpdw0wd] [dpdwdwdw][drdkdwdw] [BdwiwdrG][wdwdwdpd] [dw0wdwdw][dwdwdwdw] [wdw4wdbd][wgw4wdbd] [dKdwdwdw][dwdBdwdw] w------ww------w Helpmate in 2, (b) turn 90° clockwise. * (a) 1.Kc5 Bb3 2.Bd4 B×e7‡ (b) 1.Kc5 Bb3 2.Bd4 B×e7‡ ------It may be noted that turning the formation 90° is not quite the same as turning the position (consisting of board and men) 90°, since the latter reverses the chequering pattern, while the former moves the pieces relative to the board, leaving a1 as a dark square.

Types of Exact Echo In geometrical terminology, the echoed formation is related to the original by an isometry (also termed a ‘congruence’), that is a transformation in which all the relative distances and angles remain the same. Geometrical theory shows that these transformations are of five possible types: ‘identity’, ‘translation’, ‘rotation’, ‘reflection’ and ‘glide’ (also termed ‘glide reflection’). See for example Introduction to Geometry by H. S. M. Coxeter (John Wiley & Sons, 2nd edition 1969, page 46). Many works on geometry make no mention of the fifth type of isometry. In place of the terms ‘glide’ or ‘glide reflection’ I coined the more systematic name ‘transflection’, however the shorter term is often convenient, as is ‘shift’ for translation or ‘turn’ for rotation, where space is limited. In an identity the two formations are the same and similarly placed on the board. As mentioned earlier in the introduction, if there are two or more pieces alike it may be that they interchange places, since it is the visual pattern that is echoed. In a translation or ‘shift’ the pieces are in the same relative position to each other and the pattern is in the same orientation with respect to the board. All the pieces, in effect, move the same distance in the same direction. Translations can be of various lengths and directions, and can be specified by the leap {m, n} made by each piece (apparently) in making the transition direct from one formation to its echo. On the 8 by 8 board 35 different patterns of leap are possible, ranging from the {0, 1}, which is a single rook step, to the {7, 7}, which is a bishop move from corner to corner. The maximum area that can be occupied by the pattern echoed by an {m, n} translation on the 8 by 8 board is (8 – m) by (8 – n). Thus a {7, 7} translation could echo only a single cell. The shorter translations, with m and n taking the values 0, 1 or 2, are by far the most common types shown. Any combination of translations is equivalent to a translation or to the identity, which can be regarded as a null translation, of pattern {0, 0}. In a rotation all the pieces move through the same angle about a fixed point. A piece at the fixed centre remains unmoved. The angle of rotation, bearing in mind the chessboard pattern, can only be 90°, 180° or 270° (in other words rotations through one, two or three right angles). Following the usual convention in geometry, rotations anticlockwise are counted positive. A rotation of 270° anticlockwise is of course equivalent to a rotation of 90° clockwise. Any combination of rotations is

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EXACT ECHOES equivalent to a rotation or to the identity, which can be regarded as a null rotation, of 0° (or any multiple of 360°). The centre of rotation in the 90° or 270° cases can be at either the centre or corner of a cell. In the case of a 180° rotation, which is also known as a ‘half turn’, the centre may also be at the middle of the edge of a cell. It may also be noted that a 180° rotation can be regarded as a ‘reflection in a point’, namely the centre of rotation. However this is a different kind of transformation to reflection in a line which is what we now consider. In a reflection there is a line that acts like a sort of ‘mirror’, although it should be noted that a geometrical ‘mirror’ reflects on both sides. Pieces on the mirror line stay there while other pieces pass perpendicularly across the mirror line to a cell the same distance beyond it as they were before it. Because of the chessboard pattern of square cells reflections that always leave the pieces at the centres of the squares can only be ‘lateral’ (parallel to the sides of the board) or ‘diagonal’ (at 45° to the sides). A diagonal mirror must pass through cell-centres, but a lateral mirror either passes through cell centres or along the edges of cells, that is between two successive ranks or files. A transflection or ‘glide’ is equivalent to a reflection combined with a translation along the line of the mirror, or equivalently a translation combined with a reflection in a line parallel to the direction of motion. The simplest illustration of this complicated type of isometry is that of a pair of successive footprints, one of the right foot and one of the left. Transflections like reflections can be lateral or diagonal. In lateral transflections, as for reflections, the lateral mirror may be either a rank or file, or the line between two successive ranks or files. However, in diagonal transflections the mirror, may be a diagonal line through cell centres, but can also be a line midway between two successive diagonal rows. This type of transflection is difficult to visualise since the reflection places the pieces at the corners of cells instead of at the cell-centres. The translation component must then be of length (n+½) diagonal steps to ensure the pieces end up at cell centres, where the integer n is usually 0 or 1.

Notations In the source-details, given above the diagrams, dates are expressed with small roman numerals i, ii, ..., xii for the months, ¶ indicates problem number, # indicates issue number, these details are given, where known, to assist those who wish to check the original publication. In the solutions: † means check, ‡ indicates mate, = indicates stalemate, × indicates capture, Bk means Black and Wt means White. Using the usual algebraic chess notation, e4 means the centre of the cell in the e-file and 4- rank. Similarly de4 indicates the mid-point of the side common to the cells d4 and e4, and d45 the mid-point of d4 and d5, while de45 indicates the corner where the four cells d4, d5, e4, e5 meet. We sometimes refer to a rank or file simply by its number or letter, thus we can speak of reflection in e, or in 4, or in ef (the line between files e and f) or in 45 (the line between ranks 4 and 5). Similarly diagonals such as a1-h8 and b1-h7 are for short referred to as the diagonals a1 and b1, and the diagonal ab1, used in a trnasflection, describes the line between these two diagonals, joining the points ab1 and h87. The length of the diagonal of a cell (equivalent to 2 lateral units) is denoted by d. Thus the translation component in a diagonal transflection my be, say, ½d or 1½d. A unit translation vertically or horizontally is denoted by 1v or 1h.

Effects of Symmetry If the formation to be echoed has symmetry of some kind, by which we mean that its appearance may be unaltered by a rotation or a reflection, then the number of different echoes possible is reduced. Invariance to a rotation, known as centrosymmetry, does not usually occur in chess problems since every legal position contains only one white king and one black king. However, centrosymmetry is possible in problems where the white king is omitted, or where two or four white kings are permitted (multirex). Invariance to reflection, known as axisymmetry, is the normal type to occur in chess problems. For example if all the pieces are in the same file the line down the centre of the file is an axis of symmetry.

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EXACT ECHOES

A complication resulting from symmetry is that an echo of a symmetric formation may be classified in two different ways. For instance a set of pieces in one file may be translated horizontally to another file, but this can also be regarded as a reflection in the line midway between the files. Similarly reflection of the formation in a diagonal, transferring it from a file to a rank, can be regarded as a rotation about the cell where the rank and file cross. Thees are just the simplest cases.

Other Considerations Transformations of position that also leave the board unaltered, apart from chequering, are easy to visualise. They consist of rotations about the centre of the board, and reflections in the main diagonals or the medians. These we can call board transformations. It is not difficult to prove that any isometric transformation can be regarded as a board transformation combined with a translation. By this method transflections could be expressed in terms of components that always keep the pieces centred on the cells. An echo in which all the pieces are moved to cells of the opposite colour, as for example in a {0, 1} translation, is sometimes called a ‘chameleon echo’, perhaps because an echo without change of colour was thought to be simpler to execute, but this seems an unnecessary term, especially as the term ‘chameleon’ has other uses in fairy chess, referring to pieces that change their powers. An echo in which one of the pieces is a line piece is only considered to be exact if it is at the same distance from the other pieces in both formations. What may be called ‘near echoes’ are often seen in which a line piece stays where it is and the rest of the pieces move one step in the direction of its line of action. Such compositions are excluded from this collection, as are other near misses. Reflections of pieces in lines of nightrider {n, 2n}, camelrider {n, 3n} and zebrarider {2n, 3n} moves are also possible on the 8 by 8 board (and more general lines on larger boards) provided the pieces off the line are in suitable positions (i.e. on similar lines perpendicular to the mirror line). Some other related types of geometrical transformations occasionally seen in chess problems are dilatations in which all distances between the pieces are magnified or decreased by the same factor. Such dilatation may also be combined with the above isometric transformations. However for such transformations to preserve chess features such as checkmates it is necessary for the moves of the corresponding pieces to be transformed at the same time, or to be invariant to the transformation. A special case of this is a dilative rotation in which lines are rotated by 45° and multiplied by 2. This is a modal transformation which has the effect for example of converting a rook into a bishop, a bishop into a dabbabarider and a knight into a camel! There may be some controversy over the admission of twinning mechanisms in exact echo problems. Obviously twinning by moving all the men in the direction required for the echo would not be acceptable! But is moving one piece in this way acceptable? Certainly I feel that echoes produced by alternative play from one given position score more highly than twinning problems.

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EXACT ECHOES

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1. Identity Echoes Erich Bartel Edgar Holladay ------¶1270 Main-Post 3/v/1969 ¶45 Ideal Mate Review #2 Helpmates w______w iii-iv/1983 ------w______w Zvonimir Hernitz [wdwdwdwd] ¶51 Chessics #19 [dw0wdwdw] [wdwdwdkd] Autumn/1984 [wdpdwdwd] [dwdwdw4w] w______w [dw0wdwdw] [wdwdwdrd] [wdndwhwd] [whkdKdwd] [dwdwdwHw] [dPdwdwdw] [db0wdwdw] [wdwdwdKd] [wdpdwdwd] [wdNdwdwd] [dwdwdwdw] [dwiwdwdw] [dwdwdwdw] [wdwdwdwd] [wdPdwdwd] w------w [dwdwdwdw] [dwdKdwdw] Helpmate in 3, set mate w------w [wdwdwdwd] * Helpmate in 3, (b) g8 g7 [dwdwdwdw] 1._ Sa3‡ * 1.Ba4 Sd4 2.Bd1 Sb5 (a) 1.Kh8 Kh5 2.Rh6† K×h6 w------w 3.Bb3 Sa3‡ 3.Rg8 Sf7‡ Helpmate in 2, set play * (b) 1.Kh8 Kh5 2.R6g7 Kh6 * Tempo-loss manoeuvre by Bk 3.Rf7 S×f7‡ 1._ b8Q 2.Sb6 Q×f8‡ B. * 1.Sd7 b×c8Q 2.Sb6 Qf8‡ ------Changed capturing piece. ------Alexander George ------Eugene Albert ¶169 Ideal Mate Review #5 Eugene Albert ¶271 Ideal Mate Review #6 ix-x/1983 ¶52 Ideal Mate Review #2 xi-xii/1983 w______w iii-iv/1983 w______w [wdwdwIwd] w______w [wdwdwdwd] [GwdwdNdw] [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dkdwdwdw] [wdwdwdwI] [dwdwdwdw] [wdwdwdwd] [dwdwdwHw] [w)Ndwiwd] [dKdwdwdw] [wdwdwiwd] [dwdwdwdw] [w)wdwdwd] [dwdwHwdw] [wdwdwdwd] [dbdwdwdw] [wdwdwdwd] [dwdwdwdw] [w)wdwdwd] [dwdwdwdw] w------w [dwdwdwdw] w------w Helpmate in 3, 2 ways w------w Helpmate in 3, set play * Helpmate in 3½, (b) b5 b4. * 1.Kf5 Sb6 2.Ke6 Sd8† * 1._ Sh3† 2.Kg3 Sf2 3.Kd6 Bb8‡ (a) 1.Kc5 Ba4 2.b3 Ka6 3.Kh4 Sf5‡ 1.Ke4 Sd8 2.Kd5 Sb6† 3.b5† Ka5 4.b4‡ 1.Kg3 Se4† 2.Kh3 Sf2† 3.Kd6 Bb8‡ (b) 1.Kc3 Kb6 2.Kd4 Ka5 3.Kh4 Sf5‡ * 3.Kc5 Ba4 4.b4‡ * Two routes of Bk K f4-d6 form Changed routes by Bk K and The two routes of knight g5 - f2 hexagon. Pb2, while Wt K and other P form a square. moves form a circuit.

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5 EXACT ECHOES

------Eugene Albert Edgar Holladay Eugene Albert ¶20 Ideal Mate Review #1 (after T. R. Dawson) ¶275 Ideal Mate Review #6 i-ii/1983 ¶256 Ideal Mate Review #6 xi-xii/1983 w______w xi-xii/1983 w______w [wdwdwdwd] w______w [kdwdwdwd] [dwdwdwiw] [wdkdwdwd] [dwdwdwdw] [wdwdwdrd] [dNdNdwdw] [wdwdwdwd] [dwdwdwHw] [wdwdwdwd] [dwdw0wdw] [wdwdwdKd] [dwdwdwdw] [wdw0wdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdw)w] [wdwdwdwd] [dwIwdwdw] [wdwdw)Nd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdK] w------w [dwdwdwdw] w------w Helpmate in 3½, w------w (a) Helpmate in 4½, (b) h1 e4, (b) all up one rank Helpmate in 4, 2 variations a8 h1, Helpmate in 5 * * * (a) 1.Kh4 Kh8 2.Kh5 Rg7 1.Kc7 1... Sb6 2.Kb8 Kb4 (a) 1.Kg1 Kb7 2.Kf1 Kc6 3.Kh6 Rg8 4.Sf7‡ 3.Ka7 Sc8† 4.Ka6 Sc5‡ 3.Ke2 Kd5 4.Se3† Ke4 (b) 1.Kh5 Kh7 2.Se5 Kh8 1.... Sd6 2.Kc6 Sc8 5.f3‡ 3.Kh6 Rg8 4.Sf7‡ 3.Kb7 Kb4 4.Ka6 Sc5‡ (b) 1.Kh2 Kd3 2.Kh3 Kd2 * * 3.Kg4 Ke2 4.Kf5 Se3† Waiting by R in (a), K in (b). Interchange of knights (6-move 5.Ke4 f3‡ ------circuit). Two Bk K routes. ------William Anderson ------Jean-Marc Loustau ¶436 Ideal Mate Review #8 Frank Fillery and Michel Caillaud iii-iv/1984 ¶251 Ideal Mate Review #6 ¶244 Ideal Mate Review #6 w______w xi-xii/1983 xi-xii/1983 [wdwdwdwd] w______w w______w [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdNdwdw] [dwdwdwdb] [dwdwdwdw] [wdw0wdwd] [wdwdwdwd] [wdwdwdBd] [gwdkdwdw] [dwdwdwdw] [dwdwdr)w] [w0wHw0rd] [wdwirdwd] [wdwdk)Kd] [dwdKdwdw] [dPdwdwdK] [dwdwdwdw] [wdwdwdwd] [wdP)wdwd] w------w [dwdwdwdw] [dwdwdwdw] Helpmate in 3½, (b) e2 g2 w------w w------w * Helpstalemate in 4, (b) a5 g5 Helpmate in 5, (b) h7 g6 (a) 1.Bh3 Rf4 2.Kg1 Kf3 * * 3.Kf1 Rg4 4.Bg2‡ (a) 1.b3 S×b3 2.Bb2 S×d2 (a) 1.Re6 Kg4 2.Rg6† Kf5 (b) 1.Ke1 Rf4 2.Bh3† Kf3 3.f3 S×f3 4.Rd4† S×d4= 3.Rg4† Ke6 4.Bd3 Kd6 3.Kf1 Rg4 4.Bg2‡ (b) 1.f3 S×f3 2.Bd2 S×d2 5.Re4 c3‡ Triangle to parallelogram. 3.b3 S×b3 4.Rd4† N×d4= (b) 1.Re1 Kg4 2.Bh5† Kf5 K routes form circuit. Both ways round knight circuit. 3.Be2 Ke6 4.Bd3† Kd6 ------5.Re4 c3‡ R circuit in (a) switchback in (b) ------

6 EXACT ECHOES

------Helpstalemate Fairy Pieces Erich Bartel ------¶134 Kold B 23/xi/1969 Norman A. Macleod Erich Bartel w______w ¶323 Ideal Mate Review #7 Frankfurter Notizen [wdwdwdwd] i-ii/1984 10/x/1968 [dwdwdwdw] w______w w______w [wdwdwdwd] [Kdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [iw1wdwdw] [iwdwdwdw] [dwdwdwdw] [wdKdPdwd] [Pdwdwdwd] [wdwdw1wd] [dwdwdwdw] [dwdwdwdw] [dwdQdKdw] w------w [wdwdwdwd] [wdwdwdwd] Equihopper [dwdwdwdw] [dwdwdwdk] Helpstalemate in 5, set play w------w w------w * Helpstalemate in 5½, set play Equihoppers 1._ e4 2.Eg5 e5 3.Ec5 e6 * Helpmate in 2, set play 4.Ka2 e7 5.Ka1 e8E= 1._ Kb6 2.a5† Kc7 3.Ka7 Kc8 * 1.Ec1 e4 2.Eg7 e5 3.Ka2 e6 4.Kb6 Kb8 5.a6 Ka8 6.a7= 1._ Kg3 2.Eh2 Kf2‡ 4.Ec5 e7 5.Ka1 e8E= 1.Kb8 Ka6 2.Kc7 Ka7 3.a5 Ka8 1.Eb2 Ke2 2.Eh2 Kf2‡ ------4.Kb6 Kb8 5.a6 Ka8 6.a7= ------Eugene Albert ------Erich Bartel and P. Kniest feenschach 1964 Serieshelpstalemate Diagramme und Figuren w______w ------1968 [wdwdwdwd] Erich Bartel w______w [dwdwIwdw] ¶254 Ideal Mate Review #6 [wdwdwdwd] [wdwdwdwd] xi-xii/1983 [dwdwdwdw] [Hwdqiqdw] w______w [wdwdwdwd] [wdwdpdwd] [wiwIwdwd] [dwdwdwdw] [dwdwdw)w] [dPdpdwdw] [wdwdKdwd] [wdwdwdwd] [wdBdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [ndwdwdwd] w------w [wdwdwdwd] [iwdwdw!w] Grasshoppers [dwdwdwdw] w------w Helpmate in 3, set mate [wdwdwdwd] Equihopper * [dwdwdwdw] Helpmate in 4, (b) g1 e7. 1._ Sc6‡ and w------w * 1.Gd3 Sb3 2.G5f5 Sd4 Serieshelpstalemate in 7, (a) 1.Sb4 Ec7† 2.Sd5 Ee3 3.G3d5 Sc6‡ (b) d7 e7 3.Sc3† Kd3 4.Sa2 Kc2‡ * (a) 1-5.d1(B) 6.Bg4 7.Bc8 (b) 1.Sc1 Ee1† 2.Se2 Ee3 Interchange of Gs b7×c8(S)= 3.Sc3† Kd3 4.Sa2 Kc2‡ ------(b) 1-5.e1(Q) 6.Qe6 7.Qc8† * b7×c8(S)= Two different Bk knight ------circuits. ------

7 EXACT ECHOES

------P. Kahl feenschach 1951 Erich Bartel, Poldal-Tournier Erich Bartel w______w d.S.K.Kriegshaber ¶9678 feenschach v-vi/1976 [wdwdwdwd] 16/viii/1969 w______w [dwdqdwdw] w______w [wdwdwdwd] [wdwdNdwd] [wdwdwIwd] [dwdw1wdK] [dwdwdwdw] [dwdwdwdw] [wdwdwiwd] [wdwdwdwd] [wdwdqiwd] [dwdwdwdw] [Iwdwdwdw] [dwdwHHdw] [wdwHwdwd] [wdwdwdwd] [wdwdqdwd] [dwdN1wdw] [iwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w [wdwdwdwd] [dwdwdwdw] Grasshopper [dwdwdwdw] w------w Helpmate in 4, set play w------w Grasshoppers and Nightrider * Grasshoppers and Nightrider Helpstalemate in 2, 1._ Sd4 2.Gd3 Se2 Helpstalemate in 2, set play 2 ways and set play 3.Gf1 Sc1 4.Gb1 Sb3‡ * * 1.Gf5 Sf4 2.Gf3 Se2 1._ Sf3 2.G4g6 Nh1= 1._ Nf4 2.G3g5 Nd3= 3.Gd1 Sc1 4.Gb1 Sb3‡ 1.G6g6 Nh1 2.G4e6 Sf3= 1.Gc5 Sf5 2.G5g5 Sd4= ------* 1.Gg5 Se6 2.G3e7 Sd4= Erich Bartel Interchange of Gs ------¶1695 Europe Echecs ------W. H. Reilly Fairy Chess 5/iii/1971 Erich Bartel Review 1944 w______w ¶Feladv. Lapja xi/1969 w______w [wdwdwdwd] w______w [wdwdwdwd] [dwdwdwdw] [wdwdKdwd] [dwdwdwdK] [wdwdwdwd] [dwdwdwdw] [adwdwdwd] [dwdw1wdK] [wdqiwdwd] [dwdwdwgw] [wdwdNiwd] [dwdwdwdw] [wdwdwdkd] [dwdwdwdw] [wdqdwdwd] [dwdwdwdw] [wdwdwHwd] [dwdNdwdw] [wdwdwdwd] [dwdw1wdw] [wdwdwdwd] [dwdwgwdw] w------w [dwdwdNdw] w------w Grasshoppers and Nightrider w------w Joker a6, (a) Helpmate in 2 Helpstalemate in 2, set play Grasshoppers and Nightrider (b) Helpstalemate in 2. * Helpstalemate in 2, * 1._ Sd2 2.G1g3 Nd1= 2 ways and set play The Joker takes the powers of 1.G5g3 Nd1 2.G1e5 Se2= * the last piece moved by the * 1._Nd5 2.G4e6 Nf1= opponent. Interchange of Gs 1.Ge2 Se5 2.G2e6 Sd3= * * 1.Ge6 Sc5 2.G4c6 Sd3= (a) 1.Kh5 Jb7 2.Beh4 Jf3‡ The first of four settings with Switchbacks by White. (b) 1.Beh4 Je2† 2.Kh5! Jf3= the same scheme. In the second Gs interchange. The final mate and stalemate ------positions are identical! ------

8 EXACT ECHOES

------2. Unit Zvonimir Hernitz Edgar Holladay Translations ¶1 Chessics #17 ¶574 Chessics #15 1983 The following are exact Spring/1984 w______w echo problems in which the w______w [wdwdwdwd] echoed configurations are [wdwdwdwd] [dwdKdwdw] related by a shift of one rank or [dwdwdwdw] [wdwdwdwd] file, i.e. each piece makes a [wdwdwdw!] [dwiwdwdw] {0,1} move. This type of echo [dwdwdkdn] [wdrdpdwd] is by far the most common and [wdwdwdwd] [dwdwdwdw] easiest to show. [dwdKdwdw] Most vertical shifts depend [wdwdwdwd] on the use of a pawn. So the [wdwdPdwd] [dwdNdwHw] examples are divided into three [dwdwdwdw] w------w sections: 2a vertical shifts with w------w Helpmate in 2½, set play pawns, 2b horizontal shifts with Helpmate in 2, 2 ways * pawns, 2c pawnless settings, * 1._ Kd5 2.Sf3 Rc5 3.Se3‡ which usually remain sound 1.Sf6 Kd4 2.Sg4 e4‡ 1.Sf2 Kd4 2.Kd6 e3 3.Se2‡ when rotated 90°. 1.Sg3 Qh5† 2.Kf4 e3‡ ------Edgar Holladay F. M. Mihalek ¶575 Chessics #15 1983

2a. Vertical Shift ¶82 Ideal Mate Review #3 w______w with pawns v-vi/1983 [wdwdwdwd] ------w______w Helpmates [dwdwHNdw] ------[wdwdwdwd] [wdwdwdwd] Carl-Eric Lind [dwdwdwdn] [dwdpdwdw] Tids. f. Schack 1942 [wdwdwdw0] [wdwiwdwd] (¶198 Ideal Mate Chess [dwdwdwdk] [dwdrdwdw] Problems) [wdwdwdwd] [wdwdKdwd] w______w [dwdwdwdK] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] w------w [dwdwdwdw] [dwdwdwdR] Helpmate in 2½, set play [wdwdwdwd] w------w * [dwdwdwdp] (a) Helpmate in 2, 1._ Ke4 2.Sg6 Rd4 3.Sd6‡ [wdwdwdwd] (b) Helpmate in exactly 3 1.Ke1 Ke3 2.Sg5 d4 3.Sd5‡ [dwdwdw4k] * ------[wdwdwdwd] (a) 1.Sf8 Rf1 2.Sg6 Rf5‡ (b) 1.Sg5† Kh2 2.Kh4 Rf1 [dwdwHwdK] 3.h5 Rf4‡ w------w ------Helpmate in 2, set play * 1._ Sd3 2.h4 Sf2‡ 1.Kh4 Kh2 2.Rg4 Sf3‡ ------

9 EXACT ECHOES

------Edgar Holladay Edgar Holladay Jean Marc Lousteau ¶576 Chessics #15 1983 ¶2 Chessics #17 ¶116 Ideal Mate Review #4 w______w Spring/1984 vi-viii/1983 [wdwdwdwd] w______w w______w [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdNdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdw4k] [wdkHNdwd] [wdwdwdw0] [wdwdwdwd] [dw0NIwdw] [dwdwIwhk] [dwdwdwdP] [wdwdwdwd] [wdwdw)wd] [wdwdwdwI] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdPd] w------w [dwdwdwdw] [dwdwdwdw] Helpmate in 2½, set play w------w w------w 1._ Kh4 2.Sd4 Rh5 3.Sf3‡ Helpmate in 2½, 2 ways Helpmate in 3, set play 1.h4 Rg6 2.Kh3 Rh6 3.Sf4‡ * * ------1.Sec7 Kd7 2.Sa6 Kc6 3.Sb8‡ 1._ f5 2.Sf3† Kf4 3.Sh4 g4‡ Edgar Holladay 1.Ke4 c4 2.Sd4† Kc5 3.Sb7‡ 1.Sh3 Ke4 2.Kh4 Kf3 3.h5 g3‡ ¶578 Chessics #15 1983 Cyclic shift of roles for the ------w______w 3 Wt Knights. - [wdwdwdwd] ------Eugene Albert [dwdwdwdw] Jean Marc Lousteau ¶239 Ideal Mate Review #6 [bdwdwdwd] ¶168 Ideal Mate Review #5 xi-xx/1983 [gkdwdwdw] ix-x/1983 w______w [wdwdwdwd] w______w [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdndwdw] [K)Pdwdwd] [dwdwdwdw] [wdw0wdwd] [dwdwdwdw] [pdwdwdwd] [dwdkdwdw] w------w [ipdwdwdw] [wdwdwdwd] Helpmate in 2½, set play [wdwdwdwd] [dRdKdPdw] * [Iw)wdwdw] [wdwdwdwd] 1._ Ka4 2.c3 Bb5 3.b3‡ [w)wdwdwd] [dwdwdwdw] 1.Ka3 Bb6 2.c4† Ka5 3.b4‡ [dwdwdwdw] w------w ------w------w Helpmate in 3, set play Helpmate in 3, set play * * 1._ f4 2.Sb8 f5 1._ c4 2.Kb6 c5† 3.Ka5 b4‡ 3.Sc6 Rb5‡ 1.b4† Ka2 2.Ka4 c4 3.a5 b3‡ 1.Sc5† Kd2 2.Kd4 f4 ------3.d5 Rb4‡ ------

10 EXACT ECHOES

------Edgar Holladay J. D. Beasley Janen Berkovec ¶415 Ideal Mate Review #8 ¶582 Chessics #15 1983 Sach 1942 iii-iv/1984 w______w (¶427 Ideal Mate Chess w______w [wdwdrdwd] Problems 1966) [wdwdwdwd] [dwdrdwdw] w______w [dwdwdwdw] [wdwiwdwd] [wdwdwdwd] [wdKdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdw0wdw] [wdwIPdwd] [wdwdpdwd] [wdwdkdwd] [dwdwdwdN] [dw4rdwdw] [dwdwGwdw] [wdwdwdwd] [wdkdwdwd] [wdPdBdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w [wdK)Pdwd] w------w Helpmate in 3, set play [dwdwdwdw] Helpmate in 3, set play * w------w * 1._ e5† 2.Ke6 Ke4 Helpmate in 3, set play 1._ Bd2 2.Kd4 Kd6 3.eRe7 Sg5‡ * 3.e4 c3‡ 1.Re6 Ke3 2.Ke5 Sf2 1._ d3† 2.Kd4† Kd2 1.Kf5 Kd7 2.Ke4 Bd3† 3.dRd6 Sg4‡ 3.e5 e3‡ 3.Kd5 c4‡ ------1.Rd6 d4 2.Kd5† Kd3 ------3.Rcc6 e4‡ J. D. Beasley Edgar Holladay ------¶581 Chessics #15 1983 ¶414 Ideal Mate Review #8 Anders Lundstrom w______w iii-iv/1984 ¶312 Ideal Mate Review #7 [wdwdwdwd] w______w i-ii/1984 [dwdndw$w] [wdwdwdwd] w______w [wdw0wdwd] [dwdwdwdw] [w4wdwdwd] [dwdkdwdw] [wdwdw0wd] [dNdwdwdw] [wdwdw)wd] [dwdwdwdw] [wdwdwdwd] [dwdKdwdw] [wHwdpdKd] [dqdwdwdw] [wdwdwdwd] [dNdwiwdw] [w0kdKdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] w------w [dwdwdwdw] [wdw)wdwd] Helpmate in 3, set play w------w [dwdwdwdw] * Helpmate in 3, set play w------w 1._ f5 2.Sb8 Rb7 * Helpmate in 3, set play 3.Sc6 Rb5‡ 1._ Kh5 2.Kf4 Sd3† * 1.Sc5† Kd2 2.Kd4 Rb7 3.Kf5 Sd4‡ 1._ Sa5† 2.Kc5 Ke5 3.d5 Rb4‡ 1.f5† Kh4 2.Kf4 Sd2 3.Rb6 d4‡ ------3.e3 Sd3‡ 1.b3 Sc5 2.Qb4 Sa4 ------3.Rb5 d3‡ ------

11 EXACT ECHOES

------Edgar Holladay Josef Kricheli Rudolf Forsberg ¶416 Ideal Mate Review #8 ¶308 Ideal Mate Review #7 ¶77 Chessics #20 iii-iv/1984 i-ii/1984 Winter/1984 w______w w______w w______w [wdwdwdwd] [wdwgwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdw1w] [wdw0wdwd] [wdwdwdwd] [wdwdwdkd] [dwdrdwdw] [dkdwdwdw] [dwdwdwdw] [K)kdwdwd] [wdwdwdwd] [wdwdwdrd] [dwgbdwdw] [dKdwdwdw] [dwdwdwHw] [w)wdwdwd] [w)Pdwdwd] [wdwdwdwI] [dwdwdwdw] [dwdwdbdw] [dwdwdwdw] w------w w------w w------w Helpmate in 3, set play Helpmate in 3, 2 ways Helpmate in 3, 2 ways * * * 1._ Ka3 2.Rd4 Ka4 1.Ba5 Ka2 2.Ka4 c3 1.Kh6 Kh3 2.Rg6 Kh4 3.d5 b3‡ 3.Bb5 b3‡ 3.Qh7 Sf5‡ 1.Bd4 b5 2.Kc5 Ka5 1.Ka5 Ka3 2.Ba6 c4 1.Rg5 Se2 2.Kh5 Kh3 3.Bc4 b4‡ 3.Bb6 b4‡ 3.Qh6 Sf4‡ ------Edgar Holladay Eugene Albert M. Bily ¶25 Chessics #18 ¶411 Ideal Mate Review #8 ¶378 Ideal Mate Review #8 Summer/1984 iii-iv/1984 iii-iv/1984 w______w w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdpdwdw] [dwdwdwdw] [wdNdndwd] [wdwdwdwd] [Khwdwdwd] [dwdwdKdw] [dwdwdkdw] [dwdwdwdw] [wdpdw$wd] [wdwdwdwd] [wHwdwdwd] [dwdkdwdw] [dNdNIwdw] [dkdwdwdw] [wdwdwdwd] [w)Pdwdwd] [w)wdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w w------w w------w Helpmate in 3, set play Helpmate in 3, 2 ways Helpmate in 3, (b) b6 d6 * * * 1._ Rf2 2.Sd4† Kf4 1.d5 Ke2 2.Ke4 Sd2† (a) 1.Sd5 Sd3 2.Sb4† Kb6 3.c3 Se5‡ 3.Kd4 c3‡ 3.Ka4 Sc5‡ 1.Sc7 Sd8 2.Sd5 Rf3† 1.Ke6 Sd4† 2.Kd5 b3 (b) 1.Sb5 Kb7 2.Ka4 b3† 3.Kd4 Se6‡ 3.d6 c4‡ 3.Ka5 Sc6‡ ------

12 EXACT ECHOES

------Frederick M. Mihalek Edgar Holladay Edgar Holladay ¶75 Ideal Mate Review #3 ¶76 Ideal Mate Review #3 ¶579 Chessics #15 1983 v-vi/1983 v-vi/1983 w______w w______w w______w [wdwdwdwd] [Bdwdwdwd] [wHrdwdwd] [dwdwdwdw] [dRdwdwdw] [Hwdwdwdw] [wdw0wdwd] [wdkdwdwd] [wdwdwdwd] [dw4pdwdw] [dwdwIwdw] [dwdwdwdw] [wdkgwdwd] [wdwdwdwd] [wdwdwdwd] [dwdbdwdw] [dwdwdwdw] [dwdwdwdw] [K)wdwdwd] [w)wdwdwd] [wdPdkdwd] [dwdwdwdw] [dwdwdwdw] [dKdwdwdw] w------w w------w w------w Helpmate in 3½, set play Helpmate in 3, (b) a8 b6 Helpmate in 3½, set play * * * 1._ Bc3 2.Ka3 d4 (a) 1.Kc5 Rb8 2.Kc4 Bd5† 1._ Kd2 2.Sa6 Kc3 3.Ka4 d5 4.b3‡ 3.Kc5 b4‡ 3.Kc1 Rc4 4.Sb5‡ 1.Ka3 Rc6 2.Ka4 Kc5 (b) 1.Kb5 Ke4 2.Kb4 Bd4† 1.c3 Kd3 2.Sd7 Kc4 3.Ka5 Bc4 4.b4‡ 3.Kc4 b3‡ 3.Kc2 Rc5 4.Sb6‡ ------Michael McDowell Edgar Holladay E. Holladay, Rex Multiplex version ¶1162 US Problem ¶185 Ideal Mate Review #5 w______w Bulletin i/1986 ix-x/1983 [wdwdwdwd] w______w w______w [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdw0wd] [dwdwdwdK] [dpdwdwdw] [dwdw4pdw] [wdwdw1wd] [w1wdwdwd] [wdKdkdwd] [dwdwdkdw] [dkdwdwdw] [dwdNdwdw] [wdwdwdrd] [w0wdwdwd] [wdwdqdwd] [dwdwdndw] [dwdwdwdw] [dwdwdwdw] [wdw)P)Pd] [w)wdwdwd] w------w [dwdwdwdw] [dKdwdwdw] Helpmate in 3½, set play w------w w------w * Helpmate in 3½, set play Helpmate in 3, (b) b5 b4 1._ Qe3 2.Se1 f4 * * 3.Sf3 f5 4.Sg5‡ 1._ Kf4 2.d3 Qf5† (a) 1.Ka4 Ka1 2.Qa5 Ka2 1.Kb4 Re6 2.Sf4 Ke5 3.Kh6 Se5 4.e3‡ 3.b5 b3‡ 3.Kc5 Qe4 4.Sg6‡ 1.g3 Sd4 2.f3 Se6 (b) 1.Ka5 Ka2 2.Qa6 Ka3 ------3.d4 Rg5 4.e4‡ 3.b6 b4‡ * ------An attempt at an ideal mate echo with maximum pieces. A later problem in IMR showed a ten-piece echo, the maximum without pins. ------

13 EXACT ECHOES

------Andrew Kalotay J. M. Lousteau Andrew Kalotay ¶6 Chessics #17 Die Schwalbe 1982 ¶240 Ideal Mate Review #6 Spring/1984 w______w xi-xii/1983 w______w [wdwdwdwd] w______w [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdpdw] [wdndwdwd] [dNdwdwdw] [wdwdwdwH] [dwhr0wdw] [wdw0wdwd] [dwdwdwdw] [wdrdkdwd] [dwdwdwdw] [wdwdk)wd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [wdwdPdKd] [dwdPIwiw] [wdwdwIPd] [dwdwdwdw] [wdwdPdwd] [dwdwdwdw] w------w [dwdwdwdw] w------w Helpmate in 4, set play w------w Helpmate in 3½, 2 ways * Helpmate in 4, 2 ways * 1._ Kf2 2.Kd4 Ke1 * 1.f5 Kf4 2.g4 Kg5 3.e4 Kd2 4.Se5 e3‡ 1.d5 Kd2 2.Kf4 Sc5 3.Kg3 f6 4.Sf7‡ 1.Rd6 Kf2 2.Kd5 Ke3 3.Ke5 Sd7† 4.Kd4 e3‡ 1.Sg8 Kf5 2.g3 Kg4 3.Se6 Kd3 4.Rc5 e4‡ 1.Kg4 d4 2.Kf5 Kd3 3.Kg2 f5 4.Sf6‡ ------3.Ke6 Sd8† 4.Kd5 e4‡ ------Edgar Holladay ------Frederick M. Mihalek Schach-Echo 1974 Jean-Marc Louseau ¶5 Ideal Mate Review #1 w______w Rex Multiplex 1982 i-ii/1983 [wdwdwdwd] (¶363 Ideal Mate Review) w______w [dkdwdwdw] w______w [wdwdwdwd] [r0rdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdpdwdw] [wdwHwdwd] [wdwdwdwd] [wdniwdwd] [dwdwdwdw] [dKdwdwdw] [dwdwdwdw] [wdwiwdwd] [w)wdwdwd] [w)wdKdwd] [)Kdwdwdw] [dwdwdwdw] [dwdPdwdw] [w)wdwdwd] w------w [wdPdwdwd] [dwdwdwdw] Helpmate in 4, 2 ways [dwdwdwdw] w------w * w------w Helpmate in 3½, (b) a3 a4 1.b5 Kb4 2.Kb6 Kb3 Helpmate in 4, 2 ways * 3.Ka5 Ka3 4.Rcb6 b4‡ * (a) 1.Ka2 Kc5 2.Se4† Kb5 1.Ra7 Kb4 2.Ka6 Ka4 1.Se5 Ke3 2.Kd5 Ke2 3.b4 Ka4 4.Sc3‡ 3.Rcc7 b4 4.Rcb7 b5‡ 3.Kd4 Kd2 4.d5 c3‡ (b) 1.Ka3 Kc5 2.b4† Kb6 * 1.Sd8 d4 2.Se6 Kd3 3.b5 Ka5 4.Sc4‡ Asymmetry. 3.Kd5 b5 4.d6 c4‡ ------Tempo moves by wK. ------

14 EXACT ECHOES

------Josef Kricheli Jean-Marc Loustau Jean-Marc Loustau ¶388 Ideal Mate Review #8 ¶393 Ideal Mate Review #8 ¶316 Ideal Mate Review #7 iii-iv/1984 iii-iv/1984 i-ii/1984 w______w w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdw1piwd] [wdwdwdwd] [iwdwdwdw] [dwdwdwdw] [dwIwdwdw] [wdwdwdwd] [wdPdKdwd] [kdwdwdwd] [hwdwdwdw] [dwdPdwdw] [dw)wdwdw] [w)Pdqdwd] [wdPdwdwd] [w)P1wdwd] [Iwdwdwdw] [dwdwdwdw] [drdwdwdw] w------w w------w w------w Helpmate in 4, 2 ways Helpmate in 4, 2 ways, Helpmate in 4, (b) b1 f1 * (b) c4 b4 * 1.Qa6 c3 2.Sb5 Kb1 * (a) 1.Qf4 b4 2.Rb3 b5 3.Ka4 Ka2 4.Qa5 b3‡ (a) 1.Qc5 Kf3 2.Ke5 Ke2 3.Ka5 c×b3 4.Qb4† c×b4‡ 1.Sc4 Ka2 2.Sb6 Ka3 3.Kd4 Kd2 4.e5 c3‡ (b) 1.Qf4 Kd5 2.Qb4 c×b4 3.Qb5 c4 4.Qa6 b4‡ 1.Ke7 d4 2.Qc6† Kd3 3.Rf3 Kc4 4.Rb3 c×b3‡ * 3.Kd6 c5† 4.Kd5 c4‡ ------Black and white tempo moves (b) 1.Qd5† Ke3 2.Ke5 Ke2 Edgar Holladay ------3.Kd4 Kd2 4.e5 c3‡ TheProblemist 1984 Michael McDowell 1.Ke7 d4 2.Kd7 Kd3 w______w ¶H1148 The Problemist 3.Kc6 b5† 4.Kd5 c4‡ [wdwdwdwd] i/1987 Swap of Q-block and P-guard [dwdwdwdw] w______w ------[wdwdw1wi] [wdwdwdwd] Eugene Albert [dwdwdwhw] [dwdwdwdw] ¶413 Ideal Mate Review #8 [wdwdwdKd] [wdwdwdwd] iii-iv/1984 w______w [dwdwdw)w] [dwdpdwdK] [wdwdwdPd] [wdkdBdwd] [wdwdwdNd] [dwdwdwIw] [dwdwdwdw] [dwdrGw1w] w------w [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] Helpmate in 4½, set play [dwdwdwdw] * w------w [wdwdwdwd] 1._ Qg6 2.Kf4 Sf3 Helpmate in 4, 2 ways [dNdwdpdw] 3.g4 Sh4 4.g5† Kh5 5.g4‡ * [wdwdw)wd] 1.Kh4 Sh3† 2.Kg4 Qg5† 1.Rd4 Bh7 2.Qf3† Kg6 [dkdwdwdw] 3.Kf3 Kh5 4.g4† Kh4 5.g3‡ 3.Kd3 Bf4 4.Ke4 Kg5‡ w------w * 1.Qf2 Bh6 2.Kd4 Kg5 Helpmate in 4, (b) f3 f4 Quasi-symmetrical. 3.Ke3 Bf3 4.d4 Kg4‡ (a) 1.Kc2 Kg6 2.Kd3 Sc1† Only one legal first move. * 3.Ke4 Sf6+ 4.Kf4 Sd3‡ ------Discovered check (b) 1.Kc2 Sh6 2.Kd3 Sf7 ------3.Ke4 f3† 4.Kf5 Sd4‡ ------

15 EXACT ECHOES

------Jean-Marc Loustau Edgar Holladay M. Havel Zlatá Praha 4/x/1912 Probleemblad 1981 The Problemist 1980 (¶535 in Dedrle) (also ¶159 Ideal Mate Review) (from 1979 lecture report) w______w w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdkdw] [Iwdwdwdw] [dwdwdwdw] [wdwdpdwd] [wdwdpdwd] [wdwdwdwd] [dw!wdwdK] [dwdq0wdw] [dwdwdwdw] [wdwdwdwd] [wdw0pdwd] [wdRIPgkd] [dwdwdwdN] [dwdwiwdw] [dwdwdwdw] [wdwdwdwd] [wdPdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w w------w w------w Mate in 4 Helpmate in 5, (b) a7 d1 Helpstalemate in 3, 2 ways * * * 1.Qd6 (a) 1.Qd8 c3 2.Kd3 Kb7 1.Be3† Kd3 2.Kf4 Rc6 1... e5 2.Qd7† Kf6 3.Kc4 Ka6 4.Kd5 Kb5 3.Ke5 K×e3= 3.Sf2 e4 4.Sg4‡ 5.Qd6 c4‡ 1.Bc7 e5 2.Kf5 R×c7 1... Kf6 2.Kh6 Kf7 (b) 1.d3 Kc1 2.Kd4 Kb2 3.Ke6 Ke4= 3.Qd8 e5 4.Sg5‡ 3.e3 Ka3 4.e4 Kb4 ------5.e5 c3‡ Direct Mates M. Havel Hampshire ------Telegraph and Post Helpstalemates F. Lindgren 9/iv/1920 (¶127 in Dedrle) ------Itvar & Dag 2/xii/1920 w______w Eugene Albert (¶257 in Dedrle) [wdwdwdwd] ¶118 Ideal Mate Review #4 w______w [dwdwdwdw] vii-viii/1983 [wdwdwdwd] [wdwdp0wd] w______w [dKdwdwdw] [dwdwHNdw] [wdwdwdwd] [wdwdwdwd] [wdwdkdwd] [dwdwdwdw] [dwdPdwdR] [Iwdwdw!w] [wdwdwIwd] [wdkdwdwd] [wdwdwdwd] [dwdwdRdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdPd] [wdwdwdwd] w------w [dwdwdwdk] [dwdQdwdw] Mate in 4 [wdwdwdwd] w------w * [dwdwdwdw] Mate in 3 1.Kb4 w------w * 1... e×f5 2.Kc5 f×e5 Helpstalemate in 2, 2 ways 1.Qf3 3Kc4 f4 4.Qd3‡ * 1... Kb5 2.Qf4 Ka/c5 3.d6‡ 1... K×f5 2.Qg4† K×e5 1.Kg3 Rf3† 2.Kh4 Kf5= 1... Kb4 2.Kb6 Ka/c4 3.Rh4‡ 3.Kc5 f5 4.Qd4‡ 1.Kh4 g5 2.Kh5 Rf4= ------(also 1... f×e5 2.Se7 Kd4 ------3.Qf3 e4 4.Qc3‡ but not an exact echo) ------

16 EXACT ECHOES

------H. Suhr, Magasinet 1944 M. Havel M. Havel w______w Zlatá Praha 15/i/1915 Zlatá Praha 7/iii/1913 [wdQdwdwd] (¶301 in Dedrle) w______w [iwdwdwdw] w______w [wdwdwdwd] [wdwdwdwd] [wIw$wdwd] [dwIpdwdw] [dwdwdwdw] [dwdNdwdw] [Bdwdwdwd] [K)wdwdwd] [wdkdwdwd] [Gwdkdwdw] [dwdwdwdw] [dwHwdwdw] [wdw)Rdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w [Pdwdwdwd] [dwdwdwdw] Mate in 4, set play [dwdwdwdw] w------w * w------w Mate in 5 1._ Kb6 2.b5 Ka7 Mate in 5 1.Re3 3.Kb4 Kb6 4.Qb8‡ * 1... K×d4 2.Bb6† Kd5 3.Ba7 d6 1.Kb3 Kb6 2.Qd7 Ka6 1.Sb6 4.Kb6 Kd4 5.Kc6‡ 3.Qc7 Kb5 4.Qb7‡ 1... K×c5 2.Kb7 Kb4 1... d6 2.Re2 K×d4 3.Kc6 d5 * 3.Rd3 Kc5 4.a3 Kb5 5.Rd5‡ 4.Kb5 Kd3 5.Kc5‡ Same mate as in the Havel 1... K×b6 2.Sb7 Kb5 ------problem below. 3.Rd4 Kc6 4.a4 Kb6 5.Rd6‡ M. Havel Schweitzerische ------(also 1... Kb5 2.Kb7 Kb4 3.Rd3 Schachzeitung 1918 M. Havel Kb5 4.Sa6 Ka5 5.Rd5‡ etc, not (¶609 in Dedrle) Tidskrift för Schack 1916 exact echo) w______w (¶32 in Echo by Dedrle) ------[wdwdwdwd] w______w A. W. Galický [dwdwdwIw] [wdwdwdwd] La Strategie 1907 [wdwdwdwd] [dwdwdwdw] (¶343 in Dedrle) [dw0wdNdk] [wdwdQdwd] w______w [wdwdwdwd] [dkdwdwdw] [wdwdwdwI] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [wdwdNdPd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [w)wdwdwd] [dwdwdwdk] w------w [Iwdwdwdw] [wdwdwdw0] Mate in 5 w------w [dwdwdw$w] 1.Se3 Mate in 5 [wdwdwdw)] 1... Kg5 2.g3 Kh5 3.Sg1 Kg5 * [dwdwdwdw] 4.Sf3† Kh5 5.g4‡ 1.Qd6 w------w 1... Kh4 2.Kg6 c4 3.Sd1 Kg4 1.... Ka5 2.b3 Kb5 Mate in 5 4.Sf2† Kh4 5.g3‡ 3.Kb2 Ka5 4.Qc6 Kb4 * ------5.Qb6‡ 1.Rg8 1... Kh6 2.h3 Kh5 1.... Ka4 2.Qd5 Kb4 3.Kg7 Kg5 4.Rf8 Kh5 5.Rf5‡ 3.Kb1 Ka4 4.Qc5 Kb3 1... h3 2.Kh7 Kh4 3.Kg6 Kg4 5.Qb5‡ 4.Rf8 Kh4 5.Rf4‡ (1.... Kc4 2.Ka2 Kb5 ------3.Kb3 Ka5 4.Kc4 Ka4 5.Qa3/a6/b4‡ dual) * The echoed mate has all four pieces in one file. ------

17 EXACT ECHOES

------M. Havel Erich Bartel

Zlatá Praha 19/xi/1919 Diagramme und Figuren 2b Horizontal Shift w______w 19/xii/1964 with pawns w______w ------[wdwdwIw$] Helpmates [dwdwdwdp] [wdwdwdwi] ------[wdwdwdwd] [dwdwdw)w] Carl-Eric Lind [dpdwdwdw] [wdwdwdPd] ¶234 Ideal Mate Review #6 [wdwdwdkd] [dwdwdwdw] xi-xii/1983 [dRdwdwdw] [wdwdwdwd] w______w [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] w------w [dwdwdwdw] [wdwdwdwd] Mate in 5 w------w [4wdkdwIw] * Berolina Pawns, No Wt King [wdwdwdwd] 1.Kf7 Helpmate in 2, set play [dwdNdwdw] 1... b4 2.Kf6 h5 3.R×h5 K×h5 * [wdwdwdwd] 4.R×b4 Kh6 5.Rh4‡ 1._ f8Q† 2.Kh7 Qg7‡ [dwdRdwdw] 1... Kg5 2.Rb4 h6 3.R×h6 K×h6 1.Kh7 f7 2.Kh8 g8Q‡ 4.R×b5 Kh7 5.Rh5‡ * w------w (also partial echoes with Bk Berolina pawns move Helpmate in 2, (b) d3 d4 Ke/f4 Wt Kf6, Rd3/Rd4 and diagonally forward and capture * same one rank up) directly forward. (a) 1.Rb5 Kf5 2.Rc5 Se5‡ ------(b) 1.Ke5 Sf5 2.Rd5 Re1‡ Fairy Pieces or Conditions Erich Bartel and A. H.Kniest (discovered and direct mates) ------¶526 Frankfurter Notizen ------Unto Heinonen 20/vii/1966 Edgar Holladay ¶82 Chessics #20 w______w ¶186 Ideal Mate Review #5 Winter/1984 [wdwdwdwd] ix-x/1983 w______w [dPdwdwdw] w______w [wdwdw!wd] [wdwdwdwd] [wdwdwdwd] [dwdwdw1w] [dwdwdwdw] [dwhkdn)K] [wdwdwdwd] [wdwdwdk4] [wdwdwdwd] [dwdKdqHw] [dwdwdwdr] [dwdwdwdw] [wdwdpdwd] [wdwdwdwd] [wdwdwdwd] [dwdkdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w [wdwdwdwd] [dwdwdwdw] No White King [dwdwdwdw] w------w Helpmate in 2, (b) Berolina w------w Grasshoppers Pawn Helpmate in 3, (a) d7 e7, Helpmate in 4, 2 ways * (b) c7 e7 1.e3 Sh7 2.Gc2 Sf6 (a) 1.Rh5 b8Q 2.Kh4 Qf4‡ * 3.Ge5 Gf5 4.Ge2 Se4‡ (b) 1.Rh2 a8Q 2.Kh3 Qf3‡ (a) 1.Ke8 g8S 2.Kf8 Se7 1.Gc5 Kd6 2.Kd4 Sf7 Epaulette mates 3.Se8 Sg6‡ 3.Gc3 Gf6 4.Ge3 Se5‡ ------(b) 1.Kd8 g8S 2.Ke8 Kg7 Interposition mates 3.Sd8 Sf6‡ ------

18 EXACT ECHOES

------Fairy Conditions Josef Kricheli E. Holladay ------¶54 Chessics #19 ¶15 Ideal Mate Review #1 Ian Shanahan Autumn/1984 i-ii/1983 ¶18 Chessics #17 w______w w______w Spring/1984 [wdwdwdwd] [wdwdwdwd] w______w [$wdwdwdw] [drdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdw4k] [dNdwdwdw] [wdwdwdwd] [wdwdwdwd] [w4wdwdwd] [dwdwdwdw] [dwdwdwdn] [dkdwdwdw] [wdKdpdwd] [wdwdwdwd] [wdwdwdwd] [dwdRdwdw] [dwdwIwdw] [dKdwdwdw] [wdwdwdwd] w------w w------w [dwiwdwdw] Helpmate in 3, set play Helpmate in 3, 2 ways w------w * * Circe Chess 1._ Ke2 2.Sf4† Kf3 1.Ra4 Sd4† 2.Ka3† Ka1 Helpstalemate in 3, 2 ways 3.Sg6 Rh7‡ 3.Rb3 Sc2‡ * 1.Rg4 Ra6 2.Sg5 Kf2 1.Ka4† Ka1 2.Ra7 Ka2 1.e3 Rd2 2.Kxd2(Ra1) Rf1 3.Kh4 Rh6‡ 3.Ra5 Sc3‡ 3.Ke2 Kc3= ------1.Kc2 Kb4 2.exd3(Rh1) Re1 Edgar Holladay Josef Kricheli 3.Kd2 Kb3= ¶214 Ideal Mate Review #5 ¶53 Chessics #19 ------ix-x/1983 Autumn/1984 2c. Pawnless w______w w______w These by rotation can be shown [wdwdwdwd] [wdwdRdwd] as vertical or horizontal shifts. [dwdwdwdw] [dwdw1wdw] ------[wHwdw4k4] [wdwdwdwd] Helpmates [4k4wdwdw] [Hwdwdwdw] ------[wdwdwdKd] [wdKdkdwd] G. P. Jelliss (unpublished) [dwdwdwdw] [dwdwdwdw] w______w [wIwdwdNd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dw$wdwdw] w------w w------w [kdKdwdwd] In each part, left and right: Helpmate in 3, 2 ways [dwdwdwdw] Helpmate in 3, 2 ways * [wdwdwdwd] * 1.Ke5 Sb3 2.Kd6 Sc5 [dwdwdwdw] (a) 1.Ra6 Kb3 2.Ka5 Ka3 3.Qc7 Re6‡ [wdwdwdwd] 3.Rb5 Sc4‡ 1.Qe6 Kc3 2.Kd5 Sc4 [dwdwdwdw] 1.Rc4 Sd5 2.Ka4 Ka2 3.Qc6 Re5‡ 3.Rb4 Sc3‡ ------w------w (b) 1.Rh7 Se3 2.Kh6 Kh4 Helpmate in 2, set play 3.Rg6 Sf5‡ * 1.Rf5 Kg3 2.Kh5 Kh3 1._ Kc5 2.Ka5 Ra7‡ 3.Rg5 Sf4‡ 1.Ka5 Rc8 2.Ka6 Ra8‡ ------The simplest possile example. ------

19 EXACT ECHOES

------Russell E. Rice Rudolf Forsberg Elmar and Erich Bartel ¶303 Ideal Mate Review #7 ¶80 Chessics #20 ¶1291 Jugendschach i-ii/1984 Winter/1984 6/i/1985 w______w w______w w______w [wdrdwdwd] [wdwdwdrd] [wdwdwdwd] [dwdwdwdw] [dwdwdwiw] [dwdwdwdw] [wdkdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdrdwdwd] [wdwdwIbg] [wdwdwdwd] [dwHwdwdw] [dwdwdwHw] [dwIwdwdw] [wdNdwdwd] [wdwdwdwd] [wdwdwdwd] [dwIwdwdw] [dwdwdwdw] [dkdNdwdw] w------w w------w w------w Helpmate in 3, (b) c6 c4 Helpmate in 4, 2 ways (0,3)+(1,3)-Leaper * * Helpmate in 3, set play (a) 1.Kc5 Se1 2.Kd4 Kd2 1.Bf6 K×g4 2.Kh7† Kh5 * 3.R8c5 Sf3‡ 3.Bh8 Se4 4.Rg7 Sf6‡ 1.__ Kc1 2.Lc4‡ (b) 1.Kd3 Se4 2.Rc3 Kd1 1.Bf5 Kf3 2.Bh7 Kg4 1.Kb3 Kc1 2.La1 Kb1 3.Lb4‡ 3.R8c4 Sf2‡ 3.Kh6† K×h4 4.Rg6 Sf5‡ Symmetric mate ------* - Fairy Pieces Translation 1-step rankwise Veikko Heinonen Suomen without pawn-like powers (or Reflection in line between b Shakki 1982 ------and c files) (¶365 Ideal Mate Review) P. A. Petkow feenschach 1963 ------w______w w______w E. Holladay and F. M. Mihalek [wdwdwdwd] [wdwdwdwd] Schach-Echo 1975 [dwdwdwdw] [dwdwdwdw] w______w [wdwirdwd] [wdwdwdwd] [wdQdwdwd] [dwdwhwdw] [dwdwIwdw] [dwdwdwdw] [wdw4wdwd] [wdw1wdwd] [wdqdwdwd] [dwdw$wdw] [dwdqiqdw] [dwiwdwdw] [wdwdKdwd] [wdw$w1wd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwIwdwdw] w------w w------w [wdNdwdwd] Helpmate in 4, 2 ways Grasshoppers [dwdwdwdw] * Helpmate in 2, set play w------w 1.Sd7 Kf2 2.Sf6 Rg3 * Grasshoppers 3.Ke5 Ke3 4.dRd6 Rg5‡ 1._ Rd1 2.Gd2 Re1‡ Helpmate in 4, 2 ways 1.Re7 Rg3 2.Ke6 Ke3 1.Gf4 Ke6 2.Ke4 Re2‡ * 3.dRd7 Ke4 4.Sf7 Rg6‡ ------1.Kb5 Sa1 2.Ga5 Gc2 3.Ka4 ------Kc4 4.Ga3 Sb3‡ 1.Kb6 Kc4 2.Ga7 Gc3 3.Ka5 Kc5 4.Ga4 Sb4‡ ------

20 EXACT ECHOES

------3. Longer Andrew Kalotay Andrew Kalotay Translations ¶301 Ideal Mate Review #7 ¶390 Ideal Mate Review #8 The compositions in this i-ii/1984 iii-iv/1984 group use at least one w______w w______w translation longer than {0,1} [wdwdwdwd] [wdwdwdwd] though this may be made up of [dwdwdwdb] [dwdwdwdw] two or more unit shifts. [wdwdwdrd] [wdwdwdwd] The result of a succession [dwdwdwdw] [dwdwgwdw] of translations is another, unless [wdwiwHwd] [wdwdkdwd] they cancel each other out to [dwdwdwdw] [dwdNdwdw] give the identity. ------[wdK)wdwd] [wdwdPIwd] (0,2) Translation [dwdwdwdw] [dwdrdwdw] ------w------w w------w Edgar Holladay Helpmate in 4, 2 variations Helpmate in 4, 2 ways ¶577 Chessics #15 1983 * * w______w 1.Rd6† Sg6 2.Kd5 d4 1.Bf4 Sb4 2.Rd4 Kf1 [w4wdNdwd] 3.Bg8 Kd3 4.Be6 Se7‡ 3.Ke3 Ke1 4.Re4 Sc2‡ [Iwdwdwdw] 1.Rd6† Kc1 2.Be4 Sg6 1.Bf6 Sb2 2.Ke5 e4 3.Kd3 Kd1 4.Rd4 Se5‡ 3.Rd6 Ke3 4.Re6 Sc4‡ [wdwdwdwd] ------[dkdwdwdw] Andrew Kalotay Andrew Kalotay [wdwdwdwd] ¶302 Ideal Mate Review #7 ¶391 Ideal Mate Review #8 [dwdwdwdw] i-ii/1984 iii-iv/1984 [w)wdwdwd] w______w w______w [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] w------w [dwdwdwHw] [dwdwdwdw] Helpmate in 2½, (b) e8 d8, [wdwdwdwd] [wdwdbdwd] set play in (b) [dwiwdwdw] [dwdkdwdw] * [wdwdKdwd] [Ndwdwdwd] (a) 1.b4 Rb6 2.Ka8 Ka6 3.Sc7‡ [dwdrdwdw] [dwdwdKdw] (b) 1._ Ka5 2.b3 Rb5 3.Sc6‡ [wdw)wgwd] [wdwdPdwd] 1.Se6 Ka4 2.Ka6 Rb4 3.Sc5‡ * [dwdwdwdw] [dwdrdwdw] (a-b) shows Translation (0,2) w------w w------w (b, set - play) shows (0,1) Helpmate in 4, 2 ways Helpmate in 4, 2 ways ------* * 1.Rd5 d3 2.Bg3 Ke3 1.Bf5 Kf2 2.Ke4 e3 3.Be5 Kd2 4.Kd4 Se6‡ 3.Rd5 Ke2 4.Re5 Sc3‡ 1.Rd7 d4† 2.Kd6 d5 1.Bf7 e4† 2.Ke6 e5 3.Bh4 Kd4 4.Be7 Se8‡ 3.Rd7 Ke4 4.Re7 Sc5‡ ------

21 EXACT ECHOES

------* ------Andrew Kalotay There were also two other twins P. Leibovici feenschach 1985(?) (d) and (e) leading to a different Die Schwalbe 1938 w______w mate, but (d) was unsound. w______w [wdwdwdwd] ------[wdwdwdwd] [dwdwdwdw] M. Havel Zlatá Praha [0wdwdwdw] [wdwdwdwd] 25/v/1912 (¶624 in Dedrle) [kdwdwdwd] [dwdwdwdw] w______w [dw!Kdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwIw)wdw] [dwdwdwdw] [dwdwdwdw] [wdw)k4Nd] [wdwdwdpd] [w)wdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w [wdwdwdwi] w------w Helpmate in 5, 2 ways [dwdwIwdw] Grasshopper * [Qdwdwdw)] Helpmate in 3, set play 1.Rf6 e4 2.Kf3 e5 3.Ke4 [dwdwdwdw] * d4 4.Kd5 Kd3 5.Rc6 Sf4‡ w------w 1._ Kc6 2.Ka5 b4† 1.Rf4 Kc2 2.Kf3 Kd1 3.Rc4 Mate in 4 3.Ka6 b5‡ Sf4 4.Ke4 Sh3 5.Kd3 Sf2‡ 1.Qf7 1.... Kh5 2.Kf4 Kh6 1.Ka5 Kc4 2.Ka4 Gc3 ------3.h4 g5† 4.h×g5‡ 3.a5 b3‡ Pal Benko and 1.... g5 2.Kf2 g4 ------Andrew Kalotay 3.Qf5 g3† 4.h×g3‡ Edgar Holladay ¶12 Chessics #17 and other lines The Problemist1986 Spring/1984 ------w______w w______w Edgar Holladay [wdwdwdwd] [wHwdwdwd] ¶59 Kennst du die Bibel? [dwdw0wdw] [dwdpdwdw] 18/ix/1966 [Kdkdwdwd] [wdwdwdwd] w______w [dwdwdQdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwIwd] [dwIwdwdw] [dwdwdwdw] [dwdk)wdw] [wdwdwdwd] [wdwdwdwd] [wdw)wdwd] [dkdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w w------w [dwdwdwdw] Terror (Queen+Knight) Helpmate in 5, (b) b8 b6, [wdNdwdwd] Helpstalemate in 2, in 3 ways (c) b8 b7, d2 d6 [drdwdwdw] * * w------w 1.Kc7 Tf7 2.Kd7 Kb7= (a) 1.Kc4 d4 2.Kd5 e4+ Dragon (= Knight+Pawn) 1.e6 Tf6 2.Kd6 Kb6= 3.Ke6 Ke3 4.d6 d5+ Helpstalemate in 2, 3 ways 1.e5 Ka5 2.Kd5 Kb5= 5.Ke5 Sd7 * Symmetric finale (b) 1.d6 Sc8 2.Kc4 Kf3 1.Ka4 Kc6 2.Rb6† K×b6= * 3.Kd5 Ke2 4.Ke4 d4 1.Ka5 Dc3 2.Rb7† K×b7 Translations (0,1) and (0,2) v 5.d5 Sd6 1.Ka6 Dc4 2.Rb8 K×b8 (or Reflections in the midlines (c) 1.Kc4 Kf3 2.Kd5 e4+ ------of the translations) 3.Ke6 e5 4.Kf7 Ke4 ------5.Ke6 Sd8 * (a-b), (a-c) Translation (0,1) v (b-c) Translation (0,2) v *

22 EXACT ECHOES

------(0,3) Translation (1,1) Translation (1,2) Translation ------Christer Jonsson J. J. Lois feenschach 1974 Eugene Albert ¶57 Chessics #19 w______w ¶3 Chessics #17 Autumn/1984 [wdwdwdwd] Spring/1984 w______w [dwdNdw!w] w______w [wdwdwdwd] [wdwdwdqd] [wdwdwdwd] [dwdwdwdw] [dndwdwdw] [dwdw0wdw] [wdwdKdkd] [wdwdwIwd] [wdNdwdwd] [dwdwdwdr] [dwdkdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdkdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w [wdwdwdwd] [dwdwdNdr] Grasshoppers [dw$Kdwdw] w------w Helpmate in 3, set play w------w Helpmate in 3, 2 ways, * Helpmate in 2½, (b) e7 c4 (b) f1 e1 1._ Kf3 2.Sc3 Gb2 * * 3.Gc2 Se5‡ (a) 1.Ke2 e6 2.Se7 e5 (a) 1.Rh7 Se3 2.Kh6 Kf6 1.Sd4 Kg4 2.Ke4 Gc3 3.Rc4‡ 3.Rh5 Sg4‡ 3.Gd3 Sf6‡ (b) 1.Ra1 Kd3 2.Kc1 Kc3 1.Rh6 Ke5 2.Kh5 Kf5 ------3.Ra3‡ 3.Rh4 Sg3‡ E. Klar Revista Romana ------(b) 1.Rh8 Sf3 2.Kh7 Kf7 de Sah 1947 Eugene Albert 3.Rh6 Sg5‡ w______w ¶4 Chessics #17 1.Kg5 Ke5 2.Kh4 Kf4 [wdwdwdwd] Spring/1984 3.Rh3 Sg2‡ [dwdwdwdw] w______w * [wdwdwdwd] [wdwdwdwd] (a1-a2) (a1-b1) (a2-b2) [dwdqdwdw] [dwdwHwdw] Translation (0,1) [wdqdwdwd] [wdwhwdnd] (a1-b2) (a2-b1) Translation [dwdwdwdw] (0,2) [dwiwdwdw] (b1-b2) Translation (0,3) [wdwdwdwd] [wdNdkdwd] ------[dwdKdQHw] [dwdwdwdw] w------w [wdwdKdwd] Grasshoppers, Helpmate in 3, [dwdwdwdw] (b) f1 f3, (c) f1 f5 w------w * Helpmate in 3, 2 ways (a) 1.Gb3 Gb5 2.Gb6 Kc1 * 3.Gb4 Se2‡ 1.Sf8 Sb6 2.Ke5 Ke3 (b) 1.Kd4 Gc6 2.Gc7 Kd2 3.Se6 Sd7‡ 3.Gc5 Sf3‡ 1.Sf4† Kf1 2.Kf3 Sf5 (c) 1.Kd3 Gc5 2.Gd2 Sh3 3.Se4 Se5‡ 3.Gd4 Sf2‡ ------(a-b) (1,1), (b-c) (0,1) v, (a-c) (0,1) h. ------

23 EXACT ECHOES

------Eugene Albert Masazumi Hanazawa ¶5 Chessics #17 ¶16 Chessics #17 Spring/1984 Spring/1984 w______w w______w [wdwdwdwd] [wdwdwdwd] [dwdwdNdw] [dwdwdwdw] [w$wdwdwd] [wdwdwIwd] [dwdkdKdw] [dwdw!wdw] [wdwdwdwd] [wdwiwhwd] [dwdwdwdw] [dwHwdwdw] [wdwdwhwd] [wdwdwdwd] [dwdwdwdw] [dw1wdwdw] w------w w------w Helpmate in 3, (b) f7 d8 Grasshoppers * Helpmate in 4, set play (a) 1.Se4 Rb7 2.Kc6 Ke5 * 3.Sc5 Sd8‡ 1._ Ke7 2.Gg5 Kd6 (b) 1.Se4 Kg4 2.Kd4 Rd6† 3.Ge3 Ge2 4.Sd3 Sb5 3.Ke5 Sf7‡ 1.Gc4 Sb5 2.Ke4 Kf7 The knight mating moves are 3.Kf5 Gg3 4.Gg4 Sd6 "reciprocal". * ------Translation (1,2) ------This composition by Masazumi Hanazawa was awarded the First Prize in Chessics Exact Echoes Tourney ------

24 EXACT ECHOES

------

4. Rotation 90° Eugene Albert Eugene Albert ------¶336 Ideal Mate Review #7 ¶335 Ideal Mate Review #7 Orthodox Pieces i-ii/1984 i-ii/1984 ------w______w w______w Bruno Sommer Die Schwalbe 1934 [wdwdwdwd] [wdwdwdwd] (version ¶337 Ideal Mate [dwdwdwdw] [dwdwdwdw] Review 1984) [wdRdwdwd] [Bdwdwdwd] w______w [dwdwiwdw] [dRdwdwdw] [Qdwdwdwd] [wdwdpdwd] [wdkdwdwd] [dwHwdwdw] [dwIpdwdw] [dwdwdwdw] [wdwdwdwd] [wdBdwdwd] [wdwIw0wd] [dwdwiwdw] [dwdwdwdw] [dwdwdwdw] [wdKdwdwd] w------w w------w [dwdwdwdw] Helpmate in 2½, (b) e4 e6 Helpmate in 3, (b) f2 d7 [wdwdwdwd] * * [dwdwdwdw] (a) 1.Rf6 e3 2.Rf5† Ke4 (a) 1.Kd4 Rg5 2.Ke4 Rg4† 3.B×d3‡ 3.Kf3 Be2‡ w------w (b) 1.K×d3 Kd5 2.Ke3 e5 (b) 1.d6 Bc8 2.d5 Bf5 Helpmate in 2, set play 3.Be4‡ 3.d4 Bd3‡ * * * 1._ Qe8† 2.Kd6 Sb5‡ Rotation 90º about d4 Rotation 90º about d2 (wK) 1.Kf4 Qg2 2.Ke3 Sd5‡ ------* Eugene Albert Eugene Albert Rotation 90º about c4 (wK) ¶410 Ideal Mate Review #8 ¶333 Ideal Mate Review #7 ------iii-iv/1984 i-ii/1984 Klaus Funk w______w w______w ¶306 Ideal Mate Review #7 i-ii/1984 [wdwdwdwd] [wdwdwdwd] w______w [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdqdwdNd] [wdpdwdwd] [dwdwdwdw] [dwdkGwdw] [dwdwdwdw] [wdwdKHbd] [wdwdwdwd] [wdkdKdwd] [dwdwdwdw] [dwdwIwdw] [dwdwdwdw] [wdw4wdwd] [whwdwdwd] [wdrdwHwd] [dNdwdkdw] [dwdwdwdw] [dwdBdwdw] [wdwdwdwd] w------w w------w [dwdwdwdw] Helpmate in 3, set play Helpmate in 3, (b) c6 b3 w------w * * 1._ Bd4 2.Sc4† Kd3 (a) 1.Rd2 Ke3 2.Rd6 Sd3 Helpmate in 2, (b) e6 h3 3.Sd6 Sf4‡ 3.Kd5 Bb3‡ * 1.Sa4 Kf4 2.Qc4† Kf5 (b) 1.Ra2 Ke5 2.Ra4 Se4 (a) 1.Bd3 Sd5 2.Ke4 Sd2‡ 3.Sc5 Se7‡ 3.Rb4 Be2‡ (b) 1.Rf4 Sg4 2.Be4 Sd4‡ * * * Rotation 90º about d5 (bK) Rotation 90º about d4 Rotation 90º about e3 ------

25 EXACT ECHOES

------Eugene Albert Eugene Albert Eugene Albert ¶330 Ideal Mate Review #7 ¶408 Ideal Mate Review #8 Arbejder Skak 1965 i-ii/1984 iii-iv/1984 (¶339 Ideal Mate Review) w______w w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [Hwdwdwdw] [dwdndwdw] [wdwdndwd] [bdwdwdwd] [wdwdwdNd] [dwdNdwdw] [dwdwdwdw] [dwdk4wdw] [wdwdkdwd] [wdk0wdwd] [wdwdwIwd] [Hwdwdrdw] [dw0w0wdw] [dwdwdwdw] [wdwdwdKd] [wdwdKdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdNdw] w------w w------w w------w Helpmate in 3, (b) a3 f8 Helpmate in 3, (b) e3 d2 Helpmate in 3½, set play * * * (a) 1.Rd3 Sc3† 2.Ke3 Kg3 (a) 1.Bb7 Kd1 2.Be4 Sc6 1._ Kd4 2.Sg3 Rd5 3.Sd4 Sc4‡ 3.Kd3 Se5‡ 3.Se5 Sc5 4.Se2‡ (b) 1.Rf5 Sf6† 2.Kf4 Kf2 (b) 1.Bb5 Kf3 2.Kd3 Sc6 1.Sd2 Rf5† 2.Ke3 Sf6 3.Sg5 Sg6‡ 3.Bc4 Sb4‡ 3.Sf4† Ke5 4.Sc4‡ * * * Rotation 90º about f3 Rotation 90º about d3 Rotation 90º about e4 ------Eugene Albert Eugene Albert Norman A. Macleod ¶334 Ideal Mate Review #7 i- ¶409 Ideal Mate Review #8 iii- feenschach 1979 ii/1984 iv/1984 (¶228 Ideal Mate Review) w______w w______w w______w [wdwdwdwd] [wgwdwdwd] [wdwdwdwd] [dwdwhwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwHwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [iwdwdwdw] [wdwdkdwd] [wdwdwdNd] [wdw0wdwd] [4wdwdwdw] [dbdkdwdw] [dwdwdKdw] [wdwINdwd] [wdwdwdwd] [wdwdwdwd] [dwdBdwdw] [dwdwIwdw] [dRdwdwdw] w------w w------w w------w Helpmate in 3, (b) e2 c4 Helpmate in 3, (b) e1 f2 Helpstalemate in 4, (b) d4 b7 * * * (a) 1.Ra5 Ke1 2.Re5 Kf2 (a) 1.Bc4 Sf5 2.Be5 Kd1 (a) 1.Ka4 Ke4 2.Ka3 K×d4 3.Sd5 Bc2‡ 3.Bc3 Sf2‡ 3.Ka2 Rb2† 4.Ka1 Kc3= (b) 1.Rf3 Ba4 2.Rf4 Kc3 (b) 1.Bc2 Sb5 2.Bf4 Kf3 (b) 1.Ka6 Ke4 2.Ka3 Kd5 3.Sf5 Bc6‡ 3.Bd2 Se5‡ 3.Kb8 R×b7† 4.Ka8 Kc6= * * Symmetric Finale Rotation 90º about e4 (Bk K) Rotation 90º about d3 (Bk K) Rotation about centre. ------(or Reflection in 4|5 line) ------

26 EXACT ECHOES

------Fairy Pieces and Conditions Elmar and Erich Bartel Eugene Albert ------¶101 Chessics #21 ¶231 Ideal MateReview Ronald Brain Spring/1985 w______w ¶81 Chessics #20 w______w [wdwdkdwd] Winter/1984 [wdwdwdwd] [dwdwdwdw] w______w [dRdwdwdw] [wdwdNdwd] [wdwdwdBd] [wdwdwdwd] [dwdwdwdw] [dPdwdwdw] [dwdwdwdw] [wdwdNdwd] [wdwdwdwd] [wdwdwdwd] [dwdwIwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdkdwd] [wdwIwdwd] [dwdwdwdw] [Iwdwdwdw] [dkdwdwdw] w------w [wdwdwdwd] w------w Slipped Grid [dwdwdwdw] (0,3)+(1,3) Leaper b7 = Normal grid moved (1,1) w------w Mate in 3 Helpmate in 4, 2 ways Princess (= Bishop + Knight) * * Helpmate in 2, 1.Kc3 1.Ke7 Nf2 2.Kf6 Nd4 (b) rotate 90º clockwise 1.... Ka2 2.La4 Ka3 3.Ld3‡ 3.Kg5 Kf4 4.Kh4 Nf3 * 1.... Ka1 2.Kb3 Kb1 3.Lb4‡ 1.Kd7 Kd4 2.Kc8 Kc5 (a) 1.Ke5 Kb4 * 3.Kb7 Kc6 4.Kc8 Nd6 2.Kd6 b8(B+S) Rotation 90º about bc23 Rotation about 90º cd34 (b) 1.Kd5 B+Sg3 ------2.Ke6 g8(B+S) Elmar and Erich Bartel

Rotation 90º about de56 ¶1272 Jugendschach 6/i/1985 5. Rotation 180° ------w______w ------Elmar and Erich Bartel M. Nieroba [wdwdwdwd] ¶374 Ideal Mate Review #8 ¶1288 Jugendschach 6/i/1985 [dwdwdwdw] w______w iii-iv/1984 [wdwdwdwd] w______w [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwHwdw] [wdwdwdwd] [dwIwdwdw] [dwdwdwdw] [wdwdkdwd] [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [iwdwdNdw] [dwdwdwdw] [wdwdwdRd] w------w [Iwdwdwdw] [wdKdwdwd] (0,4)+(1,4)-Leaper [iwdwHwdw] [wdwHwdwd] Mate in 6 [dwdwdwdw] w------w * 50-Leaper = (1,7)+(5,5)- 1.Le5 Ka2 (or Kb1 leading to w------w Leaper Helpstalemate in 4, set identical play reflected in the Helpmate in 2, (b) a3 h6 play a1-h8 diagonal) 2.La5 Ka3 * * 3.Le4† Ka2 4.Kc2 Ka1 (a) 1.Kd6 Rb4 2.Kc5 Se4‡ 1.__ Ka2 2.Lf8 Ka1 5.La3 Ka2 6.Le2‡ (b) 1.Ke5 Rg5† 2.Kf4 Sd5‡ 3.La3 Ka2 4.Lh2= Symmetric Finale * 1.Kb3 Kb1 2.Ld8 Ka1 Rotation 90º about b2 Rotation 180º about centre of 3.Lc1 Kb1 4.Lb8= ------board Symmetric Finale ------Rotation 90º about b2 ------

27 EXACT ECHOES

------Paul Leibovici Eugene Albert E. Albert (2nd Prize) ¶335 Ideal Mate Chess ¶332 Ideal Mate Review #7 US Problem Bulletin 1964 Problems 1966 (also ¶338 Ideal i-ii/1984 (¶340 Ideal Mate Review) Mate Review 1984) w______w w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdB] [dwdwdwdb] [dkdwdwdN] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdw0wdw] [dwdwdwdw] [dwdwdpdw] [wdwdpdwd] [wdN0k0Kd] [wdw0wdwd] [dKdwiwdw] [dwdwdwdw] [dwdKdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwGwdw] [dwdw4wdw] [dwdwHwdw] w------w w------w w------w Helpmate in 3, (b) b3 h4 Helpmate in 4, (b) c4 d5 Helpmate in 3, (b) d3 d8 * * * (a) 1.Kd3 Bg8 2.e3 Bc3 (a) 1.Kd5 Kg5 2.Bd3 Kf6 (a) 1.Kc6 Ke2 2.Kd5 Sd3 3.e4 Bc4‡ 3.Ke4 Ke6 4.Re3 Sd2‡ 3.Ke4 Sf6‡ (b) 1.Kf4 Bf5 2.e3 Bg4 (b) 1.Kd3 Kf3 2.Re5 Kf2 (b) 1.Kc6 Ke7 2.Kd5 Sf6† 3.e4 Bg3‡ 3.Ke4 Ke2 4.Bf5 Sf6‡ 3.Ke5 Sd3‡ * * Rotation about e45 Rotation 180º about e34 Rotation 180º about e4 (Bk K) ------E. Albert ¶331 Ideal Mate Attila Benedek Colour-Change Echo Review #7, i-ii/1984 Sinfonie Scacchistica 1980 ------w______w (¶226 Ideal Mate Review) J. E. Funk ¶27 (p.362) [wdwdwdwd] w______w feenschach vii/1972 [dwdwdwdw] [wdwdwdwd] w______w [wdwdkGwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [wdwdbdwd] [dwdwdwdw] [wdw0wdwd] [dw4wdwdw] [wdwdwdnd] [dwdwdwdw] [wdwirdwd] [dwdKdkdw] [wdwdpdKd] [Iwgwdwdw] [wdNdwdwd] [dBdwdwdw] [wdwHwdwd] [dwdwdwdw] w------w [dwdwdwdw] [wdwGwdwd] Helpmate in 3, (b) g2 b4 w------w [dwdwgwdw] * Helpmate in 3, (b) a3 f6 w------w (a) 1.Kd5 Ba2† 2.Ke4 Bb1† * Helpmate in 2, duplex 3.Ke3 Bg5‡ (a) 1.Bd5 Sf3† 2.Kc4 Ka4 * (b) 1.Kd5 Ba2† 2.Ke4 Bg5 3.Rd4 Se5‡ black 1.Bh4 Bh6 2.Bf6 Se3‡ 3.Kd3 Bb1‡ (b) 1.Rd5 Kg6 2.Ke5 Kg5 white 1.Be3 Bb4 2.Bd4 Se7‡ * 3.Bd4 Sc4‡ * Rotation 180º about de3 * Rotation 180º about e5, with ------Rotation 180º about d45 colour reversal ------

28 EXACT ECHOES

------6. Lateral Edgar Holladay E. Albert Reflection ¶11 Ideal Mate Review #1 ¶112 Ideal Mate Review #4 ------i-ii/1983 vii-viii/1983 Helpmates w______w w______w ------[wdwdwdwd] [wdwdwdwd] Erich Bartel [dwdwdwdw] [dwdwdwdw] feenschach x-xi/1964 [kdwdwdwd] [wdwdwdwd] w______w [Hwdwdwdw] [dwdb)wdw] [wdrdwdwd] [wdwdwdwd] [wdw)k)wd] [dwdrdwdw] [Hwdwdwdw] [dwdw)wdw] [wdkdwdwd] [Kdwdwdwd] [wdwdwdKd] [dw)wdwdw] [dwdwdwdw] [dwdwdwdw] [PdNdPdwd] w------w w------w [dwIwdwdw] Helpmate in 2½, (c) a2 a8 Helpmate in 3, [wdwdwdwd] * (b) d5,e4,g2 b7,c6,e4 [dwdwdwdw] (a) 1.Sb1 Kb5 2.Sc6 Ka4 * w------w 3.Sc3‡ 1.Bf7 d5 2.Kf5 Kf3 3.Bg6 e4‡ Helpmate in 2, set play (c) 1.Sb5 Kb6 2.Sc4† Ka6 1.Ba8 Kd3 2.Kd5 f5 3.Bc6 e4‡ * 3.Sc7‡ * 1._ Kb4 2.Rcc7 Sa5‡ * Reflection in e-file. 1.Rb7 Kd4 2.Rcc7 Se5‡ (a-c) Reflection in 5-rank ------* [(b) a5 a8 not an exact echo] Edgar Holladay Reflection in c-file ------¶47 Ideal Mate Review #2 ------Michael McDowell iii-iv/1983 R. Richter ¶28 Chessics #18 w______w ¶381 Ideal Mate Review #8 Summer/1984 [wdwdwdwd] iii-iv/1984 w______w [dwdwdwdw] w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwHwdNdw] [dwdwdwdw] [dwdPdwdw] [wdwdwdrd] [wdwdwdwd] [wdwdKdwd] [drdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwiwdwd] [wHk0K0wd] [wdwdwiwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdKdwd] w------w [wdwdwdwd] [dwdwdwdw] Helpmate in 3, (b) c2 g2 [dwdwdwdw] w------w * w------w Helpmate in 3, 4 ways (a) 1.f1R Sc4 2.Rc1 Kf2 Helpmate in 2½, (b) e6 g2 * 3.Kd1 Se3‡ * 1.Rc6 Se6† 2.Kd5 Kd3 (b) 1.d1R Sc4 2.Rg1 Kd2 (a) 1.Kf7 Kg5 2.d8Q† Kh6 3.Rc5 Sf4‡ 3.Kf1 Se3‡ 3.Qh4‡ 1.Rf5 Sd6 2.Ke5 Ke3 * (b) 1.Kf1 Kg3 2.d8Q Kh2 3.Rf6 Sc4‡ Reflection in e-file. 3.Qh4‡ 1.Rc5 Sa6 2.Kd5 Kd3 ------Reflection in 4-rank 3.Re6 Sb4‡ ------1.Rf5 Sh6 2.Ke5 Ke3 3.Rd6 Sg4‡ Two different mates. Reflections in vertical median. ------

29 EXACT ECHOES

------E. Holladay and E. Albert Eugene Albert A. Kalotay ¶66 Ideal Mate Review #3 ¶412 Ideal Mate Review #8 The Problemist 1985(?) v-vi/1983 iii-iv/1984 w______w w______w w______w [wdwdKdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdN] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdw0wd] [wdwdkdwd] [dwdwdwdw] [dK$ndkdw] [dKdp0wdN] [wdwiP)wd] [wdwdw0wd] [wdwdwdwd] [dwdwdndw] [dwdwdwdw] [dwdwdwdN] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w w------w w------w Helpmate in 4, set play Helpmate in 3, (b) d5 e5 Helpmate in 3½, set play, * (a) 1.Ke5 Rc7 2.f5 Kc5 (b) after key of (a) 1._ f5 2.Ke5 Sg5 3.Sf6 Re7‡ * 3.Kf6 Kf8 4.Se5 Sh7‡ (b) 1.Ke4 Rc2 2.Sf3 Kc4 (a) 1._ d4 2.Sg5† Kd5 1.Sh4 e5 2.Kd5 Sf6† 3.f5 Re2‡ 3.Sf7 e4 4.Sf4‡ 3.Ke6 Sd5 4.Sf5 Sc7‡ Reflection in horizontal 1.Kb4 Kf5 2.Sg7† Ke4 Pawn pair theme median. 3.Sf2† Kd4 4.Sf5‡ * ------(b) same as (a) but set and play Reflection in ef line Edgar Holladay interchanged ------¶371 Ideal Mate Review #8 Reflection in horizontal Eugene Albert iii-iv/1984 median. ¶67(left) Ideal Mate Review #3 w______w ------v-vi/1983 [wdwdwdwd] Andrew Kalotay w______w [dwdwdwdw] ¶7 Chessics #17 [wdwdwdwd] [wdw1NIwd] Spring/1984 [dwdwdwdw] [dwdk0Ndw] w______w [wiwdwdwd] [wdwdwdwd] [wdwdwdwd] [0p0wdwdw] [dwdwdwdw] [dKdRdwdw] [pdpdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wIwdwdwd] w------w [wdrdkdwd] [dNdwdwdw] Helpmate in 3, [dwdwdwdw] w------w (b) rotate 90° a1 h1 [wdphwdwd] Helpmate in 4, 2 ways * [dwdwdwdw] * (a) 1.Qb8 Ke7 2.e4 Kd7 w------w 1.c3† S×c3 2.c4 Sd5† 3.Qe5 Se3‡ Helpmate in 4, (b) c2 d2 3.Kc5 Sc7 4.Kb4 Sa6‡ (b) 1.Ke5 Kd7 2.d4 Ke7 * 1.a3† S×a3 2.a4 Sc2 3.Qd5 Sd3‡ (a) 1.Rb4† Kc6 2.Rb2 Re7† 3.Ka5 Sd4 4.Kb4 Sc6‡ Rectangular setting. 3.Kd3 Kc5 4.Kc3 Re3‡ * Reflection in vertical median. (b) 1.Rd4 Kc6 2.Kd3 Rb7 Reflection in b-file Rotation twinning leading to 3.Re4 Kd5 4.Re2 Rb3‡ [¶67(right) not an exact echo] reflection echo! White R controls sequence. ------Reflection in cd line. ------

30 EXACT ECHOES

------A. Kalotay Chess Life ii/1984 Edgar Holladay Andrew Kalotay w______w ¶371 Ideal Mate Review #7 ¶31 Chessics #18 [wdwdwdwd] i-ii/1984 Summer/1984 [dKdRdwdw] w______w w______w [wdwdwdwd] [wdwdKdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdw0wdw] [wdwdkdwd] [wdwdwdwd] [wdwdw4wd] [hwdwdwdw] [dwdwgwdw] [dwdKdwdw] [wdp0wdwd] [wdwdrdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdRdw] [dwdwdwdw] w------w [wdwiPdwd] [wdkGPdwd] Helpmate in 4, 2 ways [dwdwdwdw] [dwdwdwdw] * w------w w------w 1.Sb5 Rf7 2.Kd3 Kc6 Helpmate in 4, (b) f3 b3 Helpmate in 5, (b) d5 c5 3.Sd4† Kd5 4.Se2 Rf3‡ * * 1.Sc4 Kc6 2.Sb2 Ra7 (a) 1.Re3 Kd7 2.Kc3 Kc6 (a) 1.Rd6+ Ke4 2.e6 Bh6 3.Kd3 Kc5 4.Kc3 Ra3‡ 3.Kd4 Kb5 4.Re4 Rd3‡ 3.Kc3 Kf3 4.Kd4 e4 * (b) 1.Bc3† Kf7 2.Ke3 Kg6 5.Ke5 Bg7 Reflection in cd line 3.Kf4 Kh5 4.Be5 Rf3‡ (b) 1.e6 e4 2.Kd3 Ba5 ------Switchbacks by black R and B 3.Ke3 Kc4 4.Kf4 Kd3 Edgar Holladay * 5.Ke5 Bc7 ¶26 Ideal Mate Review #1 Reflection in e-file. * i-ii/1983 ------Reflection in e-file. w______w Andrew Kalotay ------[wdwdwdbd] ¶30 Chessics #18 Andrew Kalotay [dwdwdwdw] Summer/1984 ¶32 Chessics #18 [wdwdwdwd] w______w Summer/1984 [dwdwdwdw] [wdwdwdwd] w______w [wdwdwdkd] [dwdr0wdw] [wdwdwdwd] [dwdwdw4w] [wdwdwdwd] [dwdw0wdw] [wdwdwdNd] [dwdwdwdw] [wdwdwdwd] [dwdwdwIw] [wdwdKdwd] [dwdwdwdB] w------w [dwdBdwdk] [wIwdwdwd] Helpmate in 4, (b) g1 g7 [wdwdPdwd] [dwdwdwdw] * [dwdwdwdw] [wdkdPdw4] (a) 1.Bf7 Kh1 2.Bh5 Se1 w------w [dwdwdwdw] 3.Kh4 Kh2 4.Rg4 Sf3‡ Helpmate in 5, (b) d7 c3 w------w (b) 1.Be6 Se3† 2.Kh4† Kh7 * Helpmate in 5, 3.Bh3 Kh6 4.Rg4 Sf5‡ (a) 1.Kh4 Kf4 2.Kh5 e4 (a) b4 d5, (b) h2 d2 White King tempo moves 3.Kg6 e5† 4.Kf7 Bh7 * * 5.Ke6 Bg8‡ (a) 1.e5 e3 2.Rd2 Ke4 Reflection in 4-rank (b) 1.Kg4 Ba6 2.Rf3 Kd4 3.Rd5 Kf3 4.Kd3 Kf2 ------3.Kf5 e4† 4.Ke6 e5 5.Ke4 Bg6‡ 5.Rf7 Bc8‡ (b) 1.Rd5 e3 2.Kd3 Be8 Reflection in e-file 3.Ke4 Kc3 4.Rf5 Kd2 * 5.e5 Bc6‡ This and the next three form a * set in which the same mate Reflection in e-file. configuration occurs but shifted ------down one rank each time ------

31 EXACT ECHOES

------Andrew Kalotay Serieshelpmates Selfmate ¶33 Chessics #18 ------Summer/1984 William Anderson W. A. Shinkman w______w ¶4 Ideal Mate Review #1 Chess Players Chronicle 1881 [wdwdwdwd] i-ii/1983 (¶V in Dedrle) [dwdw0wdw] w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [Gwdwdwdw] [dwdwdwdw] [dwdQdwdw] [w4wdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwIw] [dwdwdwdw] [dwdbdwdw] [wdwdPdwd] [wdriwdwd] [w$wdw$wd] [dwdwdwiw] [dwdrdwdw] [dwdkdwdw] w------w [wdw!wdwd] [wdw0wdwd] Helpmate in 5, [dwdKdwdw] [dwdKdwdw] (a) a5 a3, (b) b4 d8 w------w w------w * Serieshelpmate in 4, 2 ways Selfmate in 2 (a) 1.e5 Kf3 2.Rf4† Ke3 * * 3.e4 Kd2 4.Kf2 Kd1 1-4.Ke4 Rg3 Kf3 Rf4 - Qe2‡ 1.Qd6 Kc3/e3 5.Ke3 Bc5‡ 1-4.Rb4 Kc4 Ra3 Kb3 - Qc2‡ 2.Rf3/b3† B×f3/b3‡ (b) 1.Rd4 Kh3 2.Kf2 Bd8 * Symmetry. 3.Ke3 Kg2 4.e5 Kf1 Reflection in d-file. * 5.e4 Bg5‡ ------Reflection in d-file. * Carl-Philip Nilsson ------Reflection in e-file. Tidskrift för Schack 1982 Direct Mates ------(The Problemist vii/1986) ------Completing the set of four w______w Bonus Socius compositions. Such a set is said [wdwdwdwd] Manuscript c.1350 to form a Fox Family [dndwdwdw] (¶II in Dedrle) (named after C. M. Fox who [wdw4wdwd] w______w was fond of publishing sets of [1wiwIwdw] [wdwiwdwd] related compositions). [$wdwdwdR] ------[wdwdwdwd] [dwdwdwdw] [wdwhwdwd] [dwdwdwdw] [wdwdwdRd] [dwdwdwdw] [wdwdwdwd] w------w [dwdKdwdw] Serieshelpmate in 9, 2 ways [wdwdwdwd] * [dwdwdwdw] 1.Sd8 2.Se6 3.Rd8 4.Re8 5.Qd8 w------w 6.Kc6 7.Kd7 8.Ke7 9.Sf8 Rg7‡ Mate in 2 1.Rd2 2.Sd6 3.Se4 4.Re2 5.Qd2 * 6.Kc4 7.Kd3 8.Ke3 9.Sf2 Rg3‡ 1.Rg7 Sc8,Sf7/Se8,Sb7 * 2.Rg8/Ra8‡ Symmetric. Reflection in 5-rank * ------Reflection in d-file ------

32 EXACT ECHOES

------G. F. Myhre F. Hofmann W. A. Shinkman Verdens Gang 1973 Sonntagsblatt 1887 ¶601 in Wallis 777 w______w w______w Miniatures in Three 1908 [wdQdwdwd] [wdwdwdwd] w______w [dwGwdwdw] [dw)w)w)w] [wdwdwdwd] [wdwdwdwd] [wdw)k)wd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdpdwdwd] [wdwdKdwd] [dwdwdwdR] [dwiwdwdw] [dwdwdwdw] [wdwdKdk0] [wdPdwdwd] [wdwdwdwd] [dwdwdwdR] [dwIwdwdw] [dwdwdwdw] [wdwdwdwd] w------w w------w [dwdwdwGw] Mate in 2 Mate in 3 w------w * * Mate in 3 1.Qf5 Kb4/Kd4 2.Qa5/Qe5‡ 1.e8B * Tries: 1.Qa6/e6? Kd4/b4! 1.... K×d6 2.c8R Ke6 3.Rc6‡ 1.Bd4 Asymmetry. 1.... K×f6 2.g8R Ke6 3.Rg6‡ 1.... K×h5 2.Kf5 Kh6 3.R×h4‡ * Symmetry. Underpromotions. 1.... K×h3 2.Kf3 Kh3 R×h4‡ Reflection in c-file * Symmetry. ------Reflection in e-file. Bk P is effectively a dummy. J. Scheel ------* Magasinet (Politiken) 1931 S. Loyd ¶451 in Wallis 777 Reflection in 4-rank. w______w Problems 1908 ------[wdwdwdwd] w______w R. Sahlberg [dwdwdwdw] [wdwdwdwd] Aftonbladet 23/vii/1905 [wdwdwdwd] [dwdwdwdw] w______w [dwdwIwdw] [wdwdwdwd] [wdwdBdwd] [wdwdwdwd] [dwdwdwdR] [dwdwdwdw] [dwdw!wdw] [wdwiwdwd] [wdPdKdPd] [wdwdPdwd] [dwdwdwdw] [dpdwdwdp] [dwdwiwdw] [wHwIwdwd] [w)wdkdw)] w------w [dwdBdwdw] [dPdN0NdP] Mate in 3 w------w [wdwdPdwd] * Mate in 3 [dwdw$wdw] 1.Ke4 * w------w 1.... Kd1 2.Kd3 Ke1 Qg1‡ 1.Sd3 Mate in 3 1.... Kf1 2.Kf3 Ke1 Qc1‡ 1.... Kc4 2.Ke3 Kc3 3.Rc5‡ * * 1.... Ke4 2.Kc3 Ke3 3.Re5‡ 1.Ke7 Symmetry * 1.... Kd5 2.Sf2 e×f2 3.e4‡ Reflection in e-file. Reflection in d-file 1.... Kf5 2.Sd2 e×d2 3.e4‡ ------Symmetry. * Reflection in e-file ------

33 EXACT ECHOES

------M. Havel Bohemia 1904 Fairy Pieces and Conditions A. H. Kniest (quoted in Dedrle) ------¶838 Problemist Fairy Chess w______w Frederick M.Mihalek Supplement vi/1933 [wdwdkdwd] ¶398 Ideal Mate Review #1984 w______w [dwdwdwdw] w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [iw)wdwdw] [dwdwIwdw] [dRdwdw!w] [w1wdwdwd] [wdwdwdQd] [wdk!wdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdndwd] [wdw)wdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] w------w [wdwdwdwd] [dwdwdwdw] Mate in 3 [dwdwdwdK] w------w * w------w Grasshopper. No Wt K. 1.Ke6 Grasshoppers Helpstalemate in 2, set mate 1.... Sd4† 2.Q×d4 Kf8 3.Qh8‡ Helpmate in 2½, (b) h1 a2 * 1.... Sf4† 2.Q×f4 Kd8 3.Qb8‡ * 1._ c8Q= 1.... Kd8 2.Kd6 Ke8 3.Qg8‡ (a) 1.Kg2 Kd5 2.Rb5† Ke4 1.Gd8 c8Q 2.Gb8 Qc6= 1.... Kf8 2.Kf6 Kd8 3.Qc8‡ 3.Re5‡ (Wt Kh7 would not affect the * (b) 1.Ga7 Kd5 2.Rb5† Kc4 solution) Two different echoed mates. 3.Rc5‡ * Reflections in e-file. Reflection in d-file Reflection in 7-rank If S moves instead of K on ------move 2 there are further echoes P. A.Petkow Zvonimir Hernitz but dual mate (Qd7 after Kd8). feenschach 1964 ¶17 Chessics #17 ------w______w Spring/1984 Michael McDowell [wdwdwdwd] w______w ¶74 Chessics #20 [dwdwdwdw] [wdwIwdwd] Winter/1984 [wdwdwdwd] [dRdw0wdw] w______w [dwdq1wdw] [wdwdwdwd] [wdwdQdwd] [wdwdwdwd] [dwdwiwdw] [dwdwdwdw] [dwdwdwdQ] [wdwdwdwd] [wdwIwdwd] [wdwiwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwiwdwd] w------w [dwdwdwdw] [dwdwdwdw] Grasshoppers. No Wt K w------w [w)wdPdwd] Helpmate in 3, 2 ways Equihopper [dwdwdwdw] * Helpstalemate in 4, (b) b7-g5 w------w 1.Kd1 Qe3 2.Ge2 Qd3† * Mate in 3, set play 3.Gd2 Qb1‡ (a) 1.Ke6 Eh5 2.Kf6 Ed7 * 1.Ke1 Qd3 2.Gd2 Qe3† 3.Kg7 K×e7 4.Kh8 Kf7= 1._ Kc4 2.Qa4 3.Ge2 Qg1‡ (b) 1.Kd5 Ea5 2.Kc6 E×e7 1.Kc6 Kc4 2.Qb8 Kd4 3.Qf4 [originally with Wt Kh8] 3.Kb7 Kd7 4.Ka8 Kc7= Reflection in cd Reflection in vertical median. Reflection in vertical median ------

34 EXACT ECHOES

------Russell E. Rice Elmar Bartel and Hans Gruber Hilmar Ebert version ¶15 Chessics #17 ¶103 Chessics #21 ¶77 Ideal Mate Review #3 Spring/1984 Spring/1985 v-vi/1983 w______w w______w w______w [r$wdwdwd] [wdwdwdwd] [wdwdwdwd] [0wdwGwdw] [dwdwdwdw] [dwdwdwdw] [Bdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdKdkdwH] [dwdKdkdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwiNdwd] [wdwdwdwd] [dwdwdwdw] [dKdwdwdw] [dqdwdwdw] w------w w------w w------w Dababba = (0,2)-mover (1,2)+(1,3)+(2,3) Leaper e2 Captureless Chess Serieshelpstalemate in 8, Stalemate in 12 Helpmate in 5, 2 ways (a) d3 e5, (b) f3 b1 * * * 1.Lg5 Kd1 2.Kb2 Kd2 1.Ke5 Kc5 2.Kf6 Kd6 (a) 1-8.Kg4-h5-g6-f7-×e7- 3.Kb3 Ke3 4.Kc4 Kf4 3.Kg7 Ke7 4.Kh8 Kf8 d7-c7-×b8 Kd6= 5.Lf7 Kf5 6.Kd5 Kf4 5.Qh7 Sg6‡ (b) 1-4.R×b8-b6-×a6-a1 5- 7.Ld6 Kg3 8.Ke4 Kf2 1.Qb8 Sf5 2.Kf3 Kd3 8.a54321 Ba3= 9.Lf5 Ke1 10.Ke3 Kf1 3.Kg2 Ke2 4.Kh1 Kf1 * 11.Kf3 Ke1/g1 12.Lg3=/Le3= 5.Qh2 Sg3‡ Reflection in horizontal median Length record. Reflection in horizontal median [Original had knight b8.] Reflection in f-file. ------D. L. Brown ¶406 Ideal Mate Review #8 iii-iv/1984 w______w [wdwdkdr4] [dwdwdwdw] [wdwdwIwd] [dwdwdwHw]

[wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] w------w Circe Chess Helpmate in 3, (b) g5 d8 (a) 1.Rh3 Sh3(Ra8) 2.Kf8 Sg5 3.Re8 Sh7‡ (b) 1.Rg7 Sc6 2.Re7 Kg6 3.00 Se7(Rh8)‡ Reflection in fg line. ------

35 EXACT ECHOES

------7. Diagonal Jozef Pinter G. E. Schoen Reflections ¶23 Chessics #18 ¶188 Ideal Mate Review #5 ------Summer/1984 ix-x/1983 Helpmates w______w w______w ------[wdwdwdwd] [wdwdwdwd] Josef Kricheli [dwdwdwdw] [dwdwdwdn] version ¶52v Chessics #19 [w!Ndwdwd] [wdwdwdwd] Autumn/1984 [dwdwdwdw] [IwdwdwdN] w______w [wdwdkdwd] [ndwdwdwI] [wdwdwdwd] [dwdwdwdw] [Hwdwdwdw] [dwdwdwdw] [wdKdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [iwdwdwdk] [dwdwdwdw] w------w w------w [wdwdRdwd] Helpmate in 2, set play, Left: Helpmate in 2½, [4wdkdwdw] (b) c6 g2 (b) a3 a5 [wdRdwdwd] * Right: Helpmate in 3, [dKdwdwdw] (a) 1._ Kd1 2.Kd3 Qd4 (b) h5 h3 w------w 1.Kf3 Qg1 2.Ke2 Sd4 * Helpmate in 2, set play (b) 1._ Kb3 2.Kd3 Qe3 Left: (a) 1.Kb4 Sc3 * 1.Kd5 Kd2 2.Kc4 Se3 2.Kb3 Sb1 3.Sc2‡ 1._ cRc4 2.Rc3 cRd4‡ * (b) 1.Kb3 Sc3 1.Ra2 cRe2 2.Rd2 2Re3‡ Exact echo only in set plays. 2.Kc2 Sa2 3.Sb3‡ * Reflection in b1 diagonal. Reflection in a1 diagonal. Reflection in b1 diagonal ------* ------C. E. Lind Right: (a) 1.Sg5 Kg3 Manfred Zucker after J. Bajtay and A. Kniest 2.Sf3 Kf2 3.Sh2 Sg3‡ ¶124 Ideal Mate Review #4 ¶453 Ideal Mate Review #8 (b) 1.Sg5 Kg4 vii-viii/1983 iii-iv/1984 2.Sf3 Kg3 3.Sg1 Sf2‡ w______w w______w Reflection in h1 diagonal [wdwdwdwd] [wdwdwdwd] ------[dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [wdwdKdwd] [wdwdNdwd] [dwdwdwdR] [dwdwdK0w] [wdwdwdkd] [wdwdwdwd] [dwdwdRdw] [dwdwdwdk] w------w w------w Helpmate in 2, 2 ways Helpmate in 2, (b) g3 f2 * * 1.K×f1 Ke3 2.Ke1 Rh1‡ (a) 1.g2 Kg3 2.g1S Sf2‡ 1.K×h3 Kf4 2.Kh4 Rh1‡ (b) 1.f1S Kf2 2.Sh2 Sg3‡ Symmetry * Reflection in h1 diagonal Reflection in h1 diagonal ------

36 EXACT ECHOES

------J. Kubecka E. Holladay Josef Kricheli (dedicated to E. Holladay) ¶455 Ideal Mate Review #8 ¶241 Ideal Mate Review #6 ¶376 Ideal Mate Review #8 iii-iv/1984 xi-xii/1983 iii-iv/1984 w______w w______w w______w [wdwdwdwd] [wdwdRdwd] [wdwdwdwd] [dwdwdwdw] [dpdrdwdw] [dwdwdwdw] [wdkdwdwd] [wdwdwdwd] [wdwdw)wd] [dwdwdwdw] [dbdkdwdw] [dwdkdwdw] [NdwdKdwd] [wdwdwdwd] [wdwgrdwd] [dwdwdwdw] [dwdwIwdw] [dwdwdKdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwGwdwdw] [dwdwdwdw] [dwdwdwdw] w------w w------w w------w Helpmate in 3½, (b) a4 e4 Helpmate in 4, (b) rotate 180° Helpmate in 3, 2 ways * * * (a) 1.Sc5 Kb5 2.Kd5 Kb4 (a) 1.Rd6 Kf4 2.Ra6 Kf5 1.Re6 f7 2.Bf6 f8Q 3.Kc6 Ka5 4.Bd2‡ 3.Kc6 Ke6 4.Rb6 Rc8‡ 3.Ke5 Qc5‡ (b) 1.Sd6 Kd7 2.Kb5 Ke7 (b) 1.Rf2 Rh1 2.Bd1 Ke6 1.Bc3 f7 2.Rc4 f8Q 3.Kc6 Kd8 4.Bg5‡ 3.Kf3 Kf5 4.Be2 Rh3‡ 3.Kd4 Qd6‡ * Tempo moves by R and B. * Reflection in h1 diagonal Reflection in a1 diagonal Reflection in h1 diagonal ------Rotation twin, reflection echo! ------A. Kalotay ------Frederick M. Mihalek The Problemist 1985(?) Edgar Holladay ¶29 Chessics #18 w______w ¶8 Chessics #17 Summer/1984 [wdwdwdwd] Spring 1984 w______w [dwdwdwdw] w______w [wdwdwdwd] [wdwhwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [drdwdwdw] [wdwdwdwd] [wdwdkdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdw1wdw] [wdwdwdwd] [w$Kdbdwd] [wdwdkdwd] [dwdwdKdw] [dwdrdwdw] [dwdwHwdw] [wdwdwhBd] w------w [wdwdKdwd] [dwdwdwiw] Helpmate in 4, 2 ways [dwdwdwdw] w------w * w------w Helpmate in 3, (b) f2 = black P 1.Rd4 Kc1 2.Bc4 Rf2 Helpmate in 5, 2 ways * 3.Kd3 Kd1 4.Se4 Rf3‡ 1.Qa1 Kf2 2.Kd3 Sd5 (a) 1.Sh3 Bf1 2.Kh1 Kg3 1.Rd3 Rb5 2.Re3 Kb2 3.Kc2 Ke2 4.Kb1 Kd1 3.Sg1 Bg2‡ 3.Kd3 Kb3 4.Se4 Rd5‡ 5.Rb2 Sc3‡ (b) 1.f1S Bh3 2.Kh1 Kf2 * 1.Qh8 Sd5 2.Kf5 Kf3 3.Sh2 Bg2‡ Reflection in b1 diagonal 3 Kg6 Kg4 4.Kh7 Kh5 * ------5.Rg7 Sf6‡ Reflection in h1 diagonal Reflection in h1 diagonal. ------

37 EXACT ECHOES

------Frank Fillery and Helpstalemates Eugene A. Dugas Edgar Holladay ------¶322 Ideal Mate Review #7 ¶320 Ideal Mate Review #7 Frederick M. Mihalek and i-ii/1984 i-ii/1984 Eugene Albert ¶122(b) w______w w______w Ideal Mate Review #4 [kdwdwdwd] [wdwdwdwd] vii-viii/1983 [dwdwdwdw] [dwdwdwdw] w______w [wIwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwgwdw] [dRdwdwdw] [wdPdwdwd] [wdwdwiwd] [wdwiwdwd] [dwdwdwdw] [dwdwdwdw] [dwdNdwdw] [wdwgwdwd] [wdwdwdKd] [wdwdKdwd] [dwdwdwdw] [dwdwdBdw] [dwdwdwdw] w------w w------w [wdwdwdwd] Helpstalemate in 3, (b) c4 d4 Helpmate in 5, (b) f1 h3 [dwdwdwdw] * * w------w (a) 1.Be3† Kc7 2.Ba7 c5 (a) 1.Ke3 Kh3 2.Kf2 Kg4 Helpstalemate in 2, set play 3.Bb6† c×b6= 3.Kg1 Kf3 4.Kh1 Kf2 * (b) 1.Bf4 d5 2.Bb8 d6 5.Bh2 Bg2‡ 1._ Sf6 2.Ke6 Se8= 3.Bc7† d×c7= (b) 1.Bd4 Kf1 2.Kg3 Ke2 1.Kc5 Sc3 2.Kc4 Sa4= * 3.Kh2 Kf3 4.Kh1 Kg3 Reflection in h1 diagonal (a-b) Reflection in h1 diagonal 5.Bg1 Bg2‡ [(a) Sd5 at h7, echoes not exact] [(c) d2 c2, 1.Be4 c5 2.Bb7 c6 Reflection in h1 diagonal ------3.Kb8 c×b7= not an echo] ------K. Hannemann ¶499 ------Edgar Holladay Problemnoter xii/1955 Hilmar Ebert Bulletin d'Information du w______w ¶117 Ideal Mate Review #4 Club d'Echecs de Geneve 1970 [wdwdwdwd] vii-viii/1983 (¶191g Ideal Mate Review 983) [dwdwdwdw] w______w w______w [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwHwdwd] [wdwdwdwd] [wdwdwdwd] [dKdwdwdw] [dwdwiwdw] [dwdwdwhw] [wdwdwdwd] [wdwdwdwd] [wdwdwdkd] [iwdwdwdw] [dwdKdwdw] [dwdwdwdw] w------w [wdwdwdwd] [wdwdwdKd] Helpstalemate in 3, set play [dBdwdwdw] [dwdwdwHw] * w------w w------w 1._ Kb1 2.Se2 Ka1 3.Sc3= Helpstalemate in 3½, 2 ways Helpmate in 5, 2 variations 1.Kc2 Ka2 2.Sb5 Ka1 3.Sc3= * 1.Sf3 Kf1 2.Kg3 Pendulum key 1.Ba2 Kf6 2.Ke4 Kg7 2... Ke2 3.Kh2 Kf2 Reflection in a1 diagonal. 3.Kf5 Kh8 4.Kg6= 4.Kh1 Se2 5.Sh2 Sg3‡ ------1.Kc4 Kf6 2.Kd5 Kg7 2... Sh3 3.Kh2 Kf2 3.Kg6 Kh8 4.Kf7= 4.Kh1 Kg3 5.Sg1 Sf2‡ Reflection in a1 diagonal * ------Asymmetry. Colour-symmetry. The position before the variation also has colour symmetry. Reflection in h1 diagonal ------

38 EXACT ECHOES

------Direct Mates Direct Stalemate Fairy Pieces ------G. Neukomm Zvonimir Hernitz G. P. Jelliss British Chess Chess Amateur 1924 ¶50 Chessics #19 Magazine 1976 w______w Autumn 1984 w______w [wdwdwdwd] w______w [wdwdwdwi] [dwdwdwdQ] [wdwdwdwd] [dwdw4wdb] [wdwdwdwd] [dwdwdwdw] [Qdwdwdwd] [dwdwdKdw] [wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [dwdwdwdw] [wdwdwdwG] [dwdkdwdw] [wdwdwdwd] [dwdwdwdw] [w$Ndwdwd] [dwdwdwdw] [wdwdwdwd] [dw$wdwdw] [wdwIwdwd] [Iwdwdwdw] w------w [iwdBdwdw] w------w Mate in 2 w------w Grasshopper * Stalemate in 3 Helpmate in 3, 2 ways 1.Qa7 1.Kc3 * 1.... Kc4/Kc3 2.Qd4‡ 1.... Ka2 2.Bc2 Ka3/Ka1 1.Re2 Gf1 2.Rg2 Gh3 1.... Ke2/Kd2 2.Qe3‡ 3.Bb3/Kb3= 3.Rg8 Bf6‡ Asymmetry. 1.... Kb1 2.Bb3 Kc1/Ka1 1.Rb7 Bd8 2.Bg8 Gc8 Two different echoed mates. 3.Bc2/Kc2= 3.Rh7 Bf6‡ Reflections in b1 diagonal. The three-piece trick, Double-check mates. Each ------remarkable [R.Brain]. individual check W. Pauly * can be defended but not both. Deutsche Schachzeitung 1913 Reflection in a1 diagonal. * (¶320 in Dedrle) ------Reflection in a1 diagonal. w______w Wt K participates in echo but [Rdwdwdwd] not mate. It stops 1.Ra7 etc. [dwdwHwdw] ------[wdwdwdwG] [dwdwdwdw]

[wdwdkdwd] [dBdwdwdw] [wdwdwdwd] [dwdwdwdK] w------w Mate in 5 * 1.Sc6 1.... Kf5 2.Bf7 Kf6 3.Ra7 Kf5 4.Ra4 Kf6 5.Rf4‡ 1.... Kd3 2.Bc1 Kc3 3.Rb8 Kd3 4.Re8 Kc3 5.Re3‡ Reflection in h1 diagonal ------

39 EXACT ECHOES

------J. Dohrn-Luttgens ¶2023 Zvonimir Hernitz feenschach 1954 ¶59 Chessics #19 w______w Autumn/1984 [wdwdwdwd] w______w [dwdwdwdw] [ndwdwdwd] [wdwdwdwd] [dNdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdKdwd] [dwdwdwdw] [dwdwdwdB] [wdwdwdwd] [wdwdQdwi] [dwIwdwdw] [dwdwdwdq] [wdwdwdwd] w------w [iwdwdwdw] Grasshoppers w------w Helpmate in 3, set play, Nightriders (b) after key of (a) Helpstalemate in 2, 3 ways * * (a) 1._ Bf1 2.Ge1 Kf3 1.Nd2 Nh4 2.Nb3 K×b3= 3.Gg1 Bg2‡ 1.Ne6 Nd8 2.Nc2 K×c2= 1.Kg1 Kf3 2.Gh4 Gg4 * 3.Gh2 Bg2‡ Reflection in a1 diagonal (b) set and play interchange ------Reflection in h1 diagonal E. Holladay feenschach 1965 ------(also Ideal Mate Chess P. Kniest Problems) Die Schwalbe 1964 w______w w______w [wdwdwdwd] [wdwdwdkd] [dwdwdwdw] [dwdwdw1w] [wdwdwdwd] [wdwdwdKd] [dwdwdwdw] [dwdwdwGw] [wdwdwdwd] [wdwdwdwd] [dwdwdKdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwdkdN] [dwdwdwdw] w------w w------w Reflecting Zebrarider h1 Grasshopper Helpmate in 3, set play Helpmate in 4, 2 variations * * 1._ Zb5 2.Kg1 Ke3 1.Kh8 3.Kh1 Kf2‡ 1.... Kf7 2.Ge7 Kf8 1.Kg1 Zd7† 2.Kh2 Kf4 3.Gh4 Bh6 4.Gh7 Bg7‡ 3.Kh1 Kg3‡ 1.... Be7 2.Gg5 Kh6 (Zb5 guards h2 via d8, 3.Gd8 Bf8 4.Gg8 Bg7‡ Zd7 guards g1 via a5) Reflection in a1 diagonal Reflection in h1 diagonal ------

40 EXACT ECHOES

------*

8. Transflections Michael McDowell 1.Ke6 Ke4 2.Gf7 Sc5 ------¶27 Chessics #18 1.Gd4 Ke2 2.Ke4 Sg3 Orthodox Pieces Summer/1984 Reflection in e with (0,2) shift ------w______w * M. Schwalbach 1.Kf6 Kf4 2.Lg7 Sd5 ¶2030 Die Schwalbe 1977 [wdwdwdwd] [dwdwHwdw] 1.Lc4 Kd2 2.Kd4 Sf3 w______w Reflection in e with (0,2) shift [wdNdwHwd] [wdKdkdwd] [dwdwdwdw] ------[dwdp0wdw] T. Steudel [wdwdwdwd] [w4wdndwd] feenschach 1960 [dwdkdwdw] [dwdwdwdw] w______w [wdwdwdwd] [wdwdNdwd] [wdwdwdwd] [dwdwIwdw] [dwdwdwdw] [dwdKdwdw] [wdwdwdwd] w------w [wdwdwdwd] [dwdwdwdw] Helpmate in 3, 2 ways [dwdwdwdw] * w------w 1.Rd4 Kb5 2.Rd6 Sc6 [wdndkdwd] Helpmate in 3, set play 3.Kd5 Sf4 [dwdw)ndw] * 1.Sf6 Kc5 2.Re4 Sd4† [wdQ)wdwd] 1._ Kd3 2.d6 Sd7 3.e6 Se7‡ 3.Ke5 Sg6 [dwdwdwdw] 1.e5 Ke2 2.Ke4 Se6 3.d5 Sd6‡ Reflection in 5 and unit shift. w------w * ------Grasshopper Reflection in de and unit shift Fairy Pieces or Conditions Helpmate in 3, set play ------* Michael McDowell G. P. Jelliss, Unpublished 1._ Ke6 2.Sb2 Ga2 version ¶26 Chessics #18 (Composed 7 August 1988) 3.Sd3 Ge2‡ Summer/1984 w______w 2.Sg5 Gf5 2.Kd5 d4 w______w [wdwdwdwd] 3.Se4 Gd3‡ [wdwdBdwd] [dwdwdwdw] Reflection in de with unit shift [dwdbdwdw] [wdwdw1wd] ------[wdwdwdwd] [dwdqiNdw] Erich Bartel and A. H. Kniest [dwdwdwdw] [wdwdwdwd] Diagramme und Figuren [wdwiwdwd] 1/xii/1964 [dwdNIwdw] w______w [dwdwHwdw] [wdwdwdwd] [wdKHwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w w------w [w!w0wdwd] Grasshoppers (or Alfils) [dwdkdwdw] Helpmate in 2½, (b) c2 f3 Helpmate in 2, 2 ways * w______w [wdwdwdwd] (a) 1.Sf3† Ke4 2.Sg2 Bf5 [wdwdwdwd] [dwdKdwdw] 3.Bc6‡ [dwdwdwdw] [wdwdwdwd] (b) 1.eSc4 Kd5 2.Sb3 Bc6 [dwdwdwdw] 3.Bf7‡ [wdwdwdnd] [dwhwiwHw] w------w * Checkless Chess Reflection in de and unit shift [wdwdwdwd] Helpstalemate in 2, set play ------[dwHwIwdw] * [wdwdwdwd] 1._ Qa7 2.Kc6 Kc4= [dwdwdwdw] 1.Ke5 Ke3 2.d5 Qg6= w------w * Lancers = (2, 4) Leapers Reflection in d-file and unit Helpmate in 2, 2 ways shift ------

41 EXACT ECHOES

------

Multiple Echoes Edgar Holladay Edgar Holladay The exact echoes here show ¶9 Chessics #17 version Schach Echo 1975 two or more of the five types of Spring/1984 (¶273 Ideal Mate Review #6 transformation. w______w xi-xii/1983) ------w______w Helpmates [wdwdwdwd] ------[dw)wdwdw] [wdwdwdwd] Edgar Holladay [wdwdkdwd] [dwdwdwdw] ¶24 Chessics #18 [dwdw4wdw] [wHwdwdwd] Summer/1984 [wdw1wdwd] [dkdwdwdw] w______w [dwdwdwdw] [wHwdwdwd] [wdwdwdwd] [wdKdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdQd] w------w [dKdwdwdw] [dwdwiwdw] Helpmate in 2½, w------w [wdwdwdwd] (b) c2 c8, (c) d4 d5, Helpmate in 2½ [dwdKdwdw] (d) c7 d6, (e) c8 g7 (b) b1 b2, (c) b1 b3, [wdwdwdwd] successive twinning. (d) b1 b7, (e) b1 b8 [dwHwdwdw] * (all positions of Wt K on b-file) w------w (a) 1.Kb3 Qd6 2.c8Q† Kd5 * 3.Qc4 (a) 1.Sd7 Ka4 Sc5† Ka3 Helpmate in 2 (b) 1.Kb7 Kd6 2.c8Q Kd5 3.Sc2‡ 2 set plays, 2 ways 3.Qc6 (b) 1.S6d5 Ka5 2.Sc6† Ka4 * (c) 1.Kb8 Kd6 2.c8Q Re6 3.Sc3‡ 1._ Qh5† 2.Kf4 Se2 (1) 3.Qc7 (c) 1.S4d5 Ka6 2.Sc7† Ka5 1._ Ke2 2.Kf4 Sd3 (2) (d) 1.d7 Qf3 2.d8Q Qf6 3.Sc4‡ 1.Kf4 Kc4 2.Ke5 Sd3 (3) 3.Qd7 (d) 1.S6d5 Ka4 2.Sc3† Ka5 1.Kf4 Se2† 2.Kf3 Qg3 (4) (e) 1.d7 Re4 2.d8Q Ke5 3.Sc6‡ * 3.Qf6 (e) 1.S4d5 Ka5 2.Sc4† Ka6 (1-2): Reflection in c1 diag * 3.Sc7‡ (1-3): Translation (1,1) (a-b) Reflection in 5-rank * (2-3): Reflection in b1 diag (a-c) Reflection in 5|6 line (a-b), (b-c), (d-e) translation 1v (4) Different mate (a-d) Rotation 90° about e5 (a-c) translation 2v ------(a-e) Transflection: (= reflect in (a-d) reflection in 4

h12 diagonal and shift ½d) (a-e) (b-d) reflection in 45

(b-c) Translation (0,1) (b-e) (c-d) reflection in 5

vertically (c-e) reflection in 56

(b-d) Reflect in h2 diagonal ------

(b-e) Rotation 90° about de45

(c-d) Transflection: (= reflect in

h23 diagonal and shift ½d)

(c-e) Rotation 90° about d5

(d-e) Transflection: (=reflect in

e-file and shift 1v)

------

42 EXACT ECHOES

------Edgar Holladay See also the Helpmates in 4 for Edgar Holladay and Eugene Albert other settings with the same ¶78 Chessics #20 Second Prize in Chessics force and mate configuration. Winter/1984 Exact Echoes Tourney ------w______w ¶10 Chessics #17 Edgar Holladay [wdwdwdwd] Spring/1984 ¶79 Chessics #20 [dwdwdwdw] w______w Winter/1984 [wdwdwdwd] [wdwdwdwd] w______w [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dqdwdKdw] [dwdk0pdw] [wdwdwdwd] [wdrdNdwd] [wdwdndwd] [dwdNdndr] [dwdkdwdw] [$wdKdwdw] [wdwdKdkd] w------w [wdwdwdwd] [dwdwdwdw] Helpmate in 3½ [dwdwdwdw] [wdwdwdwd] (b) all men up one rank, w------w [dwdwdwdw] (c) c2 a2, (d) c2 h1 Helpmate in 3 w------w * (b) a3 h2, (c) f5 d6, Helpmate in 3½ (a) 1.Kf2 Kd2 2.Sf4 Kc1† (d) f5 e6, (e) d3 f7 (b) d5 f5, (c) f5 f3 3.Ke1 Qb1 4.Sd3‡ * * (b) 1.Sc4† Kd1 2.Ke4 Rc1 (a) 1.Sf6 Ke2 2.Ke4 Rc3 (a) 1.Ke5 Rh2 2.Kf6 Kh3 3.Kd3 Qe1 4.Sb2‡ 3.Sd5 Rc4‡ 3.Kg5 Sg3 4.Sf4‡ (c) 1.Kg2 Ke1 2.Kg1 Qd1 (b) 1.Sg5 Ke2 2.Ke4 Kf2 (b) 1.Sd4 Kh4 2.Kf3 Sf6 3.Sd4 Re2 4.Sf3‡ 3.Kf4 Rh4‡ 3.Kg2 Sg4 4.Sf3‡ (d) 1.Ke4 Ke1 2.Sf4 Qd1 (c) 1.Sc5† Kd2 2.Kd4 Rb3 (c) 1.Ke3 Rh6 2.Kf2 Kh5 3.Ke3 Rf1 4.Sg2‡ 3.d5 Rb4‡ 3.Kg3 Sg5 4.Sf4‡ * (d) 1.Kc6 Kc4 2.Kd6 Kb5 * Two different mates 3.Kd5 Rd3‡ (a-b) Reflection in 34 (a-c) Translation 2h (e) 1.Sg5† Kf8 2.Ke6 Rh3 (a-c) Reflection in 4 (b-d) Reflection in de 3.Kf6 Rh6‡ (b-c) Translation 1v ------* ------(a-b) Reflect in ef (a-c) Translate 1h (a-d) Reflect in a1 diagonal (a-e) Rotation 180° about ef5 (b-c) Reflect in de (b-d) Rotate 90° about ef56 (b-e) Reflect in 5 (c-d) Transflection (= reflect in a1a2 diagonal and ½d shift) (c-e) Rotate 180° about e5 (d-e) Transflection (= reflect in h23 diagonal and ½d shift) ------

43 EXACT ECHOES

------* Edgar Holladay ¶H971 Edgar Holladay (a-b) (d-e) (f-g) Reflection in de The Problemist vii/1984 ¶1326 Ideal Mate Review (a-c) Translation (1,1) w______w #16, vii-viii/1985 (a-d) (b-e) (b-f) Translation 1v, [wdwdwdwd] w______w up or down [dwdwdwdw] [wdwdwdwd] (a-e) (b-d) Transflection (= [wdRdwhwd] [dwdwdwdw] reflect in de and 1v shift) [dwdk0Kdw] [wdRdndwd] (a-f) (b-g) 180° turn about de34 [dwdkdKdw] (a-g) Reflection in 34 [wdw0wdwd] (b-c) Transflection (= reflect in [dwdwdwdw] [wdw0wdwd] d and 1v shift) [wdwdwdwd] [dwdw0wdw] (c-d) Translation 1h [dwdwdwdw] [wdwdwdwd] (c-e) Reflection in d file w------w [dwdwdwdw] (c-f) Rotation 180° about d4 Helpmate in 4, (b) f6 b6, w------w (c-g) Transflection (= reflection (c) f5 f3, (d) b6 g2 Helpmate in 4 in 4 and 1h shift) (progressive twinning) (b) e6 f6, (c) e3 c5, (d-f) (e-g) 180° turn about de4 * (d) c5 e5, (e) f6 b6, (d-g) (e-f) Reflection in 4 (a) 1.Sh5 Rg6 2.Sf4 Kf6 (f) f5 f3, (g) b6 h3, (h-i) 1v shift 3.e4 Ke7 4.Ke5 Rg5‡ (h) d4 e6, (i) h3 e3 * (b) 1.Sc4 Rb6 2.Kc5 Ke6 (progressive twinning) The other transformations 3.e4 Kd7 4.Kd5 Rb5‡ * from (a,...,g) to (h,i) involve (c) 1.Sc4 Ke2 2.Ke4 Kd1 This composition is a much 90° turns and diagonal glides: 3.Kd3 Rb6 4.e4 Rb5‡ extended version of the (a-h) Rotation 90° about f4 (d) 1.Sf4 Kf2 2.Ke4 Ke1 preceding example (d, e, f, g) (a-i) Rotation 90° about ef34 3.Ke3 Rg6 4.e4 Rg3‡ giving the same mates. (b-h) Transflection (= reflect in * * ab1 diagonal and 1½d shift) (a-b) (c-d) Reflection in de. (a) 1.Sg5 Rg6 2.Sf3 Kf6 (b-i) Transflection (= reflect in (a-c) (b-d) 180° turn about de4 3.Ke4 Ke6 4.d3 Rg4‡ b diagonal and 1d shift) (a-d) (b-c) Reflection in 4 (b) 1.d3 Rb6 2.Kd4 Ke6 (c-h) (d-i) 90° about e4 ------3.Sd5 Kd6 4.Sc3 Rb4‡ (c-i) Rotation 90° about de34 (c) 1.Kc4 Ke6 2.Se4 Kd7 (d-h) Rotation 90° about ef45 3.Kd5 Rf6 4.c4 Rf5‡ (e-h) Transflection (= reflect in (d) 1.Sh5 Rg6 2.Sf4 Kf6 a1 diagonal and 1d shift) 3.e4 Ke7 4.Ke5 Rg5‡ (f-h) Rotation 90° about d5 (e) 1.Sc4 Rb6 2.Kc5 Ke6 (g-h) Transflection (= reflect in 3.e4 Kd7 4.Kd5 Rb5‡ ab8 diagonal and ½d shift) (f) 1.Sc4 Ke2 2.Ke4 Kd1 (e-i) Transflection (= reflect in 3.Kd3 Rb6 4.e4 Rb3‡ ab1 diagonal and ½d shift) (g) 1.Sf4 Kf2 2.Ke4 Ke1 (f-i) Rotation 90° about de45 3.Ke3 Rg6 4.e4 Rg3‡ (g-i) Reflect in h1 diagonal (h) 1.Sg5+ Kg4 2.Ke4 Kh5 ------3.Kf5 Rc3 4.Se4 Rf3‡ (i) 1.e4+ Kg3 2.Ke5 Kh4 3.Kf4 Rc2 4.e5 Rf2‡ *

44 EXACT ECHOES

------Pal Benko and Helmut Mertes Deutsche Helpstalemate Andrew Kalotay Schachzeitung 1974 ------¶11 Chessics #17 w______w Russell E. Rice Spring/1984 [wdwdwdwd] ¶14 Chessics #17 w______w [drdwdwdw] Spring/1984 [wdwdwdwd] [wdwdwdwd] w______w [dwdw0wdw] [dwIwdwdw] [wdwdwdwd] [wdwdwGwd] [wdwHkdwd] [dwdBdwdw] [dwdwIwdw] [dwdwdwdw] [wdwdpHwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwiwdw] [dwdwdwdw] [wdkdKdwd] [wdwdPdwd] w------w [dwdwdwdw] [dwdrdwdw] Helpmate in 5, (b) c5 c4, [wdwdwdwd] w------w (c) e4 e6, (d) d4 d7 [dwdwdwdw] Helpmate in 5, (b) f6 b7, * w------w (c) b7 e8, (d) d1 f1, (a) 1.Kd3 Sb5 2.Kc2 Kb4 Helpstalemate in 2½, (e) e8 h7, (f) h7 d6 3.Kb1 Ka3 4.Ka1 Sd4 (b) d7 d8, (c) d7 e7 Successive twinning. 5.Rb1 Sc2‡ * * (b) 1.Rh7 Sf5 2.Kf3 Kd3 (a) 1.Ke3 e5 2.Se4 Kd5 (a) 1.Kd2 Kf4 2.e5† Kg3 3.Kg2 Ke2 4.Kh1 Kf1 3.Kd3= 3.Ke3 Kg2 4.Rd4 Kf1 5.Rh2 Sg3‡ (b) 1.Sg4 Kc5 2.Se5 Kd6 5.e4 Bg5‡ (c) 1.Kd7 Sb5 2.Kc8 Kb4 3.Kd4= (b) 1.Rf1 Kd5 2.Kf4 Kd4 3.Kb8 Ka5 4.Ka8 Ka6 (c) 1.Kf4 Kd4 2.Kg5 Ke5 3.Kf5 e4† 4.Ke6 e5 5.Rb8 Sc7‡ 3.Bc5= 5.Rf7 Bc8‡ (d) 1.Kf5 Kd6 2.Kg6 Ke7 * (c) 1.Kd2 e3 2.Kd3 Kf4 3.Kh7 Kf8 4.Kh8 Se5 (a-b) Translation 1v 3.e5† Kg3 4.Ke4 Kf2 5.Rh7 Sg6‡ (b-c) Rotation 90° about e6 5.Rd5 Bg6‡ Mate in the four corners. (a-c) Rotation 90° about de56 (f), (e) and (d) reflect these in * ------the e-file. (a-b) (c-d) 90° Rotation about * de45 (centre of board) (a-f) (b-e) (c-d) Reflect in e (a-c) (b-d) Reflection in 45 (a-c) (d-f) Translate 1v (horizontal median) (a-d) (c-f) Transflection (= (a-d) Reflection in h1 diagonal reflection in e and 1v shift) (b-c) Reflection in a1 diagonal (b-d) (c-e) Translate 2v ------(b-c) (d-e) Transflection (= reflection in e and 2v shift) (a-e) (b-f) Translate 3v (a-b) (e-f) Transflection (= reflection in e and 3v shift) ------

45 EXACT ECHOES

------* ------Direct Mates (a-b1) Reflection in c Ladislav Knotek Zlatá Praha ------(a-b2) (b1-d1) (b2-d2) 6/iii/1924 (¶VI in Dedrle) Edgar Holladay Rotation 90° about c4 w______w ¶75 Chessics #20 (a-c) (b1-d2) (b2-d1) [wdwGwdwd] Winter/1984 Reflect in 4 [dwdwdwdw] w______w (a-d1) (b1-b2) [wdwdwdwd] [wdwdwdwd] Reflect in a2 diag [dwdwdwdw] [dwdwdwdw] (a-d2) (b1-c) Rotation 180° about c4 [wdwdwiwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] (b2-c) (d1-d2) Reflect in a6 diag [wdwdwdwd] [wdNdkdwd] (a-e1) Rotation 90° about cd34 [dQdwIwdw] [dwdwdwdw] (a-e2) Reflection in cd w------w [wdwIw!wd] (e1-e2) Reflection in a1 diag Mate in 4 [dwdwdwdw] (a-f1) Transflection (= reflect in * w------w d and 1v shift) 1.Qb5 Mate in 4, (b) d2 b3, (a-f2) Rotation about 90° cd23 1.... Ke4 2.Bc7 Ke3 (c) d2 b7, (d) d2 a4, (f1-f2) Reflection in c1 diag 3.Qc4 Kf3 4.Qe2‡ ... (1) (e) c4 d4, (f) f2 h3 (b1-e1) (b2-e2) Transflection (= 1.... Kf3 2.Qe5 Kg2 * reflect in a12 diag and ½d shift) 3.Bc7 Kf3 4.Qe2‡ ... (2) (a) 1.Qf6 Kd5 2.Kd3 Kc5 (b1-e2) (b2-e1) Translate 1h 1.... Ke3 2.Qd5 Kf4 3.Qb6+ Kd5 4.Qd6‡ (b1-f1) (b2-f2) Translate (1,2) 3.Kf2 Kg4 4.Qf3‡ ... (3) (b) 1.Qf7 Kd4 2.Qe6 Kc5 (b1-f2) (b2-f1) Transflection (= [1.... Ke4 2.Bc7 Kd4 3.Qd6+ Kb5 4.Qb6‡ reflect in ab1 diag and ½d shift) 3.Kd2 Ke4 4.Qd3‡ [2.... Kd3 3.Qe3‡] (c-d1) Rotation 90° about c4 1.... Kg3 2.Qf5 Kh2 1.... Kd3 2.Qe6/7/8 Kd4 (c-d2) Reflection in c 3.Bc7† Kg2 4.Qf1‡] 3.Qe5+ Kd3 4.Qe3‡ (c-e1) Transflection (= reflect * (c) 1.Kc6 Kd3 2.Kd5 Kc3 in a67 diagonal and ½d shift) (1-2) Identity 3.Qb2+ Kd3 4.Qd2‡ (c-e2) Rotate 180° about cd4 (1-3) (2-3) Translation (1,1). (d) 1.Kb5 Kd5 2.Qe2 Kd4 (c-f1) Rotate 180° about d34 The other lines are near echoes, 3.Qe3+ Kd5 4.Qe5‡ (c-f2) Transflection (= reflect in the Wt B being at different 1.... Kd3 2.Qe3+ Kc2 a67 diag and shift 1½d shift) distances from the Bk K 3.Qd2+ Kb3 4.Qb2‡ (d1-e1) ... and more ------[3.... Kb1 4.Qb2 (mate 2)] * - dual 2.Qe1 Mate 2 (d-f) Rotation 90° (e) 1.Qf6 Kd5 2.Kc3 Ke4 about centre 3.Qf5+ Ke3 4.Qf3‡ ------[2... Kc5 3.Qc6‡] (f) 1.Qh5 Kd/f4 2.Se3 Ke4 3.Qf5+ Kd4 4.Qd5‡ 1.... Kf4 2.Se3 Kg3 3.Qg4+ Kf2 4.Qg2‡ [3... Kh2 4.Qg2 (mate 2)] *

46 EXACT ECHOES

------Fairy Pieces C. E. Kemp Fairy Chess Oswaldo Faria ------Review 1939 ¶61 Chessics #19 C. E. Kemp Fairy Chess w______w Autumn/1984 Review 1939 [wdwdwdwd] w______w w______w [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdndw] [dw!w4wdw] [wdNdwdNd] [wdwdndwd] [wdwdwiwd] [dwdw0wdw] [dw!wdwdw] [dwdKdwdw] [wdwdkdKd] [wdKdkdwd] [wdwdw4wd] [dwdwdrdw] [dwdwdwdw] [dwdwdNdw] [wdwdwdwd] [Ndwdwdwd] w------w [dwdwdwdw] [dwdwdwdw] Grasshopper w------w w------w Helpmate in 3 Rook + Zebra Grasshopper (b) c5 h5, (c) c5 f7 Helpmate in 3, (b) g6 g2, Helpmate in 3 * (c) g4 e6, (d) e6 c4, (b) a2 a3, (c) a2 b5 (a) 1.Rf5 Kc4 2.Ke4 Gg5 (e) c4 e2, (f) g2 c2 * 3.R2f4 Sd2‡ successive twinning (a) 1.Ke5 Kd3 2.Sd6 Ge7† (b) 1.Rg2 Kd4 2.Rg4 Sg3 * 3.Kd5 Sb4‡ 3.R5g5 Se2‡ (a) 1.RZf6 Kh4 2.Kf5 Kh5 (b) 1.Sh6 Sb1 2.Sf5 Gg5 (c) 1.Re6 Sd2 2.Ke5 Ke3 3.e4 Sd4‡ 3.Sf4 Sd2‡ 3.R2f6 Sc4‡ (b) 1.RZf2 Kh4 2.Kf3 Kh3 (c) 1.Sfg5 Gc3 2.Sf3 Gg3 * 3.e4 Sd4‡ 3.Sf4 Sd6‡ (a-b) Translation 1h (c) 1.RZc5 Ke7 2.Kd5 Kd7 * (b-c) Reflection in b1 diagonal 3.e4 Se3‡ (a-b) Reflection in a1 diagonal (a-c) Transflection (= reflect in (d) 1.RZd6 Kb4 2.Kd5 Kb5 (b-c) Reflection in 4 rank ab1 diagonal and ½d shift) 3.e4 Sf4‡ (a-c) Rotation 90° about d4 ------(e) 1.RZg3 Ke1 2.Kf3 Kf1 ------3.e4 Se5‡ (f) 1.RZc3 Ke1 2.Kd3 Kd1 3.e4 Se5‡ Wt K tempo in each solution. * (a-b) (c-f) Reflect in 4 (a-c) (a-e) (b-f) (d-f) Rotate 90° about e4 (a-d) (e-f) Reflect in e (a-f) (b-e) (c-d) Reflect in h1 diag (b-c) (d-e) Reflect in a1 diag (b-d) (c-e) Rotate 180° about e4 ------

47 EXACT ECHOES

------* Echoes with Elmar and Erich Bartel 1.Lb4 (pendulum key) Fairy Kings ¶97 Chessics #21 1.... Wb3 2.Ld3 Wa3 The use of other fairy Spring/1985 3.Lc5+ Wa2 4.Fc3 Wa1 pieces in place of the Kings is w______w 5.La4 Wa2/b1 6.Fb4/d2 Wa1 in many ways a specialised [wdwdwdwd] 7.Lc3‡ genre of its own, so I have [dwdwdwdw] 1.... Wb1 2.Ld3+ Wa1 chosen to present such [wdwdwdNd] 3.Fc3 Wa2 4.Lc5 Wa1 compositions in a separate [dwdwdwdw] 5.La4 Wa2/b1 6.Fb4/d2 Wa1 section. 7.Lc3‡ [wdwIwdwd] The Fers helps in the play, but ------[dwdwdwdw] Direct Mates not in the mate. ------[wiwdwdwd] * Elmar Bartel ¶1235 [dwdwdwdw] Identity and Reflection in the a1 Jugendschach x/1984 w------w diagonal. The set plays also w______w Royal Dabbaba b2, reflect in this diagonal [wdwdwdwd] Royal Knight d4 ------[dwdwdwdw] Mate in 3 Direct Stalemates * ------[wdwdwdwd] 1.Se5 (symmetric position) Erich Bartel Diagramme und [dwdwdwdw] 1.... Db4† 2.Kc6† Db6/b2 Figuren 7/x/1964 [wdwdwdwd] 3.Sc4‡ w______w [dwIwdwdw] 1.... Dd2† 2.Kf3† Df2/b2 [wdwdwdwd] [wdwdNdwd] 3.Sd3‡ [dwdwdwdw] [dkdwdwdw] * [wdRdwdwd] w------w Reflection in the a1 diagonal [dwdkdwdw] Royal Fers b1, Royal Wazir c3 [A part (b) with the stipulation [wdwdRdwd] Mate in 3 Stalemate in 3 was unsound.] ------[dwdwdwdw] (b) after black move [wdwdwdwd] * Elmar and Erich Bartel (a) 1.Sd4 Ka2 2.Kc2 Kb1† ¶96 Chessics #21 [dwdwdwdw] 3.Kb2‡ Spring/1985 w------w (b) Ka2 1.Sd4 Kb1 2.Kb3 Ka2† w______w Royal Wazir d5, No Wt K 3.Kb2‡ [wdwdwdwd] Stalemate in 2, 4 ways The knight does not participate [dwdwdwdw] * in the mate [wdwdwdwd] Set stalemate * [dwdwdwdw] 1.Rb6 Kc5 2.Rd4= Reflection in a1 diagonal 1.Rc7 Kd6 2.Re5= [wdwIwdwd] 1.Re3 Kd4 2.Rc5= ------[dwdwdwdw] 1.Rf4 Ke5 2.Rd6= [wiwHwdwd] * [dwdwdwdw] Translations of diagram w------w position one unit up, down, left Royal Wazir b2, Royal Fers d4, and right. Combinations of Knight+Alfil d2 these can be regarded as (1,1) = (1,2) + (2,2) Leaper or (0,2) translations. Mate in 7, set plays ------*

48 EXACT ECHOES

------* ------Elmar and Erich Bartel (a) 1.Ke4 Kb2 2.Se5 Kd1/a4 Helpmates ¶99 Chessics #21 3.Sc4= ------Spring/1985 (b) 1.Kd5 Kb2 2.Se5 Kd1/a4 A. H. Kniest Frankfurter w______w 3.Sd3= Notizen 18/xi/1963 [wdwdwdwd] Reflection in a1 diagonal w______w [dwdwdwdw] ------[wdwdwiwd] [wdwdwdwd] Elmar and Erich Bartel [dwdwHw1w] [dwdwdwdw] ¶100 Chessics #21 [wdwdwdwd] Spring/1985 [dwdwdwdw] [wdwiwdwd] w______w [Hwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [wdwdwHwd] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] w------w [dwdwdwdw] Royal Wazir d4, No Wt K w------w [wdwdwdwd] Stalemate in 2, (b) f2 f6 Royal Fers f8, No Wt K * [dwdwIwdw] Lion g7 (a) 1.Sb5+ Wd5/c4 2.Sd3= [wdwGwdwd] Helpmate in 3, set mate (b) 1.Sc2+ Wc4/d3 2.Se4= [iwdwdwdw] * Rotation 90º about d4 w------w 1._ Sg6‡ * Royal Knight a1, 1.Lc7 Sc6 2.Lc3 Se5 Further successive twinning is Royal Ferfil e3 3.Lg7 Sg6‡ possible, viz: Ferfil d2 = (1,1)+(2,2) Leaper Circuits by L and S. (c) a3 c1, (d) f6 b6, Stalemate in 4, set play A Wt K would have to be tied (e) c1 g5, (f) b6 b2, * up so as not to make a waiting (g) g5 e7, (h) b2 f2, 1._ Kc2 (Kb3? 2.Lc3=) move. but the play is basically the 2.Kc5 Ka1 3.Ka3 Kb3/c2+ ------same. 4.Lc3=/Kb2= Elmar and Erich Bartel ------1.Lc3+ Kb3 (1.... Kc2+? ¶102 Chessics #21 Elmar and Erich Bartel Kc1/c5=) 2.Lb4 Ka1 3.Kc1 Spring/1985 ¶98 Chessics #21 Kc2/b3+ 4.Lc3=/Kb2= w______w Spring/1985 Translation (1,1) [wdwdwdwd] w______w ------[dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [dwdwdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdKd] [dwdwdwdw] [dwdwdwdw] [wdwdwdNd] [wdkdRdwd] [dwdwdwdw] [dwdwdwdw] [wdwIwdwd] w------w [dwdkdwdw] Royal Zebra c2, w------w Royal Wazir g4 Royal Knights Wazir e2 Stalemate in 3, (b) d2 f4 Helpmate in 3, set play * * 1._ We3 2.Ke5 We4+ 3.Kg2 Kg3‡ 1.Ka5 Kg3 2.Kd3 We3+ 3.Kg1 Kg2‡ * Translation unit vertical ------

49 EXACT ECHOES

------Elmar and Erich Bartel Helpstalemates Elmar and Erich Bartel ¶1136 Problemkiste iv/1985 ------¶1130 Problemkiste iv/1985 w______w Elmar and Erich Bartel w______w [wdwdwdwd] ¶1043 Problemkiste ii/1985 [wdwdwdwd] [dwdwdwdw] w______w [dwHwdwdw] [wdwdwdwd] [wdwdwdwI] [wdwdwdwd] [dwdwdwdR] [dwdwdwdw] [dKdwdwdw] [wdwdwIwd] [wdwdwdwd] [wdwdwdwd] [dwdwiwdw] [dwdNdwdw] [dwdwdwdw] [wdwdwdwd] [wdwdwdwd] [wiwdwdwd] [dwdwdwdw] [dwdwdwdw] [dwdwdwdw] w------w [wdwdwdwd] w------w Royal Knight e3, [iwdwdwdw] Royal 5-Leaper b2, Royal Wazir f4 w------w Royal Wazir b5, Wazir h5 Royal Fiveleaper a1 Giraffe c7 = (1,4)-Leaper Helpmate in 4, set play = (0,5)+(3,4)-Leaper, Helpstalemate in 3, set play * Royal Wazir h8 * 1._ Wh4 2.Kd1 Wh3 Helpstalemate in 3, set play 1.__ Kc5 2.Kf5 Kd5 3.Kf2 Kf3† 4.Kh1 Wh2‡ * 3.Kb8 Ke5= 1.Kc4 Wh6 2.Ke5 Kf5† 1._ Kg8 2.Kf1 Se3† 1.Kg2 Gb3 2.Kd6 Kc5 3.Kf7 Kf6† 4.Kh8 Wh7‡ 3.Kb4 Kf8= 3.Ka2 Kd5= * 1.Ke4 Kh7 2.Ka7 Se7 * Reflection in horizontal midline 3.Kd3 Sc6= Symmetric Finale ------* Rotation 90º about centre of Elmar and Erich Bartel Transflection (= reflection in board ¶1132 Problemkiste iv/1985 the a12 diagonal and ½d shift) ------w______w ------[wdwdwdwd] [dwdwdwdw] [wdwdwdwd] [Hwdwdwdw]

[wdwdwdwd] [dwdkdwdw] [wdwdwdwd] [dwdKdwdw] w------w Royal Wazirs, Gnu a5 = (1,2)+(1,3)-Leaper Helpmate in 4, set play * 1_ Ke1 2.Kd2 Kf1 3.Kd1 Kf2 4.Ke1 Lb2‡ 1.Kc3 Ld6† 2.Kb3 Kc1 3.Ka3 Kb1 4.Ka2 Lb5‡ * Rotation about cd34 ------

50