«Double transposition of two pieces on one line»

by Zlatko Mihajloski & Zoran Gavrilovski

(originally published in The Macedonian Problemist № 47, 2015)

Extensive research of Klasinc, Rehm and other line themes in helpmate moremovers was recently supplemented by another line combination. Its essence is the reciprocal change of positions of two white (оr black) pieces on different sides of one and the same line, which is a kind of reminiscence of the children’s game “leapfrog”.

The author of 12 problems in this article defines this combination or (new?) theme in the following way: Two pieces of the same colour both stand on any line of the board. А is the front piece, and B the rear piece in one direction. They change position such that 1) А becomes the rear piece, and B becomes the front piece; and then again such that 2) А again becomes the front piece, and B the rear.

Below we give 14 problems showing this theme. Thirteen of them are presented in order of the strength of the thematic pieces used (P, S, B, R and Q) and finally there is a bicolour example of the theme.

№ 1
Zlatko Mihajloski
The Macedonian Problemist № 47, 2015
white Pd2 Kc2 black Bh8 Kd4 Qg7 Pe4c3c5c7e6e7 Sf2c6 Rd1
h#5(2+12)
№2
Zlatko Mihajloski
The Macedonian Problemist № 47, 2015
white Kg7 Sh7 black Pd7b6 Sc7b5 Rf8 Kd5
h#4.5(2+6)
№ 3
Zlatko Mihajloski
The Macedonian Problemist № 47, 2015
white Sh4 Kf6 black Sa8 Rh7 Kd4
h#5.5(2+3)

I ) ♙ and ♔

Problem № 1 shows double transposition of wP and wK. The piece closer to the direction of movement of both pieces on the thematic c-line is the front piece (wP after 1...dxc3) and the wK is the rear piece. The wK becomes a front piece in two moves (2...Kb3 3...Kc4), and then the wP returns to the front position on the c-file (4...cxd4 5...dxc5#).

1.Kd4-e5 d2*c3 2.Rd1-d7 Kc2-b3 3.Ke5-d6 Kb3-c4 4.Qg7-d4 + c3*d4 5.Bh8-e5 d4*c5 # {(model mate)}


II ) ♘ and ♔

№ 2 achieves double transposition on an orthogonal line: The king is the front piece on the h7-e7 line and the white knight (wS) the rear; on the second white move the wS arrives in front of the wK; just before the final position the wK again becomes the front piece (4...Ke7).

1...Sh7-g5 2.Rf8-f5 Sg5-f7 3.Kd5-c6 Kg7-f8 4.Rf5-c5 Kf8-e7 5.d7-d5 Sf7-d8 # {(ideal mate)}

The minimal Tanagra (Malyutka) labeled as № 3 in this article is the most economical presentation of the theme. The thematic transposition here occurs on the h4-d8 line.

1...Sh4-g6 {[Sf5+?]} 2.Rh7-b7 Sg6-e7 3.Kd4-c5 Kf6-f7 4.Kc5-b6 Kf7-e8 5.Kb6-a7 Ke8-d8 6.Ka7-b8 Se7-c6 # {(ideal mate)}

№ 4
Zlatko Mihajloski
The Macedonian Problemist № 47, 2015
white Kc2 Bd3 black Be2 Kd5 Qh3 Pf6 Sg2 Rd1
h#6.5(2+6)
№ 5
Zlatko Mihajloski
Special Prize, V. Chepizhny - 80 JT 2014
white Kg1 Bd4 black Bc3 Ke7 Qe4 Pd6d5 Sc2 Rd2
h#6.5(2+7)
№ 6
Zlatko Mihajloski
4th Prize, Olympic Tourney 2010
white Kh2 Be5 black Qf1 Pe7e6 Kg8 Rd3g1 Bb2
h#6.5(2+7)

III ) ♗ and ♔

The problem № 4 shows transposition of wK and wB (most commonly thematic pieces used so far) on the same thematic line: with the wB in front of the wK on c2-g6; but after 3....Ke4 the wK becomes a front piece. Following Bristol play by the bB and the wB and nice play by the bQ (5.Qa3!), the wB by arriving on g6 again becomes a front piece on the same line before moving on the line to give a model mate.

1...Kc2-c3 2.Kd5-e6 Kc3-d4 3.Be2-h5 {!} Kd4-e4 4.Bh5-f7 Bd3-e2{!} 5.Qh3-a3{!} Be2-h5 6.Qa3-e7 {[Rd6?]} Bh5-g6 7.Rd1-d6 Bg6-f5 #

The thematic character of problem № 5 is disputable, as before the wK’s arrival on the other side of the diagonal line g1-d4 (5...Ke3), the wB has already left that line (4...Be1). Regardless of this thematic inconsistency, this problem is important because of its ideal mate and the wB‘s round-trip, which is why the tourney judge praised the author’s high composing technique.

1...Bd4-f2 {!} 2.Qe4-e6 Kg1-g2 3.Ke7-f6 Kg2-f3 4.Kf6-e5 Bf2-e1 5.Sc2-d4 + Kf3-e3 6.Rd2-f2 Be1*c3 7.Rf2-f5 Bc3*d4 #

Problem № 6 has very rich content: in addition to the wB and the wK performing the theme elaborated in this article, the wB and the bB also exhibit the Rehm theme, and the wB after the critical first move completes the round-trip on the last move.

1...Be5-g3{!} 2.Qf1-f7{!} Kh2-h3 3.Kg8-g7 Kh3-g4 4.Kg7-f6 Kg4-f4 5.Bb2-d4{!} Bg3-e1{!} 6.Rg1-g6 Be1-c3 7.Bd4-e5 + Bc3*e5 # {(model mate)}

№ 7
Zlatko Mihajloski
2nd Prize, Die Schwalbe 2010
white Ke2 Bb5 black Bh1 Kd8 Qd6 Ph7b6 Sa3 Rh3c1
h#6.5(2+8)
№ 8
Zlatko Mihajloski
2nd Pr. The Macedonian Problemist 2010
white Kf4 Bg3 black Ph5d4a5b7 Sd2 Bb2 Kc8 Rd5c5
h#6.5(2+9)
№ 9
Zlatko Mihajloski & Fadil Abdurahmanović
E158, SuperProblem, 19-08-2015
white Kg2 Bg1 black Qf5 Pg7 Ka1 Rd3e7 Bg5
h#9(2+6)

In problem № 7 the wK reaches the front on the fourth move; the wB after a critical first move and round-trip again becomes the front piece (6...Bxb5#).

1...Bb5-d3 {!} 2.Rc1-c8{! [Rc7?]} Ke2-d2 3.Kd8-c7 Kd2-c3 4.Sa3-b5 + {[S~?]} Kc3-c4 5.Bh1-b7{! [Kc6?]} Bd3-c2 6.Kc7-c6 Bc2-a4 7.Rc8-c7 Ba4*b5 # {(model mate)}

In the next problem (№ 8) it is the wK that stands at the front. The wB reaches the front after 3...Be5, in order to allow a passage for the wK to take his turn. The bRs play in Bristol manner on the fifth rank and on the a-file.

1...Bg3-h4{! [Bf2?]} 2.a5-a4 Bh4-f6{! [Bxd4?]} 3.Rc5-a5 Bf6-e5 4.Ra5-a8{!} Kf4-f5 5.Rd5-a5 Kf5-e6 6.Ra5-a7{!} Ke6-d6 7.Kc8-b8 Kd6-d7 #

The nice task № 9 doubles the theme on the second rank.

1.Bg5-e3{!} Bg1-f2{!} 2.g7-g5 Kg2-f1 3.g5-g4 Kf1-e2 4.g4-g3 Bf2-e1 5.g3-g2 Be1-d2 6.g2-g1=S + Ke2-d1 7.Sg1-e2 Kd1-c2 8.Se2-c3{[Sc1?]} Bd2-c1 9.Sc3-a2 Bc1-b2 # {(model mate)}

№ 10
Zlatko Mihajloski
The Macedonian Problemist № 46, 2015
white Kd1 Rf2 black Bf4a4 Ke7 Qb2 Pc6b5e6d4c3g2 Sg5f6 Re5c2
h#5.52 solutions(2+14)
№ 11
Fadil Abdurahmanović
Tovariš 1969
white Sf2 Kc5 black Qg3 Ke8 Rh8 Sg7 Bh2
h#4(2+5)
№ 12
Fadil Abdurahmanović & bernd ellinghoven
Comm., Soumen Tehtäväniekat 1999
white Ph3 Ke1 Rh1 black Ph4d4e4 Ke3 Rd2
h#4.5(3+5)

IV ) ♖ (♜) and ♔ (♚)

The only example of double transposition in two solutions is problem № 10. Note how efficiently white and black pieces co-operate to determine the choice and order of moves. Some nice tactical details (such as arrivals on vacated squares) embelish this interesting problem.

1...Rf2-e2{!} 2.Sf6-h5{!} Kd1-e1 3.Ke7-f6 Ke1-f2 4.Sg5-h3 + Kf2-f3 5.Kf6-g5 Re2*g2 + 6.Kg5-h4 Rg2-g4 # {(line d1-g4),
 } 1...Rf2-d2 2.Re5-c5{!} Kd1-e2 3.Ke7-d6 Ke2-d3 4.Kd6-d5 Rd2-f2{!} 5.Rc2-e2{!} Rf2*f4 6.Re2-e5 Rf4*d4 # {(line d1-d4)}


Castling as a special type of transposition

The next two problems show a special type of the theme, because the first part of the thematic transposition is performed by castling.

Problem № 11 is the oldest example of the theme of which we are aware and in this article it is the only example with black thematic pieces and the shortest one, too. Rh8 and Ke8 use a single half-move to arrive on the opposite sides of the thematic line and then the bR by round-trip returns to the initial position.

1.0-0 Sf2-e4 2.Rf8-f4 Kc5-d6 3.Rf4-h4 + Kd6-e7 4.Rh4-h8 Se4-f6 # {(model mate)}

In № 12 after the castling the wR in a round-trip manner returns to the initial position, becoming a rear battery piece.

1...0-0 2.Ke3-e2 Rf1-f2 + 3.Ke2-e1 Rf2-h2 4.e4-e3 Rh2-h1 5.e3-e2 Kg1-g2 #


V ) ♕ and ♔

№ 13
Zlatko Mihajloski
The Macedonian Problemist № 46, 2015

№ 13 is the only rendering of the theme in this article using the strongest white piece (which returns to e4 in in a triangular manner). It goes without saying that owing to the wQ’s strength it would be too much to ask from a composer to show the thematic combination in an economical setting and with a model mate.

1...Qe4-e2{!} 2.Bd4-f6 Ke1-f2 3.Qe7-d6 Kf2-e3 4.Kd7-e6 Qe2*d3{[Qxf3?]} 5.Ke6-e5 Qd3-e4 #

white Qe4 Ke1 black Bd4g2 Kd7 Qe7 Pc3c2d3f3 Sb6 Rd2
h#4.5(2+10)

VI ) ♗ and ♝

№ 14
F. Abdurahmanović & Z. Mihajloski
1st Prize, StrateGems 2011

The paradox of the transposition increases if both thematic pieces of the same kind can move along the thematic line, but for some reason it is necessary to transpose them twice. In this article № 14 is the only problem with double transposition of pieces of different colours and the only one without bK or wK as the thematic piece. The judge Christer Jonsson commented this h# as follows: “A clear winner. First goes white Bishop b2 around black Bishop c3 (Ba3-Bd6-Bxe5). Later, the black Bishop c3 does the same thing (Bb4-Bf8-Bg7). A brilliant geometric experience!”.

1...Bb2-a3{!} 2.Sc5-d7 Ba3-d6 3.Sd7-f6 Bd6*e5 4.Bc3-b4 + Ke3-f4 5.Bb4-f8 Kf4-g5 6.Bf8-g7 Kg5-g6 7.Sf6-g8 Be5*g7 #{(model mate)}

white Ke3 Bb2 black Bc3 Kh8 Qg2 Pe6e5e4 Sc5g3 Rb3
h#6.5(2+9)

Examples from this article illustrate only some of the possibilities offered by the double transposition of pieces on the same line. Although nowdays it is difficult to discover something new in the over-explored field of moremover helpmate, the aforementioned creative opus contributes to the theory and practice of chess composition, by systematically rendering the idea with typical helpmate motifs.

We invite problemists to state their views whether the line combination elaborated in this article deserves to be treated as a distinct theme and to be named Mihajloski theme, as well as to compose new thematic examples, including renderings with black pieces, doubling or combining the theme with other themes. We are preparing a new article, in which your original problems could be published. You are welcome to submit your comments and/or original problems to Zoran Gavrilovski (mprobl@yahoo.com).

(Language control of the English text has been made by Stephen Emmerson)



Published on the website superproblem.ru: November 28, 2015

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