## Sunday, September 21, 2008

### Theme Dombrovskis (1)

The theme Dombrovskis shows a paradoxical reversal of movements.
First we see tries, which have threats, which are refuted with some defenses.
Then the key brings a different threat. If this new threat is answered with the defenses used after the tries, the mates are achieved with the (corresponding to the defenses) same moves that were refuted previously as threats of the tries.

Let us describe it with football terms : If a shoot is done, the goalkeeper dives and catches the ball. If the goalkeeper dives first, then the shoot can become easily a goal.

Symbolizing with Capital letter a white move, and with small letter a black move, we have :
1.X? [2.A#] a!,
1.Y? [2.B#] b!,
1.Z! [2.W#]
1...a 2.A#
1...b 2.B#

 Theme Dombrovskis : In the post-key play at least two defenses, which have refuted some threats of the tries, are subdued with exactly the same threats of the tries.

This theme is named after the composer Alfred Dombrovskis, born 1923-04-19 in Aizpute of Latvia, who was the first to present it.

Theme Dombrovskis in directmates

 (Problem 224) Marjan Kovacevic, Myllyniemi Jubilee tourney 1980, Mate in 2. #2 ( 11 + 9 ) [3B3s/8/p1P1R3/pk1B1S1Q/pb1P4/qb1P4/SR6/4sK2]

In this problem the half-pin of the black Bishops is used (when one of them moves, the other remains pinned).

Tries : {1.Sf5-d6+? Bb4xd6!}, {1.Bd5-c4+? Bb3xc4!}, {1.Qh5-f7? Sh8xf7!}, {1.Qh5-h2? Bb4-d6!}, {1.Qh5-h7? Sh8-f7!}, {1.Sf5-e7? Se1xd3!}, {1.Sa2-c3+? Bb4xc3!}. We especially observe the next two tries and correlate them with the solution :
Try : {1.Bd5-e4? [2.Sf5-d6# (A)] Bb3-d5! (a)}
Try : {1.Sf5-e3? [2.Bd5-c4# (B)] Bb4-d6! (b)}

Key : 1.Qh5-e8! [2.c6-c7#]
1...Bb3xd5 (a) 2.Sf5-d6# (A)
1...Bb4-d6 (b) 2.Bd5-c4# (B)

In the next problem-225, (which we have taken from the page for three-movers of the British Chess Problem Society BCPS), we note that the contemporary composers extend a two-move-theme, as is theme Dombrovskis, to a three-move-mechanism.

 (Problem 225) M. Keller, First Prize, Schweizerische Schachzeitung 1985, Mate in 3. #3 ( 11 + 9 ) [4R3/7S/3p1Rp1/BP1k2Ps/1Kpp1p2/1p4P1/2ps4/5SQb]

The straightforward attack does not prove fruitful :
Tries : {1.Rf6-f5+? g6xf5!}, {1.Rf6xd6+? Kd5xd6!}, {1.Qg1xd4+? Kd5xd4!}, {1.Sf1-e3+? d4xe3!}. We observe closely the following tries :
Try : {1.Ba5-b6? [2.Qg1xd4# (A)] Sd2-f3! (a)}
Try : {1.Ba5-c7? [2.Rf6xd6# (B)] Sd2-e4! (b)}
If the wQ captures bBh1 with check, the Pawn bPf4 can interfere supported by the Knight bSd2.
Try : {1.Qg1xh1+? f4-f3!}
Could we remove this Knight?
Try : {1.Sf1xd2? c2-c1=Q!}.
We should rather remove the Pawn. Let us use wRf6.
Try : {1.Rf6xf4? Bh1-e4!}.

Finally, the actual play starts when we capture the bPf4 with the wPg3.
Key : 1.g3xf4! [2.Qg1xh1+ Sd2-f3 (a) / Sd2-e4 (b) 3 Qh1xf3# / Qh1xe4#]
1...Sd2-f3 (a) 2.Qg1xd4+ (A) Sf3xd4 / Kd5xd4 3.Sf1-e3# / Rf6xd6#
1...Sd2-e4 (b) 2.Rf6xd6+ (B) Se4xd6 / Kd5xd6 3.Re8-e5# / Qg1xd4#
1...Bh1-e4 2.Ba5-c7 [3.Rf6xd6#] Sh5xf6 3.Sh7xf6#
1...Bh1-f3 2.Ba5-b6 ~ 3.Qg1xd4#
1...Bh1-g2 2.Qg1xg2+ Sd2-e4 / Sd2-f3 3.Qg2xe4# / Qg2xf3#
1...d4-d3 (very weak, 2.Bb6 / Qb6 / Se3+ all lead to mate in the third move).
1...Sh5xf4 2.Rf6-f5+ g6xf5 3.Sh7-f6#
1...Sh5-g3 2.Rf6-f5+ Sg3xf5 / g6xf5 3.Sh7-f6# / Sh7-f6 #

Theme Dombrovskis together with theme Arguelles

 (Problem 226) Byron Zappas, Third Honourable Mention, “U.S.P.B.” 1988, Mate in 2. #2 ( 7 + 12 ) [8/6p1/1p1p2p1/1k3p2/2RBS3/Rp4qQ/4Bpr1/5Kbs]

Tries : {1.Se4-c3+? Qg3xc3!}, {1.Se4xd6+? Qg3xd6!}, {1.Bd4-c3? / Be2-d3? Qg3(x)d3!}, {1.Rc4-c5+? Kb5-b4!}, {1.Qh3xf5+? g6xf5!}, {1.Qh3xg3? Sh1xg3+!}. Let us give special attention to the next two tries :
Try : {1.Bd4-e3? [2.Se4-c3# (A)] Qg3-e5! (a)}
Try : {1.Bd4-e5? [2.Se4xd6# (B)] Qg3-d3! (b)}.

Key : 1.Qh3-h8! [2.Qh8-e8#]
1...Qg3-e5 (a) 2.Se4-c3# (A)
1...Qg3-d3 (b) 2.Se4xd6# (B)

We know the theme Dombrovskis and we have shown it in this solution. What is the Theme Arguelles?

 Theme Arguelles : A black line of influence is neutralized with energetic and with pathetic interference.

The bQg3 has two lines towards the arrival squares of wSe4, namely c3 and d6.
In the tries Be3? / Be5? the interference of wBd4 to these lines of the bQ is energetic.
In the actual play, after the defenses Qe5 / Qd3, the interference of wBd4 to the lines of action of the bQ is pathetic.

Since the interference, in problem-226 by Zappas, happens for two black lines, we have double application of the theme Arguelles.

Theme Dombrovskis in Selfmate

 (Problem 227) S. Seider, Second Prize, Bulgaria 1300 Years Tourney 1982-83, Selfmate in 2. s#2 ( 13 + 9 ) [1B6/4r3/1P1Sp3/1B1k2P1/pP5R/K1P1S1s1/bp1PR1Q1/qr6]

Tries : {1.Sd6-e4+? / Sd6-f5+? / Sd6-e8+? / Sd6-c8+? / Sd6-b7+? Re7-c7!}, {1.Rh4-e4+? / Qg2-e4+? Sg3xe4!}, {1.Se3-g4+? Ke5-f4!}, {1.Qg2-d5+? e6xd5!}.
A good plan is to check bKd5 with one of the Knights on c4, forcing bBa2 to capture it, allowing the bQa1 to check-mate wKa3. Since the two Knighs fire batteries when they move, let us try to dismantle these batteries.
Try : {1.Ba7? [2.Sdc4+ (A) Bxc4#], not 1...Kxd6 2.Sec4+ Bxc4#, but 1...Rc7! (a)}
Try : {1.Rf2? [2.Sec4+ (B) Bxc4#] Se4! (b)}

In the actual play the White is threatening something different, which can be answered with the previous defenses of the Black, but unfortunately these defenses break the batteries of the White and the Knights are free to act :
Key : 1.Qc6! [2.Qc5+ Bd5#]
1...Rc7 (a) 2.Sdc4+ (A) Bxc4#
1...Se4 (b) 2.Sec4+ (B) Bxc4#

Expanding Theme Dombrovskis to three variations

At the web page of the mathematician K. R. Chandrasekaran from India, I have spotted a Dombrovskis problem with three variations. It sounds complicated, but I present it here for you to see how simple it really is.

 (Problem 228) K. R. Chandrasekaran, First Commendation, I.C.P.S. II Composing Tourney, 1995, Mate in 2. #2 ( 8 + 5 ) [1Q6/6P1/6b1/4pB2/3rpk1K/4SP2/5BP1/8]

Tries : {1.Qb8xe5+? Kf4xe5!}, {1.Qb8-d8? Rd4xd8!}, {1.Se3-d5+? Rd4xd5!}, {1.g2-g3+? Kf4xf3!}, {1.Bf2-g3+? Kf4xe3!}.
We give special attention to the following tries :
Try : {1.Qb8-h8? [2.Qh8-h6# (A)] Bg6-h7! (a)}
Try : {1.Qb8-b3? [2.Bf2-g3# (B)] Rd4-d3! (b)}
Try : {1.Bf5-g4? [2.g2-g3# (C)] e4xf3! (c)}

Key : 1.Qb8-b6! (zz).
1...Bg6-h7 (a) 2.Qb6-h6# (A)
1...Rd4-d3 (b) 2.Bf2-g3# (B)
1...e4xf3 (c) 2.g2-g3# (C)
non-thematic variations : 1...Bg6-~ 2.Qb6-h6#, 1...Rd4-~ 2.Bf2-g3#.

The judge B. P. Barnes has noted that the problem has remarkable economy, and should be used as an example.

(This post in Greek language).