Symmetry

We will see the subject of the symmetry in the arrangement of the pieces. In his book "Caissa's Fairy Tales", 1947, the founder of the Fairy Chess T. R. Dawson has studied the apparently simple subject of the symmetry of the position.

The axis of symmetry may be parallel to a row, or parallel to a file (and we usually call it vertical axis), or parallel to a diagonal line. There is also the case of symmetry around a point.

From the Dawson's analysis we gather a few observations :
1. In an apparently symmetrical position, it is possible for the White to have some abilities on the one side (let us say : a move to a side file, a castling move, etc.) which are not available on the other side of the position. This means that the solution is probably non-symmetrical.
2. In an apparently symmetrical position, it is possible for the Black to have different abilities on each of the two sides of the position, resulting in a non-symmetrical solution.
3. In a diagonal symmetry, the Pawns do not have equal abilities of movement on the file or on the row, thus the solution may be non-symmetrical.

When we study a symmetrical position, we decide whether we will maintain the symmetry with the key, or we will break the symmetry of the position.


Let us see the Problem-162, by (the famous in Greece troubadour of rebetico songs) Mr. Nikos Pergialis.

	(Problem 162) Nikos Pergialis, Newspaper "Eleftherotypia", 17/12/2006 Mate in 2 moves. #2 (7+9)
[8/3K4/2pBp3/p2k2p1/1ppPpp2/3R4/S5S1/3B4]

Tries: {1.Bc5? e5!}, {1.Be5? c5!}, {1.Sxf4+? gxf4!}, {1.Se3+? fxe3!}, {1.Sc3+? bxc3!}, {1.Sxb4+? axb4!}.

Key : 1.Rd2! (zz). If Black breaks the symmetry, he is lost.
1...a4 / b3 / c3 / c5 / e5 / e3 / f3 / g4
2.Sxb4# / Sc3# / Bb3# / dxc5# / dxe5# / Bf3# / Se3# / Sxf4#

This setting may be moved one file to the right, and the solution will be similar. (When we decide for the final form of our composition, we take care to have more pieces on white squares (or else we transpose the position) in order to be nicely-looking when it will be printed. Here the composer put on white squares 10 from the 16 pieces).
But this setting must not be moved one row upwards!
Do you see the changed detail which leaves the problem without solution?
It is the pawns above the upper Bishop, which, when they are standing on row-7, they can move with double step and thus they can interfere with the checking move of the lower Bishop (so, there is no mate in 2).


In the next Problem-163, by Dawson, it is obvious that if Knight leaves e3, the black King can move, either to d5 with flight to e4, or to f5 with flight to e4, so with the Knight on e8 at the right moment White can mate.

	(Problem 163) T. R. Dawson, Newspaper "The Times", 23/12/1920 Mate in 6 moves. #6 (9+6)
[8/8/1p2p2p/1P2P2P/2pPkPp1/2P1S1P1/4K3/8]

Tries : {1.f5? exf5!}, {1.d5? exd5!}, {1.Sxg4? Kf5!}, {1.Sxc4? Kd5!}, {1.Kf2? Kd3!}, {1.Kd2? Kf3!}.

Key : 1.Sc2! (zz, zugzwang).
And how is the Knight going to e8?
By the left side, stepping on the edge file, outside symmetry.
1...Kd5 / Kf5 2.Sb4(+) (zz)
2...Ke4 3.Sa6 (zz)
3...Kd5 / Kf5 4.Sc7 (zz)
4...Ke4 5.Se8 (zz)
5...Kd5 / Kf5 6.Sf6# / Sd6#

If we move the setting one file to left, the Knight must go to e8 by the right side.
If we move the setting one row upwards, the problem is ruined, because the white pawns can achieve solution in four moves (because e is promoted with check).
(The position has only 7 from 15 pieces on white squares, but the composer has preferred to leave the Kings on their initial file-e).


In the miniature Problem-164, by Stavros Iatridis, we see that the key maintains the symmetry, and the two variations end with echo mates. (Please compare with Problem-45, which has diagonal symmetry and similar echo mates).

	(Problem 164) Stavros Iatridis, Mate in 2 moves. #2 (4+2)
[8/8/4Q3/4p3/3SkS2/8/4K3/8]

Tries : {1.Qd5+? / Qc6+? / Sb3? / Sc2? / Sf3? / Sf5? / Sc6? / Sb5? / Kd2? Kxf4!}, {1.Qf5+? / Qg6+? / Sd3? / Sg2? / Sh3? / Sh5? / Sg6? / Sd5? / Kf2? Kxd4!}, {1.Qxe5+? Kxe5!}.

Key : 1.Qe7! (zz).
1...Kxf4 / Kxd4 2.Qh4# / Qb4# (echo-mates)

The Problem-165, by Carpenter, has similar position with the previous one but its solution is non-symmetrical.

	(Problem 165) George E. Carpenter, Dubuque Chess Journal, 1873 Mate in 2 moves. #2 (5+2)
[4B3/8/4Q3/3SpS2/4k3/8/8/4K3]

Tries : {1.Bb5? / Qc6? / Kd2? Kf3!}, {1.Bh5? / Qg6? / Kf2? Kd3!}, {1.Qxe5+? Kxe5!}.

Key : 1.Qa6! (zz). The Queen needs to reach squares c6 / g6 / e2 and steps on the side file removing one flight but abandoning the guarding of the two Knights.
1...Kxd5 / Kxf5 / Kf3
2.Qc6# / Qg6# / Qe2#

The moves of the wQ to the squares c6 / g6 are seen as tries and also when it gives mates from there.


Many problems have been composed with symmetrical position. Some resemble trees, some are sketches of musical organs, some have the shape of a letter.
Some of these problems are very difficult puzzles. (Remember that the Problem-155 needed retroanalysis in order reveal which of the two en-passant captures was the key).

We will see now the Problem-166, by Anderson, which has diagonal symmetry. The Pawn c6 can move to c5, but it cannot move to d6.

	(Problem 166) William Anderson, Honourable Mention, Ideal Mate Review, 1984 Helpmate in 5 moves. h#5 (2+4)
[R7/8/2p5/3k4/4q3/8/6r1/7K]

Key : 1.Rg1+
1...Kh2 2.Rc1 Kg3 3.Qe2 Kf4 4.Rc5 Kf5 5.Qc4 Rd8#


We close this presentation with a nice original problem, by the known chess player (ELO 2225) Mr. Emmanuel Pantavos. Here the symmetry is around a point (a unique point which is the middle of the distance of any pair of pieces similar in value but dissimilar in color).

	(Problem 167) Emmanuel Pantavos, original, 05/05/2008 Helpmate in 2 moves, Duplex. (2 solutions) h#2 duplex 2111 (4+4)
[8/5p2/8/1S2kr2/1RK2s2/8/1P6/8]

Black plays...
1.Sd5 Kd3 2.f6 Re4#
1.Ke4 Rb3 2.Re5 Sd6#

White plays...
1.Sd4 Kd6 2.b3 Rc5#
1.Kc5 Rf6 2.Rc4 Sd3#


(This post in Greek language).

Task (2), with Full Knight Wheel

As we have said, task is the composition that achieves the maximum number of variations with a specific characteristic.

Theme: Task with Full Knight Wheel is the composition which has 8 thematic variations with a Knight reaching (with one step) eight different squares.

In the next problems we see one full Knight wheel in Iatridis’s problem-63 and two full Knight wheels in Petrovic’s problem-64.

	(Problem 63) Iatridis Stavros, ”To Skaki”, 1944 White plays and mates in 3 moves #2 (8+6)
[K5B1/2p5/2SP1k2/5P2/3Sp3/6s1/1Q1B2b1/s7]

The Olympic winner Stavros Iatridis presents a task with a full white-knight wheel, where the battery Qb2 with Sd4 is ready to fire:

Key: 1.Se7! (Nice key! It gives one more flight to the black King, and also unmasks the battery Pa4-Bg2 so, if pawn e4 moves, Bg2 checks the white King).
1...e3+ (but this move stops the guarding of g5 by the Bishop Bd2) 2.Sf3#
1...Se2 [2...Sc3] 2.Sxe2#
1...Sc2 [2...Sd4] 2.Sxc2#
1...Sb3 [2...Sd4] 2.Sxb3#
1...Ke5 2.Sb5#
1...cxd6 2.Sc6#
1...Kg7 2.Se6#
1...Sxf5 [2...Sd4] 2.Sxf5#


Two years after the publication of Iatridis’s problem, the excellent composer Nenad Petrovic presented a problem with two full Knight wheels, one full white-knight wheel and one full black-knight wheel! He was compelled to use all sixteen white pieces to achieve the double task, with an admirable result.

	(Problem 64) Nenad Petrovic, ”The Chess”, 1946 White plays and mates in 2 moves #2 (16+6)
[3B2r1/2P3P1/KR3P1R/2PskS2/2P3p1/2P2PPB/1Q4S1/5s1r]

Try: {1.c8=Q? Re8!}
Key: 1.Rh5! (The Rook with the Knight form a battery, which gives mate if the Knight moves, for example 2.Sh6#)

black S wheel	white S wheel
1...Sxc7+ 2.Bxc7#	1...Rxg7 2.Sxg7#
1...Sxb6 2.Sd4#	1...Rh8 2.Sh6#
1...Sb4+ 2.cxb4#	1...Rxh3 2.Sh4#
1...Sxc3 2.Qxc3#	1...Sxg3 2.Sxg3#
1...Sde3 2.Sfxe3#	1...Sfe3 2.Sfxe3#
1...Sf4 2.gxf4#	1...Sxb6 2.Sd4#
1...Sxf6 2.Bxf6#	1...gxf3 2.Sd6#
1...Se7 2.Sxe7#	1...Se7 2.Sxe7#

[This post in Greek language].

Iatridis Stavros

Iatridis Stavros, (1887 – 1976), was golden Olympic winner in composition of chess problems. Apart from his objectively successful occupation with chess composition, which brought for him a lot of first prizes and many distinctions, he was a very fast solver and he was called “The Dragon of Problems”.
Iatridis was strong player of over-the-board game, having the title of Master with excellent ability in game analysis. In the first unofficial Greek championship in 1935 he won every game he played, but professional obligations kept him away from the last two rounds.
On November 25, 1964, in the 16th Chess Olympiad in Tel Aviv, the colonel of the Greek Army Iatridis Stavros was nominated golden winner in composition, in the category direct-mate three-mover. This was the fourth golden Olympic medal in the modern history of Greece, (after Tsiklitiras, Louis, and ex-king Constantine).

In 1967 chess was recognized by special legislation as intellectual sport in Greece.

Iatridis served as president of the Greek Chess Federation (G.C.F., Elliniki Skakistiki Omospondia) for almost one year.
He invited the Grand Master Dr. Petar Trifunovic as trainer for the national team.
He organized tourneys with sponsors commercial companies (Phillips, Shell).
He organized the Acropolis international tourney.
He invited Bobby Fischer in Greece for a handicap simultaneous demonstration.
Having connections with the army, he found easily office-rooms for G.C.F.
He wrote the column “Kallitexniko Skaki” (=artistic chess) in the monthly magazine “O Skakistis” (=the chess player), published by Harvatis Costas.
The enterprising and effective president Iatridis resigned because of ill health.

In October 1969 he was appointed chairman of the Preliminary Games for the World championship (Zonal 3) which were held in Athens.
In 1971, the retired colonel Iatridis, honorable president of G.C.F., co-founded the Chess Club of Ambelokipi (Skakistikos Omilos Ambelokipon).

In 1976, the likable uncle-Stavros was killed in a car accident. He was 89 years old.

We translate here an excerpt from the preface of the booklet “Kanonismos Zatrikiou” (=Chess Regulation) by Stavros D. Iatridis, publishing house Astir Papadimitriou, 1940:
“We believe that we offer service to the players of Chess, especially to young persons, with the publication of the present International Regulation translated into Greek, because now contestations and gripes will be avoided, in the quietest, most intellectual and most enjoyable game of world, a game fairly considered as the King of the games.
The playing of Chess is allowed in all the clubs, in the houses of poor and in the palaces of rich, because it is a polite and very attractive amusement. It sharps the brain and teaches what can someone achieve with patience, combination and forecast, and usually protects youth from acquiring other, bad habits. For this reason, a lot of States support its distribution with suitable efforts and subsidies...”

Those were the writings of Iatridis, back in 1940. Twenty four years later he became Olympic winner and three years after that the Greek state recognized chess as intellectual sport! For the subsidies he mentioned, the Greek problemists still wait, sixty eight years later.


The golden three-mover

	(Problem 119) Iatridis Stavros, Gold metal, “16th Olympiad”, Tel Aviv, 1964 White plays and mates in 3 moves #3 (7+8)
[8/1Ks1p3/1p5S/4p1q1/4s1S1/3R2p1/Qs2B3/7R]

The problem-119 was awarded with a gold metal, because it is a rare beauty. Watch the solution:
Tries: {1.Sf2+? gxf2!}, {1.Qd5+? Sxd5!}, {1.Qc4+? Sxc4!}, {1.Qa4+? Sxa4!}.

The problem starts as a threat-problem:
Key: 1.Rh4! (The knight Sg4 and the rook Rh4 form a battery which will fire when Sg4 moves, for example 2.Sf6#).
if 1...Kf4 2.Rf3+ Ke4 3.Sf2#

The black Queen Qg5 can capture the rook, or can step between King and Knight:
1...Qxh4 2.Qxb2 (and mate follows in the next move, with Qb4# ή Qxe5#).
1...Qf4 2.Kxb6!!
This move brings black in a zugzwang situation, and the problem is transformed to a waiter-problem! With this last move the white King is exposed to eight checks!

Four checks are given by the black Knights and are answered by the white Queen:
2...Sa4+ 3.Qxa4#
2...Sc4+ 3.Qxc4#
2...Sd5+ 3.Qxd5#
2...Sa8+ 3.Qxa8#

Four checks are given by the black Queen and are answered by the white Knight:
2...Qe3+ 3.Sxe3#
2...Qf2+ 3.Sxf2#
2...Qf6+ 3.Sxf6#
2...Qxh6+ 3.Sxh6#

Two more variations with pinning of the black Queen:
2...e6 3.Sf6#
2...g2 3.Sf2#


Now, for the completeness of this presentation of Stavros Iatridis, we post an educational game of his, that shows how Iatridis took advantage from the mistakes of his opponent during the opening and reached an end of game that he won easily. Note the comment at the tenth move, that reveals the analytic mind of Iatridis:

White: P. P., Black: Stavros Iatridis
Athens, 1937
Queen’s gambit
1.d4 d5 2.Sf3 Sf6 3.c4 e6 4.Sbd2 Be7 5.e3 0-0
6.Bd3 b6 7.0-0 Bb7 8.b3 Sbd7 9.Bb2 Se4 10.Se5
At this point Master Iatridis announces to his opponent that after the captures of the pieces they will reach an endgame with same-coloured bishops and he will win with his passed pawn.
10...Sxe5 11.dxe5
If 11.Bxe4 dxe4 12.dxe5 Qd3 13.Sb1 Rfd8 and black wins,
or 13.Re1 Rfd8 14.Bc1 Bb4 15.Re2 Bc3 16.Qxb1 and black wins.
11...Sxd2 12.Qd2 dxc4 13.bxc4 Be4 14.Rfd1 Qxd3 15.Qxd3 Bxd3
16.Rxd3 Rfd8 17.Rad1 Rxd1+ 18.Rxd1 Rd8 19.Rxd8+ Bxd8 20.Ba3 c5
21.Kf1 Kf8 22.Ke2 Ke7 23.Kd3 Kd7 24.Kc2 Kc6 25.Bb2 a6
26.a4 b5 27.cxb5 axb5 28.axb5+ Kxb5 29.Kd3 c4+ 30.Kc2 Ba5
31.Bc3 Bxc3 32.Kxc3 Kc5 33.e4 Kb5 34.f4 Kc5 35.g4 Kb5
36.h4 Kc5 37.f5 Kb5 38.g5 Kc5 39.h5 g6
Here white resigns.
If 40.fxg6 fxg6
41.hxg6 hxg6 42.Kc2 Kd4 43.Kd2 Kxe4 44.Kc3 Kxe5 and black wins.


[This post in Greek language].

Version of an Unsolvable

Dear readers, I propose to you to solve a problem with no-solution.

The composer Dr. Kurt Dittrich has published it in 1918 with stipulation “White plays and mates in 4 moves” but on square b3 he had put a black soldier and the problem had no solution. This problem has reappeared in chess books as an example of problem without solution [See Jean Bertin, ”Initiation au Problėme d’ échecs” (Introduction to chess problems), Insolubilité (lack of solution), p. 30].

	(Problem 22) Dr. Kurt Dittrich, ”Deutsches Wochenschach“, 1918, version by Iatridis Stavros White plays and mates in 4 moves #4 (7+10)
[3s4/4bpQ1/3pp1bS/8/5pRp/1P2kP2/s3P3/4K3]

The Olympic winner Iatridis Stavros (1887-1976) has corrected the problem and the stipulation is valid.

The solution of problem-22 contains line clearances, line closings, and Theme Turton.

Key: 1.Qb2! [2 Qd2#]
1...Bc2
2.Rg8 (Two pieces (Q and B) have left g-file allowing the move Rg8. The threat now is [3.Sg4#]).
2...f5
3.Qg7 (The linear piece R going up the g-file has passed over the critical square g7, then on g7 has arrived  the linear piece Q, which will move now to the opposite direction going down the g-file with threat [4.Qg1#], thus we have theme Turton. Two pieces (B and R) have moved clearing g-file and allowing the move Qg1).
3...Bg5 (The queen has come back on its previous place (switchback of wQ), but the bishop that has moved can not come back because the pawn has closed the diagonal. Now black is forced to find a different defense, giving new possibilities to white).
4.Qa7# (Two pieces (pawn and B) have left row-7 allowing the move Qa7).

The correction is the following:
On b3 must stand an obstacle, because the queen must not go from b2 to b6 to give check. The composer Dittrich had put on b3 a black pawn, and the problem had no solution:
(1.Qb2? Bd3! 2.Rg8 f5 3.Qg7 Bxe2!) and no mate exists on the fourth move.

The Olympic winner Iatridis Stavros corrected the defect of the problem with a very simple manner, changing the colour of the pawn b3 to white, thus creating the continuation:
(1.Qb2! Bd3 2.exd3 ~ 3.Qf2+ Kxd3 4.Qd2#) and this nice problem is saved.

[This post in Greek language].

(7) Good key, characteristics 11 and 12

Characteristic 11 : The key is give-and-take. Usually we give flights and take equal number of flights, but let us see here a replacement of the sacrificed piece.

	(Problem 8) Stavros Iatridis, Chess magazine “O Skakistis”, issue No.6, May 1968 White plays and mates in 4 moves #4 (6+3)
[8/8/6pR/5kS1/5p2/5P2/6SK/B7]

What it is important : to achieve mate in the number of moves stated in the stipulation. (It is completely unimportant if we can achieve mate in more moves). The golden winner of chess Olympics Stavros Iatridis (1887 – 1976) created problem-8, in order to prove that in chess compositions is not necessary only the power of the pieces but even their sacrifice in the suitable position. When we hit the target, no sacrifice is aimless.
The solution follows:
Key: 1.Rh5! (After the key the black king, which could initially take the knight Sg5, cannot move, but in exchange black can take the rook, which is considered stronger piece than the knight).
1...gxh5 (There goes the rook...)
2.Sh4+ Kxg5 (There goes the first knight...)
3.Bg7 Kxh4 (There goes the second knight...)
4.Bf6# (In three moves three white pieces are sacrificed, and then black is mated).


The positions of the legal problems should be reached, from the initial placement of the 32 pieces for a game, with a series of legal moves. If this is not true, then the position is called illegal and the problem is unacceptable.
Examples of illegal positions : White bishop on a1 and white pawn on b2 (how did the bishop go there?). Three white rooks and all eight white pawns on the chessboard (since no pawn is missing, which promotion produced the third rook?).


Characteristic 12 : The particularity. It is not readily seen what the key is.

	(Problem 9) Emmanuel Manolas, Newspaper "Peloponnissos", 07/04/1971, White plays and mates in 2 moves #2, retro, (9+3)
[8/8/P1Q5/KpP5/1P6/kB6/PS6/b5R1]

The problem-9 presents a difficulty for the unaware solver, who cannot spot readily the series of moves which mate black on the second move.
The problem needs retroanalysis, that is analysis of the moves which brought white and black pieces in the problem position.

The stipulation states that it is white’s turn to play. That means the black has just played his move. What was the move that black had just played?
The bishop Ba1 could not have played last. The king Ka3 could not have played last. Thus the black pawn (now on b5) had played last. From which square started to reach b5? Not from a6, not from c6, since there are white pieces there. Not from b6, because it was checking the king. Conclusion: the black pawn had moved last with double step from its initial position, b7-b5. That means that white has the right to take this pawn en-passant.
The solution follows:
Key: 1.cxb6 e.p. (The key is taking en-passant and with this move two lines of the queen are simultaneously open).
If 1...Bxb2 2.Qa4#
If 1...Kxb2 2.Qc1#

[This Post in Greek language]