BRITISH CHESS PROBLEM SOCIETY

Mate in two

When solving a twomover it is a good idea to consider black moves that appear to be very strong. One such defence in this position is 1...f2 since this gains a flight for the bK at f3. The only efficient way of dealing with this is for White to arrange a threat of 2.Sd2#. Unfortunately this knight is pinned and if the wK moves off the b-file then he will be checked by the bQ or by the bPd2. If we look more closely at this pawn we notice that, by extension of the line of the bRd7, 1...d2 will be a defence against the threat. In turn a white line of guard to e3 is opened. Similarly, after 1...Sf1 a white line of guard to e5 is opened. We must be on the right lines here! There are two sensible possibilities. Try 1.Rb5? (>2.Sd2) 1...d2/Sf1 2.Sg5/Sc5. In the first mate, White can cut the line h6 to e3 because Black has opened the line c3 to e3. In the second mate, White can cut the line from b5 to e5 because Black has opened the line from h2 to e5. 1...Qf4 is met by 2.Qxf4. However, there is no answer to 1...Rd5! since the bK can now escape to e5. Key 1.Qb6! (>2.Sd2) 1...d2/Sf1 2.Sc5/Sg5. (By-play – 1...Rd4 2.Qxd4) The wQ now controls e3 from a different direction so that 2.Sc5 follows the opening of the line of wRc3. 2.Sg5 follows the opening of the line of wBh2 as wRh5 remains on the east side of the e5 square. You will notice that the mates following 1...d2/Sf1 have been switched around between the two phases. This strategy is known as the reciprocal change of mates. A delightful geometry has brought the effect about. The try, 1.Rb5, is said to be a critical move because it crosses over the critical e5 square. The key, 1.Qb6, is said to be a pericritical move because it moves around the e3 square while continuing to control it. The composer intends that repeated mates after different black defences will stimulate the solver to analyse the mechanism by which this occurs.

Mate in two

A good chess problem only uses force that is necessary. A brief glance at the diagram tells us that wPg2 is out of play. Consequently we can ”solve“ this twomover at a glance! 1.Bh2! (>2.g4) This feeling is reinforced when we notice that any move by bSf4 defends by opening the line of bRd4. However, the line of wBh2 is opened to e5 and this clearly affords potential! The solving process is not just about finding the key but there is enjoyment to be had in unravelling the play, which in this instance is most complex! Let us first consider any random move of bSf4; 1...Sfxg6 appears strong but, as wBh2 now holds e5, 2.Sxd4 reclaims e6! Specific moves by bSf4 attempt to prevent this mate. 1...Se2 guards d4 but interferes with bRe1 to permit 2.Sxe7, another mate dependent on the changed control of e5. 1...Se6 likewise also guards d4 and also interferes with bRe1... but 2.Sxe7? is not mate. Black has unpinned his own bQd7! However, 1...Se6 additionally interferes with bBa2 to enable 2.Qf7#. Finally 1...Sfd5 prevents 2.Sxd4 by unpinning bPc5. This defence also interferes with bBa2 but prevents 2.Qf7? by arranging an interposition on f6. It is the interference with bRd4 that determines the mate, 2.Sd6#, and in this way the function of the last white piece is decided. The final roll call of mates might be summarised thus: 1...Sf~/Se2/Se6/Sfd5 2.Sxd4/Sxe7Qf7/Sd6. The bSf4 is said to correct the error of its random move in a number of different ways. You may have noticed two reasons for the correction 1...Se6. Not only does the bS guard d4 but it also unpins the bQ to pre-empt 2.Sxd4. The motivation for this defence is regarded as impure. In complicated problems it is often impossible to ensure a unique motivation for the moves.

Mate in two (set play and tries)

One particular feature of the diagram is the open position of the mirrored bK; all eight adjacent squares are vacant. However, the squares on the 5th rank above the bK may be occupied with interesting effect; 1...c5/Rd5/Re5 2.Qxd2/Qb4/Qxe5. Two tries confirm the self-blocks discovered in the set play. 1.Re6? (>2.Qe5) 1...c5/Rd5/Rxe6 2.Qxd2/Qb4/Sxe6 but 1...Sc6! refutes. 1.Re3? (>2.Rd3) 1...c5/Rd5/Rxe3+ 2.Qxd2/Qb4/fxe3 but 1...Bf1! has no answer. White opening moves that cut the line of wRe1 will transform elements of the set play. 1.Se4? (>2.Qc5) 1...Rd5/Re5/Rxe4 2.Qxa1/Qxd2/Rxe4. This try fails to 1...Sa6! The mate following 1...Rd5 has been changed from 2.Qb4 to 2.Qxa1. Of greater interest is the mate after 1....Re5, changed from 2.Qxe5 to 2.Qxd2. This latter mate occurred after 1...c5 in the set play; 2.Qxd2 is said to be a transferred mate. 1.Se3! (>2.Sf5) 1...c5/Rd5/Re5 2.Qxa1/Qxd5/Qb4. It will be seen from this that 2.Qxa1/2.Qb4 are also transferred mates! It is of interest to determine the mechanism by which these effects are engineered. 1.Se4? cuts a guard of e5 but adds one to c5 whereas 1.Se3! cuts a guard of e5 but adds one to d5. Thus there is an alteration of control over the c5/d5/e5 squares. The by-play is completed by 1...Rxe3+/d1Q+/g3/Rf8 2.fxe3/Rxd1/Sf3/Se6. Controversially we also have 1...Rf7/Sd6/Se7 2.Qd5/Qd5/Se6. Altogether 2.Se6# occurs twice and 2.Q(x)d5# three times! Defences giving rise to the same mates are known as black duals and these are usually regarded as undesirable repetitions. Here they could have been eliminated by the removal of bSc8 and the shift of bRe8 to e7. The post-key play is already considerably richer than that following the tries but presumably Zagoruiko valued the interferences supplied by bSc8.

Mate in two (two tries)

Moves of bRh2 and bRg1 up the “h” and “g” files respectively are set with shut-off mates delivered by the B+R battery. However, the moves of the bRs along the first and second ranks lack provision. More importantly as things stand in the diagram there are no mates arranged for the strong black defences, 1...Kf6 and 1...exf3. This suggests that White should consider a move by wBf5. Try 1.Bg4?-A (>2.Rf5) If 1...Rf2 2.Qh5-C (1...exf3 2.Re3) but 1...Rf1!-a refutes. Try 1.Bh3?-B (2.Rf5). If 1...Rf1 2.Qh5-C but 1...Rf2!-b refutes. Key 1.Qh5!-C (-) If 1...Rf1-a 2.Bh3-B or 1...Rf2-b 2.Bg4-A. We can observe an alphabetical pattern; 1.A? a! 1.B? b! and 1.Key! 1...a/b 2.B/A. This defines the Banny theme, named after the Russian composer, Dmitri Banny. The theme is enhanced in this problem by the transfer of the move, Qh5-C. It will be seen that moves A, B and C all occur as white 1st moves (tries and key) and 2nd move mates. There is additional play: 1...Kf6/bxc3/e3(exf3) 2.Bxe4/Bxc3/R(c)(x)e3 but the most important by-play is provided by the bRs. 1...Rxh5/Rb2/Rhg2/Rhh1/Rg5/Rxa1/Rgh1/Rgg2 2.Rc1/Bg4/Bg4/Rc1/Rc2/Bh3/Bh3/Rc2. The bRs are said to occupy focal positions controlling both the diagonal and orthogonal white batteries. When one black rook relinquishes its hold of one battery, the line of the other black rook is cut by White’s mating move. The moves 1...Rhg2/Rhh1/Rgh1/Rgg2 are particularly thought provoking. One bR hides behind the other and in this way complete accuracy of play is achieved. This device is known as the Mackenzie theme. Arthur Ford Mackenzie made many examples of his theme but he knew that this one was special. At the time this problem was composed, tries were viewed merely as distractions to make the solver’s task more difficult. The judge referred to the tries in his report as though they were an integral part of the content – precisely Mackenzie’s intention. Dmitri Banny was not the originator of this idea; his role was that of populariser.

Mate in two (two tries)

The wRh2 is rather out of things... 1.Be3?-A (>2.Rh4-C) 1...Sh6 etc 2.S7d6, 1...Rg1(Rh1) 2.Sa5 but 1...d1Q!-a. 1.Bxd2?-B (>2.Rh4-C) 1...Sh6 etc 2.S5d6, 1...Rg1(Rh1) 2.Sa3 but 1...e1Q!-b. Key 1.Rh4!-C (>2.B4~) 1...d1Q-a 2.Bd2-B and 1...e1Q-b 2.Be3-A. This is exactly the same pattern as was seen in the previous twomover by Mackenzie – the Banny theme. However, there is much more to Geoff Foster’s problem! If 1...Sh6/Sg5/Se5/Sd6 2.BxS or if 1...Rg1/Rh1 2.Bg3/Bh2. All possible threats by the wBf4 have been separated by unique black defences – the Fleck theme. Moreover, mates following defences by bSf7 and bRa1 have been changed across the three phases of play – the Zagoruiko theme. The elements are all well known but their exquisite combination made this #2 well worthy of its prize. There are no lines controlling the R+B battery until Black promotes one of his pawns; this too is an unusual feature. Many solvers have criticised this kind of Banny problem because the key is obviously stronger than the tries. This can be expressed another way. Rh2-h4 is always necessary, whereas in one circumstance Bf4-e3 is needed and in another it is Bf4-d2 that is required. By playing Rh2-f4 first, White avoids the mistake of premature commitment.

Mate in two (two tries)

There is set play generated by bSc4 – 1...Sa3+/Se3+/Sb2/Sb6 2.RxS. However, it seems clear that the fate of bSc4 is to be pinned for a random move by wRb3 threatening 2.Bxc4. 1...Sf4/Qe5 will be met by 2.R(x)e5 so White must concern himself with the defences 1...Qxd6/Rxa4/Sxf6. 1.Rd3? Qxd6/Rxa4 2.Rxd6/Sd8 but 1...Sxf6! 1.Re3? Sxf6/Qxd6 2.Shg5/Sfg5 but 1...Rxa4! 1.Rxf3? Rxa4/Sxf6 2.Sf8/Rxf6 but 1...Qxd6! Key 1.Rb8! (>2.Bxc4) 1...Qxd6/Rxa4/Sxf6 2.Sd8/Re8/Sf8. This fine twomover demonstrates cyclic refutation. The relevant feature for this theme is that Black should have three thematic defences and that White’s tries should fail to each in turn. The mates are changed throughout the solution – one might think that this should give (3x2) + (1x3) or 9 mates in all. In fact there are only 7 distinct mates because 2.Sd8/2.Sf8 have been cleverly transferred to follow different Black defences. The play by the wSs, both in administering mate and supporting mates on d6/f6, give this work great unity and clarity.

Mate in two

The bK has two flights and only one is set with mate; 1...Kd5 2.Sxd4. A move by wBc5 appears to be indicated for this pins the bQ, potentially extends the reach of wRg5 to b5 and releases wSe4 from the need to guard c5. The Q+S battery will clearly fire; those wPs on f2, g3 and f6 can only be present to prevent unwanted moves of the wSe4! Key 1.Bf8! (>2.Sc3) It will be noticed that the threat unpins the bQ but that as things stand Black cannot take advantage of this fact. So, 1...Qc4 2.Sxd4 (2.Sc3? Qd5). Similarly 1...Qc5 2.Sed6 (2.Sc3? Qd5) The bQ moves along the line of pin to a square where the unpinning threat will allow her to defend successfully. The weaknesses of these defences are interference with bRb4 and self-block of c5. Another related black defence is 1...d2 2.Sxd2 (2.Sc3? Qe4). Black strengthens his position by opening c2 to e4 but weakens himself by opening a white line of guard from f1 to b5. These three variations represent a variety of Schiffmann strategy. The date of the problem is interesting. In 1928 Schiffmann, the great Romanian composer, had published an article entitled “Une nouvelle defense dans le deux coups” in De Problemist in which he expounded his ideas. There is good by-play in Gavrilov’s setting. 1...Rb5 (self-block) 2.Sc5, 1...Kd5 2.Sc5 (a changed mate), 1...Kb5 2.Sxd4 (a transferred mate) and 1...Sxf6(Se7) 2.S(x)e7. This last variation is important for it explains why the key bishop must go all the way to f8 and not stop short at e7. 1.Be7? is a good try defeated uniquely by 1...Sxf6! There are clearly no other possible openings by wBc5. A modern composer would probably try to expand the try-play by removing bRb4...

Mate in two

1.Ba3? (>2.Sc3/2.Sed6) Rb4! 1.Bxd4? (>2.Sc3/2.Sed6) Kb5! (2.Sxd4?) 1.Be7? (>2.Sc3) Sxf6! 1.Bf8! (>2.Sc3). Note that it has been possible to dispense with bBa8 since an immediate 1.Sc3+? does not cook... 1...Kxc5 2.Qd5 Kb4! The removal of bRb4 has unblocked that square but clearly Gavrilov valued the self-blocking variation, 1...Rb5!

Mate in two

1...Kc5      2.Qxc6#
1...Ke5      2.Sxe4#

1.Bg8!       (2.Sd3#

1...Kc5     2.Sxe4#
1...Ke5     2.Sd5#
1...Qd4     2.Sxe4#
1...Qd5     2.Sfe6#
1...Rc5     2.Sd5#
1...Rb5     2.Sxe4#
1...Sf7,Sg6 2.S(x)f7#