Weekly Problems 2011-A

Two tries and the key trigger three connected phases of play, and bring about a remarkable combination of themes. The first try 1.Bxd2? threatens 2.Rh4, and when Black defends with the rook or the knight, White is able to mate with the b5-knight, because c3 is guarded: 1…Rh1/Rg1 2.Sa3, 1…Sd6/Se5/Sg5/Sh6 2.S5d6. But 1…e1=Q! defeats the try. The second try 1.Be3?, with the same threat of 2.Rh4, observes c5 so that the b7-knight can mate instead after the same black defences: 1…Rh1/Rg1 2.Sa5, 1…Sd6/Se5/Sg5/Sh6 2.S7d6. Now 1…d1=Q! refutes the try.

The key is 1.Rh4! which contains eight threats – any move by the f4-bishop. When multiple threats are individually forced by Black’s play, that is called mate separation or the Fleck theme, hence 1…Sd6 2.Bxd6, 1…Se5 2.Bxe5, 1…Sg5 2.Bxg5, 1…Sh6 2.Bxh6, 1…Rh1 2.Bh2, 1…Rg1 2.Bg3, 1…e1=Q 2.Be3, 1…d1=Q 2.Bd2. These post-key variations also show changed play compared with the try phases, i.e. new mating responses to the same rook and knight defences. Such a three-phase change of white moves generates the Zagoruiko theme.

Furthermore, the two try phases and the actual play are connected by the way certain moves recur but with their functions changed. For example, in the try play, Bxd2 and Be3 act as the first moves while Rh4 is the threat, a situation reversed in the actual play when Rh4 is the first move while Bxd2 and Be3 are two of the threats. A more specific form of such reversal of functions, known as the Banny theme, is also demonstrated here. To see the Banny pattern formed, we label the thematic moves with letters: Try 1.Bxd2? A?, 1…e1=Q! a!. Try 1.Be3? B?, 1…d1=Q! b!. After the key 1.Rh4!, 1…e1=Q a, 2.Be3 B; 1…d1=Q b, 2.Bd2 A. Thus the theme is characterised by how two try moves become post-key mating moves, as answers to two black defences that originally work as refutations to the same two tries, in a reciprocal way.

The white queen makes five tries and the key that can be grouped into pairs of moves to the same file, and where the second move of each pair “corrects” the first by providing for 1…Rxa8 or 1…Rxh8. 1.Qa4? (waiting) Rxh8! and 1.Qa1? (waiting) Rxh8 2.Qxh8, but 1…e5! 1.Qe5? (threats: 2.Qxe7, 2.dxe7, 2.dxc7) Rxa8! and 1.Qe4? (2.Qxe7, 2.dxe7) Rxa8 2.Qxa8, but 1…cxd6! 1.Qc5? (2.Qxc7, 2.dxc7, 2.dxe7) Rxh8! and 1.Qc3! (2.Qxc7, 2.dxc7) Rxh8 2.Qxh8, 1…exd6 2.Qf6, 1…c5/c6 2.Qa5 (1…cxd6 2.Qa5/Qxc8/Rxc8), 1…Rg8 2.Rxg8, 1…Rf8 2.Rxf8.

Steven Sugg: Very slick little problem, this one... Symmetrical, but not really. :-)

The key 1.Qxb7! unpins the black pawn on d7 and simultaneously self-pins the white queen on the long diagonal. The threat of 2.Qe4 is countered by 1…d5, but now the pawn has unpinned the queen – returning the favour – and so allows 2.Qf7. We see a complex sequence of (1) unpin of Black by White, (2) self-pin of White, (3) unpin of White by Black, and (4) mate by White, all executed by one pair of pieces. Another unpin of the queen occurs with 1…Sc6 2.Qxd7. In a supplementary pair of variations, the black bishop on f3 also gets unpinned twice, as the defensive motive, 1…Bf4 2.Sg7 and 1…Sf4 2.Sg3. There is by-play, 1…Rd5 2.Qxd5, 1…Re5 2.Sd6.

Composer: A response to a short article, by John Ling, on ‘Pin & Unpin’ in Problem Observer, Nov. 1994. The theme is ‘unpin’: W unp. B; B unp. W; B unp. B. Note, also, the Schór theme: the key unpins a black unit while pinning the key piece/a white unit; the unpinned black unit then unpins the pinned white unit, which mates.
Steven Sugg: Note that the bothersome g-pawns, which provided flight for black's king after 1.Qc7?, but after the key they cannot prevent the Qe4 mate with 1…g5/g3 or even 1…gxh5 since Qe4 successfully attacks g6, g4, and f4!

The tries 1.Rb7? and 1.Rb8?, threatening a rook mate on the d-file, fail to 1…d2!, which creates a flight on e3. A good sacrificial key 1.Bb2! (waiting) pins the c3-pawn and so provides for 1…d2/dxc2 with 2.Qd2, and if 1…cxb2 2.c3. The g4-rook is guarding against queen mates on f4 and g1, and when the piece moves its focus on the two squares is lost: 1…Rg-file/Rf4 2.Qf4, 1…Rh4/Rg1+ 2.Qg1; only 1…Re4 prevents both mates but it self-blocks, allowing 2.Sf3. 1…Ra-random 2.Rb4, 1…Rc4 2.Sb3.

Andy Sag: A nice waiter with sacrificial key and seven variations. The need to provide for 1…d2 provides a clue.

Set mates are provided for most of Black’s moves, other than a random bishop move like 1…Bc1. A very fine key 1.Sd5! (waiting) adds two variations by sacrificing the knight to a couple of black pieces, 1…exd5 2.Qf5 and 1…Kxd5 2.Se3. The latter is an indirect battery mate that also takes advantage of the pinned black bishop. Another pin-mate occurs after 1…Kd3 2.Qf3. A random bishop move, 1…B~ allows 2.Sxc3, while 1…Be1 gives 2.Rfxe1. Also, 1…S-any 2.Qd4, 1…e5 2.Qf3.

Andy Sag: Typical Saunders waiter with seven variations and sacrificial key allowing a flight capture. Pin-mates follow both flights.

In part (a), the key is similar to that of the previous problem, a double sacrifice to Black’s king and pawn – 1.Ra2! (waiting). 1…Kxa2 2.Sc3, 1…Kxc2 2.Sa3, 1…bxa2 2.Sa3, 1…bxc2 2.Sc3. In (b), White sets up an indirect battery on the b-file with 1.Rb8! (waiting). 1…Ka2 2.Sc3, 1…Kxc2 2.Sa3. No changed play between the two parts (perhaps that’s why the problem is called “The Siamese Twins”!?), but this is a neat miniature presenting five model mates; only 1…Ka2 2.Sc3 in (b) isn’t a model because the b2-bishop is doubly guarded.

Set mates are available against all of Black’s moves: 1…Sf-any 2.Se3 (1…Sd4 2.Se3 or 2.c4), 1…Sg-any 2.Re5, 1…c4 2.Ra5. After the key, 1.Re2! (waiting), a new mate follows 1…Sf-random – 2.Rd2, and the correction 1…Sd4 allows 2.c4 only, removing the dual of the set play. 1…e6/e5 2.Sf6 is an added variation, and the remaining play is unchanged, 1…Sg-any 2.Re5, and 1…c4 2.Ra5. A classy mutate!

The Novotny try 1.Se6? (threat: 2.Rc5) shuts off the e7-rook and g8-bishop, so that they no longer guard the potential mating squares e5 and d5. When Black defends with the d3-rook and c3-bishop, they cause a Grimshaw interference that permits White to mate on those squares: 1…Rd4 2.Se5 and 1…Bd4 2.Bd5 (1…Rd-else on file 2.Rxc3). But 1…Rxe3! refutes the try. The key 1.Bd4! (threat: 2.Qa6) is another Novotny but it cuts off the d3-rook and c3-bishop instead, and now it’s the e7-rook and g8-bishop pair that effects a Grimshaw: 1…Re6 2.Bd5 and 1…Be6 2.Se5. The two white mating moves are thus transferred from one pair of black defences to another. Excellent, sophisticated strategy, but it’s a pity that there is no by-play at all.

Andy Sag: Intersecting line interference defence theme. Try 1.Se6? Rxe3!

The sacrificial key 1.Qb8! (waiting) is also an ambush move, preparing to strike at e5 when the black bishop moves off the queen’s line, 1…Bxa3, etc. 2.Qxe5. 1…Bxb8/Bc7 opens the white bishop’s line to the flight on e7 and enables 2.e8=S. The other white pawn also underpromotes, when Black takes the flight, 1…Kxe7 2.g8=S, and if 1…Kxg7 2.Qh8.

The white queen unpins the black knight with the key 1.Qd7!; the threat of 2.Qf5 is stopped by any move of the unpinned knight, which pins the key-piece by discovery. Such an unpin-pin sequence is called the Dalton theme. A random knight move, 1…S~, allows 2.Qxd3. Three correction moves by the knight disable this secondary threat but permit new mates: 1…Sb4 2.Sc5, 1…Sf4 2.Sg5, and 1…Se3 2.f3. There are two by-play variations, 1…Rxb3/Rf3 2.Qxd5 and 1…e6 2.Qh7.

Composer: Dalton theme (one of Gooderson's and my favourite themes); the three corrections increase progressively in strategic complexity (the last being ‘four-line play’ with self-block).

The key 1.Sxd3! (threat: 2.S7c5) grants a flight on e4 and forms a second battery on the d-file. 1…fxe4 self-blocks and allows 2.Sf4, and 1…f4 interferes with the black queen and leads to a switchback mate 2.S3c5. The R + S battery fires in the variations 1…Qxf6 2.Sxf6 and 1…Kxe4 2.S7c5; the latter is distinct from the threat considering that 2.S7c5 has become an indirect battery mate, with the king on e4. Also, 1…cxd3 2.Qa4. A splendid battery play problem.

Not 1.Rg1? (threat: 2.Qxh5) because of 1…Kh4! The surprising waiting key 1.Rg2! gives two flights to the black king: 1…Kh4 2.Rxh2 (a pin-mate), 1…Kxg2 2.Qf1. The active white queen delivers three more mates with 1…Rxg2 2.Qxh5, 1…Rh1 2.Qxh1, and 1…Sh-any 2.Qg4. Two further variations are unchanged from the set play: 1…Rh4 2.Rg3, and 1…Sg-any 2.Rg3. This gem of a waiter deserves to be remembered from more than a century ago!

The diagram is a complete block where every black move has a set reply, 1…Bb7 2.Qxb7, 1…Bc6 2.Qc4, 1…R~ 2.Qd7, 1…Rd6 2.c6, 1…Bf~ 2.Se7, 1…Bxd4 2.c4, 1…g4 2.Sf4. Any white king move could solve by maintaining the block, but in three cases Black is able to refute with a subtle, pinning defence: 1.Ka4? Bc6!, 1.Kb4? Rb8!, and 1.Kb2? Bxd4! Only 1.Ka2! works, avoiding the pins. A classic rendition of the idea, this two-mover is perfectly constructed, with not a plug in sight.

The thematic defences are 1…Sf4 and 1…Sf2, both unpinning the white queen. As initially set, 1…Sf4 permits 2.Qe4, and 1…Sf2 leads to 2.Qh5. After the key, 1.Be4! (threat: 2.Sd3), the unpins are exploited in a different way: 1…Sf4 2.Qc3, and 1…Sf2 2.Qg3. So two orthogonal mates in the set play are changed to two diagonal ones in the actual play. The by-play consists of a pin-mate, 1…exd5 2.Qf5, and 1…Sc5 2.Qxf6.

All initial black moves have been provided with set mates, 1…Sg~ 2.Bf3, 1…Se4 2.Se3, 1…e4 2.Se3, 1…exd4 2.Bf3 or 2.Bxe6, 1…c4 2.Qxd7, 1…cxd4 2.Qc6, and 1…Sd~ 2.Rxe5. Unusually, such a block position is here solved by a key that contains a threat: 1.Rd2! (threat: 2.dxe5), making this problem an example of a block-threat. 1…Sf3+ 2.Bxf3, 1…Se4 2.Se3, 1…e4 2.Se3, 1…exd4 2.Bf3 (removing the dual of the set play), 1…c4 2.Qc6 (changed mate), 1…cxd4 2.Qc6, and 1…Ke4 2.dxc5 (added mate). Fine flight-giving key and half-pin play.

Four tries and the key (all waiting moves) deal with the three thematic pawn defences, 1…dxc4, 1…dxe3, and 1…c2, in a wonderful variety of ways. 1.Qxc6? 1…dxc4 2.Qxe4, 1…dxe3 2.Qxd5, but 1…c2! 1.Qh3? 1…dxe3 2.Qxe3, 1…c2 2.Rd2, but 1…dxc4! 1.Kf4? 1…dxc4 2.Qxd4, 1…c2 2.Rd2, but 1…dxe3! Hence each pawn defence also acts as the refutation against a different try, providing a nice balance. An additional try is 1.cxd5? 1…dxe3 2.dxc6, 1…cxd5 2.Qb5, but 1…c2! After the flight-giving key 1.Ra2!, two of the three pawn defences provoke brand new mates, 1…dxc4 2.Qxd4, 1…dxe3 2.Be2, and 1…c2 2.Ra3. If Black takes the flight, 1…Kxe3, then 2.Qh3.

A good key 1.Sxg5! (threat: 2.Qf4) self-pins two white pieces – the knight on the g-file and the rook on the long diagonal, and allows them to be captured with check. These pieces are unpinned in the variations 1…Sd5 2.Rf5 and 1…Qf7 2.Sxf7, while their captures lead to 1…Bxf3+ 2.Sxf3 and 1…Qxg5+ 2.Qxg5. The black queen forces two more mates, 1…Qxf8 2.Re6 and 1…Qc4 2.Bg7. Lastly, 1…Sd3 2.Sxd3 and 1…Bc1 2.Qd4.

The thematic key 1.Bb8! (threat: 2.Rc8) opens the 7th rank and enables the black pawn and rook pair to check by discovery. Three cross-check variations ensue, when White answers the checks by interposition and delivers mate simultaneously: 1…exd6+ 2.Rc7, 1…e6+ 2.Sd7, and 1…e5+ 2.Se7; in each case White takes advantage of the pawn’s self-block. The by-play consists of 1…Qxd6 2.Rxd6, 1…Sd4 2.c4, and 1…Se5 2.Sxe7.

The three solutions are 1.Rc8 dxc8=Q 2.Re6 Qc5, 1.Re8 dxe8=Q 2.Rd6 Qe4, and 1.Ree6 Kf4 2.Kd6 d8=Q. Each part finishes with an elegant ideal mate – a mating configuration in which every square next to the black king is covered just once (i.e. guarded/blocked by one piece only), and with every piece on the board taking part. These ideal mates given by the queen are nicely varied, as is the change of promotion squares throughout, all of which add up to a terrific miniature.

It’s well-known that two connected pawns on the 6th rank would normally beat a rook, so to win here White must make mating threats. 1.Rc3! a2/b2 2.Rg3+ Kh4 3.Kf4 g5+ 4.Kf3 g4+ 5.Kf4 a1=Q/b1=Q 6.Rh3+ gxh3 7.g3. Or 1…Kg4 2.Rxb3 a2 3.Ra3 h4 4.Rxa2 Kg3 5.Kf6 g5 6.Kf5 g4 7.Ra3+. An attractive study by one of the few Australian OTB Grandmasters.

The diagram is a complete-block position, with set mates provided for all of Black’s moves. 1…Sb~ 2.Sa5 (pin-mate), 1…Sxc5 2.Sb8, 1…Sf~ 2.Sce5, and 1…b4/bxc4 2.Qa4. White cannot preserve the set play completely, and the key is 1.Qa8! (waiting), which swaps the pin of the bishop for a pin of the knight. Now 1…B~ allows 2.Sa5 (same mate but different pin) and the correction 1…Bxc5 permits 2.Sb8. Therefore two white mates are transferred from one pair of black defences to another.

The diagram shows a homebase set-up, in which every piece on the board is on its game array square. 1.b3 d6 2.Ba3 Be6 3.Bxd6 Bxb3 4.Bxe7 Bxa2 5.Ba3 Be6 6.Bc1 Bc8, and 1.Sf3 e5 2.Sxe5 Qf6 3.Sxd7 Qxb2 4.Se5 Qxa2 5.Sf3 Qd5 6.Sg1 Qd8. Four raids are carried out by two white and two black pieces, when they capture one or more enemy units before returning to their original squares. The two solutions also effect total change – no moves are repeated across the two parts.

The key 1.Qa6! (waiting) gives a flight on f3, in addition to the three squares already available to the black king. 1…Kf3 2.Qe2, 1…Kd4 2.Qc4, 1…Kxd5 2.Qc4, 1…Kf5 2.Qg6. Any move by the black knight allows 2.Qd3. A busy white queen delivers five mates in this miniature, including a nice model after 1…Kxd5.

A give-and-take key, 1.Se7!, grants Black’s king a flight on e5 but removes the set one on f5. The threat is 2.Sfg6, firing the R + S battery and recovering the e5-flight. The defence 1…Rxf5 self-pins the rook in anticipation of 2.Sfg6+? Rf4, but now 2.Sxd3 works, taking advantage of the self-pin as well as the white rook’s guard of d3. 1…Se2 opens the white bishop’s line to e5 and permits 2.Sxe2. Also, 1…Ke5 2.Re6, and 1…Bg3 2.Qxe3. Three good battery mates, including the threat. The try 1.Sh4? generates similar play to that after the key, but fails to 1…Rxd6!, while 1.Se5? entails a new threat of 2.Sfxd3, but again 1…Rxd6! refutes.

Most of Black’s moves have been provided with mating replies, e.g. 1…Sd~random 2.Sf6, and 1…Sf~random 2.Sg3. However, no mates are set for the correction moves 1…Sxf4 (2.Sf6+ Ke5) and 1…Sfxe3 (2.g7+ Kd4); in both cases White’s would-be mating moves interfere with the h8-bishop’s control of a flight. Therefore White needs to move the bishop over the critical squares, f6 and g7, to avoid the interferences. A series of tries result: 1.Be5? Sxf4! (2.Sf6+ Kxe5); 1.Bd4? – not technically a try since it’s defeated by two moves, 1…Sfxe3! (2.g7+ Kxd4) and 1…Sdxe3! (2.Qb7+ Kxd4); 1.Bc3? dxe2! (2.c3 illegal); and 1.Bb2? Sdxe3! (2.Qb7 illegal). Only the corner-to-corner 1.Ba1! (waiting) works, leading to eight variations. 1…Sd~ 2.Sf6, 1…Sdxe3 2.Qb7, 1…Sf~ 2.Sg3, 1…Sfxe3 2.g7, 1…dxe2 2.c3, 1…dxc2 2.Qxc2, 1…c3 2.cxd3, 1…fxe2/f2 2.Qh1.

White’s Q + S battery is prepared to fire when Black unpins the e6-knight, e.g. 1…Sbd6 2.Sc5 or 2.Sg5 (a dual mate, which also follows 1…Sfd6). A good key 1.Qd7! abandons the battery and threatens 2.Qd5. After 1…Sbd6, only 2.Sg5 works, avoiding 2.Sc5? which would have interfered with the a5-rook’s attack on e5. Similarly, 1…Sfd6 has only one reply, 2.Sc5, because now 2.Sg5? would cut off the h5-rook. These variations thus demonstrate dual avoidance. If either black knight tries to defends d5 directly, with 1…Sc3/Sc7/Se3/Se7, then 2.Qd3, taking advantage of a white rook’s guard on e5 again. 1…Ke5 self-pins both black knights, which is exploited by 2.Qd4, a double pin-mate. Lastly, 1…Rxe6+ 2.Qxe6.