Weekly Problems 2012-B

White has two natural moves to d6 but they are refuted if played prematurely: 1.Bxd6? threatens 2.Bc7 but 1…Rf7!, and 1.Sxd6? threatens 2.Sb7 but 1…Re7! The key 1.Bb4!, with the short threat of 2.Ba5, aims to decoy the black rooks to the a-file. 1…Ra1 2.Bxd6 (3.Bc7) Re7 3.Bxe7, and 1…Ra2 2.Sxd6 (3.Sb7) Rf7 3.Sxf7 (2…Ke7 3.Sb7/Sf7). So the right capture on d6 ensures that White can deal with the remaining black rook defence on the 7th rank. Also 1…Re7 or 1…Rf7 2.Ba5+ Rc7 3.Bxc7.

This miniature is solved by 1.c4 Kc7 2.Ke7 Kb6 3.Kd6 Ka5 4.Kc5 b3 5.d6 b4. The parallel king marches are complemented by the farseeing square-vacation 1.c4, and the crossing of the critical square d6 before it’s self-blocked. But the main point of this appealing helpmate is the subtle 4…b3! to avoid an en passant capture, as well as the ideal-mate finish.

Except for the flight-taking 1…Kf6, every black move has been provided with a set mate. A good waiting key, 1.e4!, grants a second flight on d4. Now both king moves are followed by the same white mating response, though the effects are quite different: the pin-mate 1…Kf6 2.e5 and the battery shut-off 1…Kd4 2.e5 (not 2.exf5?). Any bishop move, 1…B~, permits another battery to fire, 2.exf5 (changed from the set dual, 2.Re6/Sf7). The g8-rook yields four distinct variations: 1…Rg~ 2.g8=Q, 1…Rf8 2.gxf8=Q, 1…Rxh8 2.gxh8=Q, and 1…Rxg7 2.Bxg7. Lastly 1…fxe4 2.Qxe4, 1…Sc3+ 2.Qxc3, and 1…Sd2 2.Qxa1.

The two solutions, 1.Ka7 2.Qa8 3.Bc8 4.Ba6 5.Rb7 Sxc6 and 1.Qb7 2.Bc8 3.Rd7 4.Kc7 5.Sb8 Se6, have dissimilar play though they both end with an ideal mate. The more interesting second phase shows a follow-the-leader sequence involving all five black pieces.

The flight-giving key 1.Ba6! threatens 2.Sc7. Black has four defences on c5 that are self-pins, but which anticipate the unpinning effect of the threat. In each case White takes advantage of the self-pin to mate in another way: 1…Qxc5 2.Se3, 1…Rxc5 2.Qf7, 1…Sdxc5 2.Sxc3, and 1…Sexc5 2.Sd4. Black’s self-pinning moves in such a scheme are known as Schiffmann defences, and the four thematic variations rendered here equal the record. Also, 1…Sxd6 2.Sxd6, and 1…Kd5 2.Sc7.

Ian Shanahan: Beautiful flight-giving key leading to a 4-fold Schiffman – the record. A superb problem!

The square-vacating key 1.Bb8! threatens 2.Sc7. Since the threat removes the white bishop’s control of d6, any move by the rook from that square will defend by creating a potential flight. 1…Rd4 2.Qxe5, 1…Rd5 2.Qf5, 1…Rd7 2.Bf7, 1…Rd8 2.exd8=S, 1…Rc6 2.Qxc6, and 1…Rb6/Ra6 2.Qc4. So a single rook generates six distinct variations, without any duals. There’s by-play with 1…Sf8+ 2.exf8=S.

The black queen is defending against two knight mates on d5 and g2, and almost all initial black moves will relinquish control of one of the two squares. Only 1…Qg5! retains the queen’s focus on both mating squares and it would defeat a simple waiting move like 1.Rb3? The surprising key, 1.Qg2! (waiting), grants a flight and changes one of the focal mates. 1…Qf7 (or to e6, etc.) 2.Qg5, 1…Qg7 (or to g6, etc.) 2.Sd5, 1…Sfg6/Shg6 2.Qg5, 1…Se6/Sf7 2.Sd5, 1…Qxg2+ 2.Sxg2, and 1…Kxe3 2.Qd2.

The black king’s final square seems likely to be the congested d5, especially since a bishop mate will cover the e6 flight. After 1.Bxe4 Bxc4, the players coordinate to activate the c2-pawn, with the aim of using it to control c5 – 2.Bd5 Ba2 3.Bb3 cxb3 4.Kd5 b4. Nice switchbacks by the two bishops; the white bishop also shows critical play by crossing over the b3-square (twice), before it’s occupied for an interference and vacated again for the battery mate.

Two prominent black checks are already provided with white responses: 1…Rxd6+ 2.Sxd6 and 1…Bxd2+ 2.Sxd2. This set play is unexpectedly changed by the key, 1.Sc5!, which threatens 2.Qf4. The extra guard on b3 frees the d3-rook to answer the checks with battery mates: 1…Rxd6+ 2.Rxd6 and 1…Bxd2+ 2.Rxd2. There is plenty of good by-play featuring two pairs of queen and rook mates: 1…Bf2/Bg3 2.Qc1, 1…Sg6 2.Qxf7, 1…Rxc5 2.Rxc5, and 1…Sb5 2.Ra4.

White has many rook tries that fail to one defence only, e.g. 1.Rd1? Bf6!, 1.Rb1? Be5!, 1.Rh1? (threat: 2.Rh8+) Ba3!, 1.Ra7? Ba3!, and 1.Re7? Ba3! It’s the latter try that points to the key, 1.Ra1! (2.Ra8), as after 1…Bxa1 the decoyed bishop cannot stop 2.Re7 and 3.Re8. Also 1…Ba3 2.Rxa3 Kh8 3.Ra8, 1…Be5 2.Ra8+ Bb8 3.Rxb8, and 1…Bf6 2.Ra8+ Bd8 3.Rxd8.

The key 1.f4! (threat: 2.f5) entails a triple-sacrifice of the pawn, while conceding a flight on d6 as well. The two main variations show a curious effect possible only with en passant captures, 1…exf3 e.p. 2.Bf5 and 1…gxf3 e.p. 2.Rxe4. In each case Black unblocks two vital white lines simultaneously – one for the mating piece, initially blocked by Black (on e4/g4), and the other for the g3-bishop, initially blocked by White (on f4). 1…Bxf4 is another line-opening, which enables 2.Qd5. Lastly, 1…Kxd6 2.f5 sees the threat working as a battery mate, and 1…f5 2.Rh6.

Set play is provided for all black moves: 1…Sc~ 2.Re7 (threat: 3.Be4) Kg6 3.Be4, 1…Sf7 2.Rg6 (3.Rf6) Kxg6 3.Be4, and 1…Sg6 2.Rf7. The waiting key 1.Rg3! changes two of the variations: 1…Sc~ 2.Be4+ Kxe4 3.Sxd6, and 1…Sg6 2.Rg4 (3.Be4/e4) hxg4 3.hxg4, 2…Sf4 3.e4, while 1…Sf7 2.Rg6 (3.Rf6) Kxg6 3.Be4 is as set. The short mate in one of the set lines is a slight flaw, but this is a difficult mutate where every white second move in the post-key play is an active sacrifice.

A fine key, 1.Re6! (threat: 2.Sg7), sacrifices the rook to four black pieces: 1…Bxe6 2.e4, 1…Sxe6 2.Qb1, 1…fxe6 2.Qh7 and 1…Kxe6 2.Bg4. In the first two variations, White exploits the half-pin arrangement on the fifth rank to produce a couple of pin-mates. Thus two ideas are neatly combined: a complete half-pin and multiple black defences on the same square. Also, 1…Qxe8 2.Qxd5.

A good key 1.e4! (waiting) offers another flight on d4 and unexpectedly obstructs the B + R battery. 1…Kc4 2.Qc3, 1…Kxd4 2.Qd5, 1…Kxe4 2.Rg4, and 1…Ke2 2.Qxa6. Four black king moves are answered distinctively, including (a little unusually) three flights to the same rank.

Black’s last move to reach the diagram wasn’t …Re8-d8 or …Re7-d7, because either would mean Black was to play while checking White. And it wasn’t …Kb8-c8 because the white bishop couldn’t have delivered the check. That leaves …0-0-0 as Black’s only possible last move. If Black has just castled, that means the black king previously had not moved from e8, and the original rook from h8 couldn’t have escaped from the top-right corner. That implies the d7-rook is a promoted piece. Regardless of where Black promoted, the new rook must have visited d1, e1, or f1 in order to leave the first rank. In all cases the rook must have displaced the white king, either by attacking or occupying e1. So we have proved that the white king has moved before, and now cannot castle.

George Meldrum: Love this week’s Van Der Klauw problem. Went from “position impossible”, to castling “yes”, to castling “no”.

White and black half-pins are combined in 1.S6g7 d8=Q+ 2.Ke6 Sg5 and 1.Bg7 Se5 2.Kd6 d8=Q, and rendered in an economical Meredith setting. The white half-pin arrangement on the 7th rank prompts Black’s unpinning moves to g7. Black’s half-pin on the 6th rank is anticipatory in that the king only walks onto the thematic line during play, and this leads to a pair of pin-mates.

No mate is set for the black king’s flight to f6, and the key 1.Qh5! (threat: 2.Qf7) provides for it with 1…Kxf6 2.Qh6. The thematic black rook – appropriately unpinned by the key – defends by creating a potential flight on f5. A random rook move 1…R~ (including 1…Rxh5) opens the f-file and permits 2.Rf3, a battery mate that covers f5 and f6. Three correction moves disable 2.Rf3 but commit new errors: 1…Rf4 2.Qxe5 and 1…Rf2 2.Rxb6 show self-interferences, while 1…Rxf6 is a self-block that forces 2.Rd3.

Some pieces on their home squares are not what they seem… 1.Sf3 Sc6 2.Se5 Sd4 3.Sxd7 Sf3+ 4.exf3 Sf6 5.Bb5 Sxd7 6.d3 f6 7.Bh6 gxh6 8.Sc3 Bg7 9.Se2 0-0 10.Sg1 Sb8. The paradoxical Sibling theme is effected twice, with the original knights from g1 and b8 getting sacrificed and replaced by their counterparts or “sibling” pieces.

White has two thematic tries, 1.Kd8? and 1.Kd6? (both with the double threats of 2.Be6 and 2.Rc7), and they are refuted by 1…Bb6+! and 1…Bb8+! respectively. A good key 1.Kc7! gives a flight and entails one threat only: 2.Be6+ Ke7 3.d6. Now both black bishop checks are playable but White has an answer to each: 1…Bb6+ 2.Kd6 (3.Be6) Bc7+ 3.Rxc7, and 1…Bb8+ 2.Kd8 (3.Be6) Bc7+ 3.Rxc7. Clever Roman decoys of the black bishop to a square where it’s liable to be captured. Also, 1…Ke7 2.d6+ Kf7 3.Be6.

Most of Black’s moves have set mates prepared, except for 1…e3 and 1…Qxc3, and the waiting key 1.e3! completes the block. Random moves by the black queen unguard e5: 1…Q~ 2.Se5. The queen has four corrections that prevent this knight mate, but all commit the error of self-block: 1…Qb5 2.Qxd4, 1…Qc5 2.Sd2, 1…Qd5 2.Qa4, and 1…Qxc3 2.Rxd4. Three pawn defences continue the accurate play – 1…dxc3 2.Rd4, 1…dxe3 2.Rxe3, and 1…exd3 2.cxd3, but 1…b5 allows multiple mates: 2.Se5/Qxd4/Qe6/Qf7. This unfortunate dual can be avoided by replacing the black pawn on b6 with a white one.

This miniature is solved by the waiting key 1.Bc5!, after which the black king has two flights. 1…Kxd5 leads to 2.Se3+ Kxc5 3.Qb6 (an ideal mate), and 2…Ke5 3.Qf5, while 1…Kf4 enables 2.Sf2 Ke5 3.Qg5 (a model mate), and 2…Kf3 3.Qg4. A fine example of the Bohemian style of composition, which aims for a variety of elegant mating nets.

The key is the striking queen sacrifice 1.Qe5!, threatening the pin-mate 2.Qf4. Captures of the queen open lines for the white bishop and permit another two pin-mates: 1…dxe5 2.Bxc5 and 1…fxe5 2.Bxg5. Two knight defences result in yet more pin-mates, now based on the immobilised e4-bishop: 1…Sxe2 2.Rxd3 and 1…Sxe6/Sh3 2.Rxf3. The problem’s economy could be improved by replacing the c5-queen and the e4-bishop with black pawns.

In this neat miniature, White must arrange the pieces to accomplish two related goals simultaneously: (1) confine the white king for the eventual mate, and (2) restrict Black’s possible play to a move that gives mate. The only configuration that works is to place the white king on f1, with the other white pieces on g1, f2, and e2 to variously self-block and control the black king. 1.e4 2.e5 3.e6 4.e7 5.e8=R 6.Rg8 7.Rg1 8.Kf1 9.Be2 10.c4 11.c5 12.c6 13.c7 14.c8=S 15.Sd6 16.Se4 17.Sf2, and now Rxg1 mate is forced.

The give-and-take key 1.Sd4! (threat: 2.Ke5) removes an unprovided flight on b5 but grants a new one on d4. The highly thematic key also unpins the black knight, which is freed to give multiple discovered checks. In doing so the knight allows d4 to be guarded by the g4-rook, and this enables White’s royal battery to fire in a variety of ways. A random check, 1…S~+, is followed by the dual 2.Kd7/Kf5. Two correction moves generate new battery mates – 1…Sxf6+ 2.Kxf6 and 1…Sxd6+ 2.Kxd6, while the dual mates are separated in the variations, 1…Sxc5+ 2.Kf5 and 1…Sg3+ 2.Kd7. If Black takes the flight, White answers with an indirect battery mate: 1…Kxd4 2.Sb3.

The surprising withdrawal key 1.Kb2! vacates c3 to threaten 2.Qc3. Two flights are offered to the black king: 1…Kd4 2.Qe5 (a double pin-mate) and 1…Kxb4 2.Qa3 (this line explains why 1.Kc2? or 1.Kd2? would fail). 1…Se5/Se3 opens the rank for the h4-rook, permitting 2.Qe3, and the unguard 1…Qxf7 allows the white queen to gain control of the two flights with 2.Qxd6.