Weekly Problems 2014-A

A good key 1.Kg5! (threat: 2.Sf6) permits three black checks, but the best variations are 1…Rd3 2.Bb3 and 1…Rxd4 2.Bc4. In both cases the black rook defends by creating a flight (on e3 and e5 respectively), but these moves also self-block, enabling the white bishop to fire the battery and self-interfere on a line of guard with impunity. The battery fires again in response to two checks, 1…Qd5+ 2.Bf5 and 1…Sxf7+ 2.Bxf7, while the third check 1…Rxg3+ is answered by 2.Sxg3.

All black moves are given set mates in the diagram. In particular, the black queen cannot move without allowing at least one of three mates on a3, e3, and c5. Some waiting move tries are 1.Rg4? Qc5!, 1.Rh5? Qg1+!, 1.Kh8? Qd4+!, and 1.Bf6? Qd4! The key 1.Rg3! (waiting) sets up an indirect battery on the third rank, so as to answer 1…Qc5 with 2.Sb2 (instead of the set 2.Rxc5). 1…Q~ 2.Sa3 or 2.Se3, 1…Ba6/Ba4 2.Sa3, 1…S~ 2.Rb4, and 1…f6/f7 2.Qe6. A mutate with one excellent change of mate.

The two harmonious solutions show an orthogonal-diagonal transformation: 1.d2 Bb1 2.Qc2 Rxc5+ 3.Kd3 Bxc2 and 1.Rc6 Ra5 2.Qb5 Bxd3+ 3.Kc5 Rxb5. In each phase, Black opens a line that is traversed by two different coloured pieces following one another – the latter manoeuvre is known as a mixed Bristol. The black king then occupies a square that has just been passed over by the two pieces (the same square vacated by Black’s initial move). Finally the white Bristol piece captures the black one to give a model mate.

White starts with 1.Bc6! to threaten 2.Ba4. The black knight has three defences that yield different mates: 1…Sc5 loses control of the R + B battery, allowing 2.Bc1; the self-block 1…Sxb4 enables the Q + R battery to fire with 2.Rc3; and 1…Sxb2 self-pins, admitting 2.Qxe3. One more variation is 1…Be8 2.Re4, another battery opening. A cleanly constructed problem with no pawns.

The clearance key 1.Bh7! (waiting) prepares for 1…axb2 2.Qg6 with the threat of 3.Qb1 – this illustrates the Turton manoeuvre (the queen steps into and then moves along the line traversed by the bishop, in the opposite direction) – 2…Ra6 3.Qxa6. Two more captures on b2 generate the variations 1…Kxb2 2.Qxc4 (waiting) Ra1 3.Qc2 or 2…Ka1 3.Qc1, and 1…Rxb2 2.Qxa3+ Ra2 3.Qc1. Also, 1…c3 2.Qf1+ Kxb2 3.Qb1. Plenty of varied play for a problem with only eight pieces.

Two black defences have set dual mates: 1…b2 2.Bb3/Bh7 and 1…exf2+ 2.Qxf2/Rxf2. The sacrificial key 1.Sd3! (waiting) removes an unprovided flight on b2 but grants a new one on d3. Accepting the sacrifice induces a castling mate: 1…Kxd3 2.0-0-0. The other lines are 1…b2 2.Sb4 (changed play), 1…exf2+ 2.Qxf2 (dual eliminated) and 1…e2 2.Rc1.

Nigel Nettheim: If the solver is aware of the impending castling, this will be easy to solve; otherwise, it would no doubt be harder. The g1-queen would have been replaced by an f1-rook if three white rooks were tolerated. Finally, when there are 8-12 units on the board solvers are of course in duty bound to drop in the word “Meredith”.
Gary Simms: My first thought was 1.Qh1, looking at the h7 check, but quickly saw that the king having the b2 escape square spoiled any thoughts like that. Then I zeroed in on solving the b2 problem and decided 1.Sd3 was the only reasonable way to stop that up. I’m surprised the location of the king and rook didn’t tip me off sooner to the castling mate. Very nice.

After the key 1.Sb5!, White threatens 2.Sxd4. The g7-knight has two defences, both interfering with the black queen: 1…Sf5 2.Qh1 and 1…Se6 2.Rd6. The former variation illustrates an idea called Gamage unpin – a black self-interference enables White’s mating move to unpin a black piece (the queen), which otherwise would have prevented the mate. The g5-rook produces three lines of play: 1…Rg6/Rg4 2.Qc1, 1…Rxb5+ 2.axb5, and 1…Rd5 2.Rc7. Lastly, 1…Qd6+ permits 2.Rxd6/Qxd6.

Nigel Nettheim: Very nice, especially 1…Sf5 2.Qh1. There is a rather unimportant dual after 1...Qd6+. I’m not sure why the e7-rook has been used instead of a c8-bishop.

Indeed, computer-testing confirms that the problem’s economy can be improved in a couple of ways. Besides replacing the rook with a white bishop on c8, we can also use a black rook on f6 instead of the queen. This means the threat of 2.Sxd4 is no longer a pin-mate, but the solution is not affected, except for a slight improvement in removing 1…Rg6 as a defence that would allow the same mate as 1…Rg4. Furthermore, the placing of the c8-bishop makes me wonder if 2.Bb7 mate could be worked into the position as an extra variation. This is in fact possible, and the setting below is the most economical way I could find to do it.

Hence after 1.Sb5!, the self-block 1…Sxd7 enables 2.Bb7. A disadvantage of the new version is that 1…Sxd7, being such a strong defence, makes the key easier to spot. But overall I think it’s worthwhile to add another variation to the problem when we actually save on the number of pieces used.

The diagram position is a complete block, with all black moves allowing immediate mates: 1…Sd~ 2.Re6 and 1…Sb~ 2.Rc5. But the set play cannot be maintained, and White’s key 1.Sf2! (waiting) changes both responses to the black defences: 1…Sd~ 2.Qe4 and 1…Sb~ 2.Qxd6. So a pair of rook mates is switched to a pair of queen mates. The fine key also grants a flight to give an added mate, 1…Kf4 2.Qe3. The try 1.Sg5? would yield similar changed play but not provide for 1…Kf4!

Nigel Nettheim: An elegant change-mate problem. There is nothing I can add, because “all change here” (taken from an announcement used in the British rail system) has been said more than enough times already!

The give-and-take key 1.Be3! entails a short threat, 2.Qf3. If 1…Kxe3 then 2.Qxb4 forcing 2…Ke2 3.Qe1. If 1…Kd5 then 2.Qf7+ leading to 2…Kd6 3.Qd7 or 2…Ke4 3.Qf3. The first two mating configurations are charming chameleon echoes. The original version of the problem has a white pawn on c6 instead of the black pawn on b7 (either pawn prevents a ruinous dual, 1…Kd5 2.Qf6 threatening 3.Qc6). But such a white pawn would guard the mating queen on d7 in the second main variation; the e5-knight is thus made redundant in the final position and the echo mates become less convincing.

Three close tries are 1.Rcb8? (threat: 2.Rxb6) a3!, 1.Qe4? (2.Qd5/Qe5) a3!, and 1.Qg8? (2.Qd5/Qxc4) Sf5+! The set variation 1…c3 2.Qd3 is discarded by the sacrificial key 1.Qd3!, which threatens 2.Qxc4. 1…cxd3 activates the white pawn to mate on the same square as the threat: 2.c4. The black knight has two defences that provoke a pair of queen mates: 1…Sc6 2.Qd5 and 1…Sf5+ 2.Sxf5. Finally, 1…bxa5 opens the b-file for 2.Rcb8.

Nigel Nettheim: 1.Qd3! is a brilliant key. A number of tries, though 1…a3 is a strong defence.

A nice key, 1.Sc3!, concedes a flight on d4 and threatens 2.Qxb4. A ‘random’ move by the b4-knight, 1…S~, opens the b-file and permits 2.Qb6. The correction move 1…Sd5!? prevents 2.Qb6 but commits a new error of self-block, allowing the c3-knight to interfere with the g2-bishop: 2.Se4. Taking the flight does not disable the threat: 1…Kd4 2.Qxb4, while capturing the key-piece gives 1…Bxc3 2.Qxc3. Another self-blocking variation is 1…Rd4 2.Rb5, and if 1…Ra4 then 2.Sxa4. This problem competed in a tourney for pawnless positions, and the judge Alex Goldstein commented that it was “a clear candidate for the prizes… but the dual 1…Sa6 2.Qb6 or 2.Sa4 ruined its chances”.

Black has just one legal move in the diagram, and surprisingly the only way to deal with it is 1.Rg7! (waiting), which gives the black king two more flights. 1…Kc4 is met by 2.Rg2 Kd3 3.Qd4. If 1…Ke4 then 2.Qe2 forces 2…Kxf5 3.Qf3. And 1…Kxe3 enables 2.Rg3+ Ke4/Kf4 3.Qe5. A pleasant miniature displaying a variety of mating nets.

The key 1.Rf6! threatens 2.Rf4 (not 1.Rg6? because of 1…Bh3!). The half-pin arrangement on the fourth rank means that when either Black’s queen or rook moves off the line, the other becomes pinned – a weakness that White exploits in the mate. 1…Qxa6 2.Qxb2, 1…Qc6 2.Sb3, and 1…Rb6 2.Qc5. Appropriately, the three thematic defences all pin the white rook, adding to the unity of the variations. Two secondary lines of play are 1…Qxd3 2.Qxd3 and 1…f2 2.Se2.

Dennis Hale: I certainly enjoyed the problem with its half-pin feature. The two queen defences and the one rook defence each self-pin and pin – I like the way the three associated white mating moves are differentiated. The key is not one of the problem's strengths. The squares e3, e4, and e5 in the black king’s field are each doubly attacked, and this tends to suggest the key is a move by the e6-rook.

The surprising key 1.Qd7! (waiting) grants the black king access to e4. Taking the flight results in a triple pin-mate: 1…Kxe4 2.Qxe6. When Black moves one of the three pieces that were pinned in the first variation, a line is opened and White regains control of e4: 1…R~ 2.Qd6, 1…Sd~ 2.Sf3, and 1…Sf~ 2.Sd3. Lastly 1…B~ enables 2.Qxd4, guarding the flight directly.

Dennis Hale: The key had me bamboozled for much longer than I normally take. The variation 1…Kxe4 2.Qxe6 is first class. Black's move self-pins the three defenders of e6. Bravo J. Willis! Your idea still furrows the brow as it would have some 135 years ago.

The strong defence 1…Sxf5 without a set mate provides a hint for the key, 1.Qd3! (threat: 2.Qe3), which answers 1…Sxf5 with 2.Qxf5. The well-used white queen gives four other mates: 1…bxc5 2.Qa6 (a switchback), 1…Rxe2+ 2.Qxe2, 1…Sc4 2.Qxd5, and 1…d4 2.Qe4. The white knight gets unpinned twice with 1…Bd2 2.Sd4 and 1…Bf2 2.Sf4. And including 1…Sf7 2.Bxf7 the problem delivers a total of eight variations.

Dennis Hale: Most pleasing are the two pairs of variations, (1) 1…bxc5 2.Qa6 and 1…Rxe2+ 2.Qxe2; (2) 1…Bd2 2.Sd4 and 1…Bf2 2.Sf4. My heart sings when I am interacting with a well-constructed two-mover!

The eye-catching diagram has just six pieces that are nicely spread out on the board. The waiting key 1.Rf7! preserves the set play for 1…Kd6 with 2.Bd4 Kd5 3.Rd7, while providing for 1…Ke5 with 2.Bc5 Kd5 3.Rf5. Both variations end with model mates, in which the five pieces form first a straight line, and then a cross.

Dennis Hale: Two pretty, closely-related variations.

Except for 1…Qxh1, every black move has been given a set mate, e.g. 1…f4 2.Qxe4, and 1…Qf3 2.Qxf3. The excellent key 1.Rg2 (waiting) unpins the black queen, and its ‘random’ move 1…Q~ allows 2.Rgd2. Four correction moves by the queen disable 2.Rgd2 but permit new white responses: 1…Qxc2+ 2.Rxc2, 1…Qe2 2.Rxe2, 1…Qf3 2.Bxf3 (a changed mate), and 1…Qxg2 2.Qxg2. Another change from the set play is 1…f4 2.Rg5, re-pinning the queen. Two more variations, 1…S~ 2.Rgd2 and 1…d6 2.Sxb6, round off a good traditional work.

Dennis Hale: I like the unpinning key, and my favourite variation is 1…f4 2.Rg5.

After 1.e4! to cut off the black queen, White threatens 2.Sf5. Three captures of the key-pawn are answered by different queen mates: 1…dxe3 e.p. 2.Qe5, 1…fxe3 e.p. 2.Qh2, and 1…Qxe4 2.Qa3. The en passant captures produce some curious line effects; the vanishing white pawn means that the black queen regains control of f5, but a black pawn’s arrival on e3 interferes with the rook on the e-file and the queen on the third rank. A fourth queen mate occurs with 1…Qh3 2.Qxd4, while one further queen defence 1…Qxb5 enables 2.Bxb5. Two variations involve unpinning the e6-pawn: 1…Sf6 2.Bc7 and 1…Rxg6 (or 1…Rf7) 2.Sf7. Lastly, the self-interference 1…Se3 allows 2.e5.

Dennis Hale: The key is excellent, and the three long-range queen mating moves (after the captures of the e4-pawn) are a feature of the problem.

Set play is provided for all black moves, including 1…S~ 2.Qg7 and 1…d3 2.Qa1. White has no simple waiting move available, however, e.g. 1.Kb2? d3!, 1.Ka3? cxb4+, or 1.Kb3? c4+! The key 1.Qf2! (waiting) changes the black knight variations to 1…S~ 2.Qxh4 and 1…Sxf4 2.Qxf4, while a concurrent change occurs with 1…d3 2.Qb2 – so this problem is a mutate. The remaining play is as set: 1…Bf7 2.Bg7, 1…Bg6 2.Sxd7, 1…Bh~ 2.Bg5, 1…c4/cxb4 2.Qxd4, and 1…cxd5 2.Sxd5.

Dennis Hale: I particularly like the pair of self-blocking variations, 1…Bf7 2.Bg7 and 1…Bg6 2.Sxd7.

The key 1.Bg7! covers h6 and h8, so as to free the white knights from guarding these squares. The only threat is 2.f7 though, aiming for 3.Sf6. Black has three moves that prepare to defend f6, but they allow the g6-knight to be activated in different ways. 1…Rb3 permits 2.Kf7 followed by 3.Sf8, since 2…Ba2 no longer checks. If 1…c2 (intending 2…Bc3), the b1-bishop is cut off and White answers with 2.S6e7; now 2…f4 is ineffective against 3.Bg6 (here the g6-knight must choose e7 to disable 2…Bb4+). Finally, 1…Sf2 interferes with the f1-rook and White continues with 2.Sf4 and 3.Bg6, as 2…Rxf4 is ruled out. Three refined variations based on black self-interference, with another connecting feature: all white second moves (including the threat) are motivated by square-vacation.

White starts with an active sacrifice of the queen, 1.Qg4! (waiting), which completes the block by guarding f5 and obstructing the g5-pawn. Three black pawn captures enable a variety of mates: 1…hxg4 2.Sxg4, 1…gxh4 2.Qxg6, and 1…gxf5 2.Qxf5. The self-block 1…Bg7 permits 2.Be7, while the remaining defences are unguards: 1…Sh~ 2.Qxg5, 1…Sb~ 2.Sd7, and 1…c6/c5 2.Rd6. The subtle try 1.Rf4? (waiting) produces similar play – with these differences: 1…gxf5 2.Rxf5, 1…h4 2.Sg4, and 1…gxf4 2.Qxg6 – but it is refuted by 1…g4!

Dennis Hale: I like the sacrificial key. The try 1.Rd7? (threatening 2.Rf7) is defeated by 1…Sxd7!
Nigel Nettheim: The d2-rook and c7-pawn take part in a minor battle; they have been added to avoid the cook 1.Sg4+ and 2.Qb2. The cook could otherwise have been avoided simply by adding a white pawn in one of several possible positions such as f2, although the rook-and-pawn method has the advantage of adding a variation.

After the flight-giving key 1.Sb3!, White threatens the battery mate 2.Rxc5. If Black takes the flight, White fires the battery again with 1…Kxe2 2.Re4. All moves by the d5-knight defend by opening a line for the g8-bishop, and a random placement 1…S5~ allows 2.Qe4. Three correction moves by the knight disable 2.Qe4 but provoke new mates: 1…S5c3 2.Rd4, 1…S5e3 2.Rd2, and 1…Sf6 2.Sxf4. The d1-knight has three defences, though two result in the same play as that created by the first knight: 1…S1c3 2.Rd4, 1…S1e3 2.Rd2, and 1…Sb2 2.Sc1. This last variation, in which a black knight interferes with a line-piece and enables a knight mate, nicely matches 1…Sf6 2.Sxf4.

Nigel Nettheim: The play is excellent, especially 1…Sb2 2.Sc1 which distinguishes the key from the try 1.Sf3?

The thematic key 1.Sxf5! self-pins the knight and threatens 2.Qe4. Black’s h5-knight sets off two variations involving sophisticated line play and dual avoidance. 1…Sf6 unpins the key-piece, which apparently has a choice of two mating moves. But the black defence has also cut off the h6-rook, and if 2.Se7? – interfering with the e8-rook – then the king would escape to e6, meaning only 2.Se3 works. 1…Sf4 again unpins the white knight, but now the h4-queen is obstructed and White must avoid 2.Se3, since that would interfere with the g1-bishop and permit 2…Kxd4; so 2.Se7 is forced. The by-play consists of two pairs of loosely related variations: 1…Sc3/Sd6 (unguard) 2.Rd6, 1…Sxd4 (square clearance) 2.Qxd4, 1…Qg4 (unguard) 2.Bxf7, and 1…Qxe5 (square clearance) 2.Rxe5.

Nigel Nettheim: The f5-pawn is a strong defender and is eliminated, even at the cost of self-pinning. 1...Sh~ leads nicely to two different mates with the key-piece, which has regained its freedom. The c6-bishop, rather than a c6-pawn, prevents the cook 1.Sxb5.

The diagram is solved by 1…Rxg4 2.Qg6 Re4 3.g4 Rf4, and part (b) by 1…Rxd5 2.Bd3 Rf5 3.d5 Re5. In both solutions, the white rook captures a pawn and performs a switchback. The aim of the each capture is to clear the square for another black pawn, which must move to unguard the mating square. The white rook then mates by swinging to the opposite direction once more. Good analogy between the two phases (including the black self-blocks). Note how the black queen is used in part (b) to prevent the alternative move 2…Rxg5 from working.

Nigel Nettheim: Very enjoyable to solve.

Set mates have been prepared for all black moves in the diagram: 1…Sc~ 2.Se7 and 1…Sd~ 2.Sf6. But White has no waiting move that could preserve these variations. A good key 1.Sf7! (waiting) gives the black king a flight, which leads to 1…Kxe6 2.Bc4, a model mate. The set play is completely replaced by 1…Sc~ 2.Rd6 and 1…Sd~ 2.Re5. This lovely mutate was sent to me by the UK expert Michael McDowell, who found it while researching in the library of the British Chess Problem Society.

Nigel Nettheim: A fine sacrifice and a complete mutate. Economical, too: the b6-pawn neatly prevents a simple waiting-move key with the b5-bishop moving on its long diagonal.
Dennis Hale: I like the light setting coupled with the sacrificial key. A pretty little problem.

The key 1.d4! prepares to fire the R + S battery with 2.Sd3 (which also opens the indirect B + S battery to cover the flight on g5). In response to various black defences, the f4-knight delivers seven more mates with each of its possible moves, to produce a very fine knight-tour. 1…Qxd5 2.Sxd5, 1…Sxe6 2.Sxe6, 1…Bxg6 2.Sxg6, 1…Sxh5 2.Sxh5, 1…Rxh3+ 2.Sxh3, 1…Rg/Rhxg2 2.Sxg2, and 1…Sxe2 2.Sxe2. The flight-taking 1…Kg5 doesn’t disable the threat 2.Sd3, but with the king mated on a different square, this may be regarded as a distinct variation that makes the knight-tour even more complete! There’s one secondary line, 1…f5 2.Qd8.

Dennis Hale: This is a beautifully constructed problem. The 1…f5 2.Qd8 variation makes clear why the try 1.e7? (threat: 2.Se6) is defeated by 1…f5! – delightful.
Nigel Nettheim: The f4-horse (the one with the Whitehead) is chafing at the bit to discover mate, muzzled by its own pawns. The position is legal, although that is not obvious. Six captures were made with white pawns, accounting for a black bishop and five pawns. It turns out that Black could make the required promotions, assisted by the capture of a white rook.