Weekly Problems 2016-A

The key 1.Qf8! prepares for an indirect battery mate, 2.Sb5, in which the opened queen-line to c5 compensates for the closure of the a5-rook’s line to the same square. Two pawn-takes-pawn defences are exploited by White as square-clearances: 1…exf2 2.Bxf2 and 1…dxc6 2.Sxc6. A couple of black moves open lines for white pieces which traverse them to give mate on the long diagonal: 1…Sxd6 2.Qf6 and 1…Rb2 2.Bxc3. The a2-bishop defends twice and is captured by the c5-rook each time: 1…Bc4 2.Rxc4 and 1…Bd5 2.Rxd5. Three corresponding pairs of variations are thereby presented. Moreover, co-composer Andy Sag claims a fourth pair of related mates in that 1…Sxf5+ 2.Sxf5 and the threat of 2.Sb5 share the same mating piece. A debatable point, but either way this is a splendid problem that shows an uncommon theme.

Andy Sag: To complete the Christmas “pair” tree, we have two tries defeated by the black bishop pair: 1.Qe8? (2.Qe4/Qxe3/fxe3) Be6! and 1.Bxd2? (2.Bxc3/Bxe3/fxe3) Bxd2!
Jacob Hoover: This was a pretty nice problem, but I feel the solution was a little too obvious in that the queen is the only white unit not doing anything in the diagrammed position.

Set mates are arranged for all possible black moves in the initial position, but White has no simple waiting move available, e.g. 1.Kh4? Sf3+! The key 1.Bg5! (waiting) unguards e5 so that after 1…e5 the set mate 2.fxe5 no longer works, but now with the queen shielded from the black rook, White can afford to unpin the latter with 2.f5 – a changed battery mate. The key also frees the f7-pawn to add the variations 1…f6 2.Qxe6 and 1…f5 2.Qe2, both of which require the key-bishop to take over the control of f4. The rest of the play is as set and also dual-free: 1…Sxb3/Sf3 2.Re2, 1…Sf1/Sc4 2.Rc4, 1…Sb~ 2.Sxd2, and 1…d5 2.Sc5. More tries that aim to maintain the block include 1.Ra2? Sf1 2.Ra4, but 1…Sc4!; 1.Rc5? Sd~ 2.Qf3/Rc4, but 1…d5!; 1.Qg5? e5! and 1.Be5? f6!

In part (a), a bishop mate cannot be organised because there are not enough black pieces in the king’s vicinity to block all of its flights. Instead, White aims for a queen-promotion mate on c8, which requires Black to sacrifice a piece on c7. The job goes to the b2-pawn, and it must promote to a queen in order to reach c7 in time. Remarkably though, Black begins with 1.e5, the sole waiting move that won’t disrupt the plan. 1…Bc2 2.b1=Q+ Bd1 3.Qh7 Bb3 4.Qc7 bxc7 5.b6 c8=Q. Part (b) has the b2-pawn shifted to c5, where it blocks a flight. Now a bishop mate along the long diagonal is possible, but a white queen promotion is still necessary to cover all of the flights. This time White clears a path for the pawn by removing the one on b7. Meanwhile, the black king needs to get out of the way of not only the white bishop but also the black one, to allow the latter to self-block on d7. 1.Kd5 Be4+ 2.Kc4 Bxb7 3.Bd7 Ba8 4.Kb5 b7 5.Kc6 b8=Q. A battery mate completes an appealing sequence in which the black king performs a rundlauf, or round-trip back to its original square.

Andy Sag: What makes part (b) so diabolically difficult is that the king goes round a circle and ends up where it started. The e6-pawn does not participate directly but provides the only first move in part (a) that does not mess up the setting, and in part (b) prevents a cook in which the black bishop gets to d7 via e6.

The key 1.Rh3! removes a flight on f3 but grants another one on f5. The threat is 2.Qg5+ Kxh3 3.Qg3, against which Black has six defences that lead to three pairs of interrelated variations. 1…f1=S frees the b5-knight since Black no longer has …f1=Q+ available; now 2.Sbd6 threatens 3.Qh4; 2…Bf6 3.Sxf6 and 2…Sg3 3.Rxg3. Another pawn defence, 1…f6, by obstructing …Bf6, allows similar play by the other white knight: 2.Sed6 and there’s no stopping 3.Qh4. Black commits the error of a distant self-block in 1…Sxe4 2.Qh5+ Kf4 3.Rf3 and again in 1…Be5 2.Qh5+ Kf4 3.Qf3, with a different mate on f3 in each case. And two unguarding moves enable White to check with the e4-knight, followed by a rook switchback mate: 1…Se2 2.Sxf2+ Kf5 3.Rh5 and 1…Bf6 2.Sxf6+ Kf5 3.Rh5. If Black takes the flight with 1…Kf5, then 2.Qg5+ Kxe4 3.Re3. This great problem shows complete accuracy of play in its seven full-length variations.

Jacob Hoover: The additional variation 1…Kf5 2.Qg5+ Kxe4 3.Re3 gives an echo mate with respect to 1…Sxe4 2.Qh5+ Kf4 3.Rf3. So four pairs of similarly-themed variations exist! This was a nice one, which kept me stumped for two days.
Andy Sag: “Give-and-take” key. The a2-rook and b1-bishop appear to be redundant and could be removed, reducing the setting to thirteen pieces.

Most of Black’s available moves are provided with set mates, with the exceptions of 1…Qc3 and 1…Qc2. The waiting try 1.d4? handles 1…Qc3 by shutting the long diagonal, so that 2.Qh6 cannot be countered by the unpinned black queen. But 1…Qc2! refutes the try. The key 1.d3! (waiting) closes two lines in anticipation of the black queen’s release. Now 1…Qc3 is answered by the changed mate 2.Qh1 (2…Qf3 prevented), while 1…Qc2 allows the transferred mate, 2.Qh6 (2…Qg6 prevented). The remaining variations are as set: 1…Qc4+ 2.Qxc4, 1…Qxc1 2.Rxc1, 1…b5 2.Qxc5, and 1…Kb5 2.Bd7 (pin-mate).

Jacob Hoover: The “Girl Power” theme strikes again (four out of the six variations feature queen mates)!

The fairly easy key 1.e4! threatens 2.Bd5. Black has two en passant capture defences that involve some curious line effects. 1…dxe3 e.p. interferes with the f2-bishop and permits 2.Sd4; this illustrates the only way by which a line-closing interference can result from a capturing move, possible since the capture square e3 is initially empty. 1…fxe3 e.p. likewise cuts off the bishop but the removal of the key-pawn has opened the fourth rank for the black queen, which stops the knight mate; White instead plays 2.Qxc7, exploiting the opening of the diagonal controlled by the g3-bishop. En passant play occurs in two more variations, 1…d5 2.cxd6 e.p. and 1…b5+ 2.cxb6 e.p., in which the thematic captures are executed by White to deliver two battery mates.

Andy Sag: En passant theme – very cute! We could add a black knight on h7 for a fifth variation, 1…Sf6 2.Se7.
Jacob Hoover: Quite the interesting idea, and it was an idea very clearly demonstrated, with no by-play to distract the solver.

Random moves by the d7-knight would threaten 2.Qd8, but they are defeated by 1…Bd6/Be7. The key 1.Sc5! ensures that the bishop refutations are not playable. Now Black has four defences against the threat, including three flight-taking moves, and they are all answered by battery mates delivered by the f7-knight. 1…Sxd5/Sd7 (enabling the a5-bishop to guard d8) 2.Sd6, 1…Ke7 2.Sxh8, 1…Kf8 2.Sxg5, and 1…0-0 2.Sxh6. Remarkably, the knight fires the batteries from four different directions, i.e. it activates four white line-pieces in turn – a maximum task achievement.

Andy Sag: The key adds two flights, including castling, and leaves the white queen en prise.
Jacob Hoover: Nice one, not only due to the battery-play theme, but also because there’s no distracting by-play.

This two-mover was selected from Chess Problems: Tasks and Records, a book by Sir Jeremy Morse. Sadly, this British composer and world authority on task problems has passed away, at the age of 87. A comprehensive article on the Life and Work of Sir Jeremy Morse can be found on the British Chess Problem Society site. 

In the initial position, set play is arranged for every possible black move. 1…Bd~ 2.Sh7 (threat: 3.Bxg5) Bxd2 3.Qh1 and 1…Be~ 2.Bxf7 (threat: 3.Qxg6) Bc2 3.Qh1. White takes advantage of the fact that Black cannot afford to move both bishops without permitting Qh1 mate. But White has no way of preserving these variations, e.g. 1.Kc7? Bxd2! 2.Bxf7 Bf4+. (Incidentally, can you work out why 1.Ke8 isn’t technically a try? That is, what are the various black moves that would defeat it?) The key 1.Sd7! (waiting) abandons the set play and replaces it with 1…Bd~ 2.Bb4 (threat: 3.Bf8) Bxb4 3.Qh1 and 1…Be~ 2.Se5 (threat: 3.Sxf7) Bb3 3.Qh1. This is a three-move mutate, an uncommon form in which the late William Whyatt excelled.

Jacob Hoover: A very clever three-mover mutate.
Andy Sag: A tale of two bishops!

The diagram position is solved by 1.Bd5 Be3 2.Kd3 Bf5. Black’s bishop move to d5 interferes with the white rook and gives the black king access to d3. White’s bishop move to e3 cuts off the black rook (besides covering two flights), an interference required for the eventual pin-mate delivered by the other white bishop. Position (b) has a white rook starting on c8, and this changes the solution to 1.Re3 Rd5 2.Kf4 Rxc4. Here Black’s rook move to e3 closes a white bishop line and enables the black king to reach f4. White’s rook move to d5 interferes with the black bishop (besides controlling the fifth rank), ensuring that Black cannot stop the pin-mate given by the other white rook. Two fabulous pairs of mutual interference between pieces of different colours, or a double bi-coloured Grimshaw.

Andy Sag: Not as hard as Feather’s No.269. In each case, Black blocks a white line then White blocks a black line; next the black king moves to self-pin the piece that first moved, then the white piece from c8 can mate. Nice twin.
Michael McDowell: I enjoyed David Shire's anticipatory self-pin helpmate, but I think a small improvement is possible. In both solutions White's first move interferes with a black piece. In (b) there are two ways of setting up a mate, but 1.Re3 Rc5 2.Kf4 Rd4 fails because of the lack of an interference. In (a) there is no choice, as 1…Be3 is the only safe way to guard d4 and d2, so the interference is incidental. If a white pawn at b2 replaced the black pawn at c3, the option of 1…Bc3 would make 1…Be3 a genuine choice. The gain in thematic unity seems to me to justify the use of the white pawn.

Two set variations of significance are 1…Raxd5 2.Qa4 and 1…Rgxd5 2.Qg4. The key 1.Qxd6! threatens two queen mates that are similar to those in the set play, 2.Qb4/Qf4. Now the rook defences to d5, instead of enabling the queen to mate on the fourth rank, prevent it by pinning the white piece. The rooks have also allowed themselves to be pinned by the white queen, however, resulting in 1…Raxd5 2.Ba7 and 1…Rgxd5 2.Sf5. The black bishop likewise self-pins itself in order to stop both threats: 1…Bxd5 2.Sc6. One further defence occurs on d5, though this knight move does not involve a pin-mate: 1…Sxd5 (or 1…Se6+) 2.Se6. The multiple defences on the same square are enhanced by a pair of changed mates.

Jacob Hoover: Super easy, but all the self-pins made me smile.

A good key 1.Se2! (threat: 2.Sxc3) sacrifices the knight to two pieces and yields a flight on e4. Two knight defences open lines for the white queen to traverse and mate on the long diagonal: 1…Sxe2 2.Qh1 and 1…Sxa4/Sd1 2.Qb7. Another pair of defences open lines of guard controlled by the white rooks: 1…dxe2 2.Se3 (also an indirect battery mate, with the white queen used to attack e4) and 1…Bb4 2.Bc6. Lastly, the flight-move 1…Ke4 is followed by the same bishop mate, 2.Bc6.

Jacob Hoover: I didn't enjoy this one as much as the previous ones, for two reasons: (1) it was very easy, and (2) nothing really stood out to me as a theme.

The solution to part (a) is 1.Bxc4 Sf5 2.Bd3 Bg7. The black bishop captures the c4-knight with the aim of clearing the diagonal for the a2-bishop (used to control two flights). The d4-knight directly opens a line for the other white bishop, which mates after it’s unpinned by the black bishop with a switchback to d3. For part (b), a black knight replaces the queen on e8, and the solution becomes 1.Rxd4 Se5 2.Re4 Sg6. Now the black rook removes the d4-knight to activate the c3-bishop (for guarding g7). The c4-knight opens the other white bishop’s line, and it mates after the black rook’s switchback to e4 to interfere with the d3-bishop. The tourney’s judge, Cedric Lytton, wrote: “Line-opening capture switchbacks are beautifully integrated with first an unpin by the black bishop, then an interference by the black rook. Both mates are models, and the pawnless construction is excellent.”

Andy Sag: A tale of two white lines.
Dennis Hale: I remember solving Kricheli's problem in 1979 and being much impressed by it. It was a deserved first-prize winner.

The black king has three flights that together form a ‘Y’ pattern, and white mates are prepared for them: 1…Kxe6 2.Qc8, 1…Ke4 2.Qb1, and 1…Kg5 2.Kc6. Black’s remaining legal move also has a set mate: 1…c6 2.Qe5. Therefore a non-disruptive move by White would solve the problem. Despite the large and mobile white force, only one such waiting move exists – 1.e7!, leaving the set play unchanged. There are many tries, including 1.Rb5? Ke4!, 1.f7?/g7? Kxe6!, 1.Ra4? Kg5!, 1.Kd5? c6+!, 1.Qxc7? Ke4!, 1.Qb2? Kxe6!, and 1.Qb3?/Qd8? c6!

Jacob Hoover: I liked this one for having themes aside from it being a complete block – Y-flights, girl-power, even one battery mate.
Andy Sag: Challenge: how can it be modified to introduce a changed mate?

Although a setting with a changed mate seems unlikely, Andy has produced the following interesting version. 

The initial position is still a complete block, but there are three set variations only. Now the surprising key 1.Bxg5! (waiting) sacrifices the bishop and generates the fourth variation, 1…Kxg5 2.Kc6. Is such an improved key worth the extra material?

White aims to place the king on c1 and compel the black bishop to mate on b2 by sacrificing the queen on that square with a check. This plan requires White to use the remaining pieces to self-block on b1, d1, and d2. And when d2 is blocked by the bishop, the only square from which the queen could play to b2 (without already checking Black) is a1. 1.Bb2 2.Sa3 3.0-0-0 4.Qd3 5.Qb1 6.Qa1 7.Kb1 8.Bc1 9.Bd2 10.Kc1 11.Sb1 12.Qb2+ Bxb2. A fine sequence of play that involves castling, switchbacks by the king and knight, and “hesitating” bishop and queen which take more moves to reach their final squares than expected. When this problem was first published, its composer challenged the readers to revise the problem so that it includes promotion. Another difficult task!

Andy Sag: Spotting queen-side castling helps.
Jacob Hoover: I don't usually do this kind of chess problem, but I took this particular one up because it seemed like an interesting challenge, and in that regard it did not disappoint.

A move by the g4-rook along the rank (to keep controlling e4) would threaten 2.Qf5. Five such moves are thematic tries that fail because the rook would close a vital white line and stop a set mate from working against a black defence. 1.Rh4? Rxh5! (2.Qxh5??), 1.Rf4? Sg3! (2.Qxg3??), 1.Rd4? Rf1! (2.Bb2??), 1.Rgc4? Sd6! (2.R2c5??), and 1.Rb4? Se7! (2.Bd6??). Only 1.Ra4! solves, avoiding the self-interferences and preserving the set variations. 1…Rxh5 2.Qxh5, 1…Sg3 2.Qxg3, 1…Rf1 2.Bb2, 1…Sd6 2.Rc5, and 1…Se7 2.Bd6. There’s by-play with 1…Bxe6 2.Qxe6. The white rook tries exemplify an idea known as “white safety play.”

Andy Sag: This is a try-fest as each defence is related to a try in which other lateral rook moves interfere with one of the intended mates.
Jacob Hoover: A great problem by a great composer.

The bishop check 1…Bxc6+ has a set mate, 2.Bxc6. The key 1.Scxe5! creates a R + S battery on the rank and threatens 2.Se-any (while also yielding a flight on a5). Black’s defences force the white knight to play each of its eight possible moves in turn: 1…Bxc6+ 2.Sxc6 (changed mate), 1…Bd7 2.Sxd7, 1…Bf7 2.Sxf7, 1…Bg6 2.Sxg6, 1…Sc4 2.Sxc4, 1…Rxd3 2.Sxd3, 1…Rf3/Sf3 2.Sxf3, and 1…Sg4 2.Sxg4. A knight-tour is thereby produced. Additional variations are 1…Ka5 2.Sc4, 1…fxe5 2.Rxe5, and 1…c2 2.Qxb4. The thematic try 1.Sdxe5? leads to a similar knight-tour – plus a nice change 1…Kc5 2.Sf3 – and it’s defeated only by 1…c2!, exploiting the unguard of b4.

Andy Sag: Multiple threats separated by defences resulting in a full knight-wheel. Key gives a flight resulting in a required double check.
Jacob Hoover: This puzzle was enjoyable enough with the knight-wheel battery play, but the changed mate is also a nice touch.

The natural tries 1.Rg1/Rg2? (threats: 2.R7g5, etc.) are defeated by 1…d2! followed by a queen promotion. If 1.Re7?, aiming for 2.Re3/Re1, then again 1…d2! refutes. The key 1.Rd7! creates no threat but waits for each black pawn to make a weakening move. 1…f4 2.Re5 and 3.Re8. 1…d2 2.Rxd2 and 3.Rh2. 1…c3 2.Rxd3 and 3.Rh3.

Andy Sag: A miniature three-move waiter.
Nigel Nettheim: Technically the c4-pawn is not needed for soundness, but it makes the key less obvious and adds a variation. Easy to solve but certainly neat.
Jacob Hoover: An excellent miniature chock full of strategic play.

White’s royal battery is prepared to fire in response to many black moves, but there are no set mates against defences such as 1…Ke5, 1…Ra~file, and 1…Re~rank. The key 1.Qg7! (waiting) creates another battery on the long diagonal and completes the block. 1…Sb3/Sxd3+ 2.Kb3, 1…Sc2/Sxc4+ 2.Kc2, 1…Sxa2 2.Kxa2, 1…Sxb1 2.Kxb1, 1…Ra~rank 2.Kxa3, 1…Re~file 2.Kxc1, 1…Ra~file/Sb5/b5 2.Se4, 1…Re~rank/Se2 2.Sd5, and 1…Ke5 2.d4. Quite symmetrical but this is an impressive way to achieve four related pairs of variations, all involving battery play. Note also the changed mates with respect to two tries: 1.Qc6? 1…Ra~file 2.Qd5 and 1…Re~rank 2.Qe4, but 1…Ke5!; 1.d7? 1…Ra~file 2.Qd6/d8=Q and 1…Re~rank 2.Qf4, but 1…Se2! The dual in the latter try is removed after 1…Ra8, so a 3x2 Zagoruiko is shown, though probably not intended.

Andy Sag: The white king moves are the same after 1…Sb3/Sxd3+ or 1…Sc2/Sxc4+, but the situation is different as in one case the knight must be captured and in the other case the knight gives check but need not be captured as it has pinned itself. Five symmetrical pairs of battery variations including pin-mates after the checks. Wow!
Jacob Hoover: The 1…b5 2.Se4 line is a change from the set 1…b5 2.Qc5. I found this problem exceptionally pleasing, what with all the battery play and even two cross-checks.
Nigel Nettheim: The symmetry, which suggests the key, is the main attraction. The composer had been blind for several years.

If White advances the king to protect the c7-pawn, then 2.Rd8 will be threatened. But it would be premature to play 1.Kb6? (additional threat: 2.Bb7) bxc4+!, 1.Kc6? Rxd3! (not 1…Sb4+? 2.Qxb4 and 3.Rd8/Qf8), or 1.Kd6? g2+/Rxd3+! Instead White plays the sacrificial 1.Qc3! with a short threat, 2.Qh8. Note that although the key obstructs 1…Rxd3, 2.Kc6? is still not threatened because of 2…Sb4+. Now three black defences enable White to play each of the king moves as a continuation. 1…Rxc3 2.Kb6 and the two threats are separated by 2…Rxd3 3.Bb7 and 2…Qg2/Qh1 3.Rd8. 1…Sxc3 2.Kc6 and 3.Rd8. And 1…Qb2 2.Kd6 and 3.Rd8. The original threat is extended to a full-length variation with 1…Qh6/Qh5/Qf2 2.Qh8+ Qf8/Qe8/Qf8 3.Qxf8/Qxe8/Qxf8.

Nigel Nettheim: Very nice control of the white king’s advance. The a3-rook prevents both 1.Rd8+ Kxc7 2.Qa5 mate and 1.Qc3 Qb2 2.Kd6 Qa3+. It’s nice to see a directmate where Black has the superior force.
Andy Sag: The short mate threat is a bit untidy.
Jacob Hoover: Enjoyable problem from the collective genius of Hawes and Ravenscroft.

The initial position is a complete block, with white mates prepared against all possible black moves. Tries by the white king fail to black checks: 1.Kg5? Se6+!, 1.Kh4? Sf5+!, 1.Kf3? Qxf7+! Only 1.Kh3! (waiting) works, retaining all of the set play. 1…Qxf7 2.e8=S, 1…Qxf8 2.exf8=Q, 1…Qxd8 2.exd8=S, 1…Qxe7 2.Bxe7, 1…Sg~ 2.fxe8=S, 1…Bxb7 2.c8=S, 1…Rxb8 2.cxb8=Q, and 1…Sa~ 2.bxc8=S. A promotion extravaganza in which four white pawns deliver seven mates by promoting to a queen or a knight. Furthermore, the units in the diagram form the letter ‘T’, making this is a striking shape problem (which can even be improved – see Nigel’s delightful version below).

Andy Sag: Eight variations, seven involving promotions including three symmetrical pairs.
Jacob Hoover: It's been a while since the last complete block problem, and this one was quite good.
Nigel Nettheim: The position is very nicely blocked. Moving the g4-king to h7 would make the set position even more picturesque, and the key (1.Kh8!) would still be quite attractive.

In this intricate three-mover, the key 1.Sb1! threatens 2.Sa3+ bxa3 3.Qc3/Qxb3. The black rooks defend by playing to d3, and in doing so also form a half-pin on the third rank. After 1…R4d3, 2.Qxe2 pins the rook to threaten 3.Sd6, and if 2…Bg3, then the f3-bishop – which was self-pinned by the queen move – gets unpinned for 3.Bd5. Likewise, after 1…R1d3, 2.Bxe2 pins the rook to threaten 3.Sd2, and now 2…Sf3 unpins the queen that was just self-pinned by the bishop move, allowing 3.Qc1. A third defence on d3, 1…Sd3, interferes with the d1-rook and is a self-block as well: 2.Qxd4+ Sxd4 3.Sd6. The unguard 1…Rxb1 admits 2.Bxd4 with two threats separated by 2…Bg3 3.Bd5 and 2…Sc~ 3.Sd6. Lastly, 1…Sc2 is followed by a dual, 2.Qxe2+/Bxe2+, and in either case 2…R4d3 3.Sd6 and 2…R1d3 3.Sd2. A rich strategic problem, featuring an anticipatory half-pin of two white pieces.

Andy Sag: A tough one to solve. It is all about disrupting Black’s control of the d-file by diverting, pinning and/or disconnecting the rooks.
Jacob Hoover: This was a difficult one.
Nigel Nettheim: The doubled rooks defend well, so White disrupts them in various ways. The e2-pawn seems unneeded.

In both solutions the white queen unguards c4 so that the black king has access to all four of its diagonal flights. After the first key 1.Qe7! (waiting), each flight-move is answered by a different mate: 1…Ka4 2.Qxb4, 1…Kxa6 2.Bf1, 1…Kc4 2.Qe2, and 1…Kc6 2.Sd4. The second key, 1.Qd8! (waiting), completely changes the responses to the four king moves: 1…Ka4 2.Qa5, 1…Kxa6 2.Qb6, 1…Kc4 2.Bf1 (transferred mate), and 1…Kc6 2.Sc3. An excellent doubling of the star-flights theme, accomplished in a light setting.

Andy Sag: A good example of star flights.
Thomas Thannheiser: Interesting mate changes between the two solutions.
Jacob Hoover: The 1…Kc4 and 1…Kxa6 defences switch mating pieces between the solutions. Particularly in the 1…Kc4 variations, the white queen and bishop swap roles in guarding the d5-knight and giving mate. An unusual problem, and easy as well, but it was a great one.
Nigel Nettheim: Stellar.

A random move by the c6-knight would threaten 2.Qb7, but 1…Sf4! refutes. The correction 1.Sxe7? answers 1…Sf4 with 2.Rfe3, but then Black has 1…Sxe7+! The key 1.Sd4! again covers f5 and leads to the same battery variation, 1…Sf4 2.Rfe3. The fine key also concedes a flight and unpins the c4-pawn, which is freed to give two discovered checks. Three more battery variations result: 1…Kd5 2.Rf5, 1…cxd3+ 2.Rf7, and 1…c3+ 2.Sb3. And if Black captures the key-piece with 1…exd4, then 2.Rxd4.

Jacob Hoover: The key sets up a potential battery on the fourth rank. Both 1…Sf4 and 1…cxd3+ are self-blocks, while 1…Kd5 2.Rf5 is a pin-mate!
Nigel Nettheim: Nearly a knight-wheel of tries. The knights are the star performers.

The diagram position nicely displays perfect symmetry between the white and black forces. 1.Kg7 Kb2 2.Kf6 Kc3 3.Ke5 d4+ 4.Kd5 Kd3 5.Sd6 Sb4. The two kings march towards each other to set up an ideal-mate in the middle of the board. Simple play but a good miniature find.

Nigel Nettheim: The set position is attractive. The kings come out from their corners to fight in the centre of the ring; the result is a fifth-round knockout.

White mates are prepared against all legal black moves in the diagram: 1…R~ 2.R3b4, 1…Rc4 2.Sf5, and 1…e3 2.Be5. Tries that attempt to preserve all of the set play include 1.Kg5? g6! and 1.Kxg7? Ra7+!, while 1.Rh5? leads to the change 1…Rc4 2.Sb5, but it’s refuted by 1…e3! The key 1.Bd2! (waiting) instead changes the response to the pawn move, 1…e3 2.Bxc3, and adds the variation, 1…cxd2 2.Se2. The black rook correction play is retained: 1…R~ 2.R3b4 and 1…Rc4 2.Sf5. A tricky mutate with a surprising key that sacrifices the bishop.

Nigel Nettheim: The changed mate after 1...e3 still acts on the long diagonal.
Jacob Hoover: 1…Rc4 and 1…e3 are self-blocks. Quite the clever block-mutate, with some black correction play thrown in for some added flavour.

After the square-vacating key 1.Bf3!, White threatens 2.Qe4. Black has four defences that are self-blocks, and White exploits them in a harmonious way: 1…Sxd6 2.Sc6, 1…Sf6 2.S8f7, 1…Bf5 2.S6f7, and 1…Qd4/Sd4 2.Sc4. In each case, the mating knight interferes with a white line-piece that was guarding a flight-square, now obstructed by the defending black piece. The remaining variations show black self-interferences: 1…Sc3 2.d4, 1…Sg3 2.Qf4, and 1…Rg4 2.Rf5. This striking strategic problem is even more remarkable considering its early publication date.

Andy Sag: Threat plus seven variations, most involving self-blocks or defensive line interference.
Jacob Hoover: Quite a nice problem, with a clear theme (self-interferences) that has no distracting by-play.
Nigel Nettheim: The key and threat are not hard to find, but the play is really excellent. The g7-pawn is not needed, with the white king on b8.