Weekly Problems 2019-A

The black queen is defending against mates on d7 and g4 by the e5-knight, and except for 1…Qd4, Black cannot move the piece without permitting one of these mates. The white queen can try to cut off the black piece by sacrificing itself on either line of defence, e.g. 1.Qe2? threatens 2.Sexg4 and if 1…Qxe2 then 2.Sd7, but 1…Qd4! is adequate, while other white queen tries would leave the e5-knight unprotected. The subtle key 1.c5! observes d6 and threatens 2.Qf3+ Kxe5 3.Bg7, 2…Qxf3 2.Sd7, 2…gxf3/Sf4 3.Sg4, 2…Bf5 3.Sexg4/Shxg4. Black’s first thematic defence, 1…Be4, is a distant self-block that allows the white queen to unguard the knight: 2.Qd2 (threatens 3.Sd7 while preserving control of f4) Kxe5 3.Bg7, 2…Qxd2 3.Sexg4. The second thematic defence 1…Sf4 is another distant self-block that enables 2.Qd3 (threatens 3.Sd7 while still attacking e4) Kxe5 3.Bg7, 2…Qxd3 3.Sexg4. There’s by-play with 1…Qd4+ 2.Qxd4 Sxd4 3.Sd7/Sexg4 and 1…Bf5 2.Sg8. A superb demonstration of focal play, one of Goldstein’s favourite themes.

Andy Sag: The name Alex Goldstein strikes fear into the heart of the most experienced solver. Of the 41 possible legal moves, 1.c5 is the most innocuous looking but it allows the white queen to unguard the e5-knight with impunity.

Moves by the bishop on e5 would guard that square and threaten 2.f5, but only 1.Ba1! solves. Two thematic defences by the black queen unpin the b3-knight and self-pin the queen: 1…Qxc6 2.Sc5 (regaining control of d7) and 1…Qxe4 2.Sd4 (likewise for f5). The latter mate is repeated in 1…Qb5/Qd4+ 2.Sd4, but the black queen prompts a third mate by capturing the pinned knight: 1…Qxb3+ 2.Qxb3. The white rook on d7 is also unpinned with 1…Sd6 2.Re7 and captured in 1…Rxd7+ 2.Bd5. One more variation is 1…Sxe4 2.Qh3. The key-bishop must choose the corner square, with most alternatives uniquely defeated: 1.Bb2? axb2!, 1.Bc3? Qxb3+!, 1.Bd4? Qb5!, 1.Bc7? Sxc7!, and 1.Bd6? Qxc6!

Andy Sag: A study of unpins, pins, cross-checks and tries. Except for 1…Qxe4, all variations are set. Note that the a5-pawn is there to preserve the purity of the try play (prevents 1…Qa5 after 1.Bd4?).
Jacob Hoover: Several bishop tries cause either a self-interference or a self-obstruction that allows the black queen to safely unpin the b3-knight. There is also a queen try that has the same threat as the key, but this one also allows the black queen to unpin the knight with impunity: 1.Qc3? Qxe4! (2.Sd4+? Qxd4!).
George Meldrum: Classic key move; checks to White’s king; pins; double checks; all the elements of fun.
Ian Shanahan: A stunning to-the-corner key. In the two thematic mates, the black queen unpins the white knight and pins herself by capture, thereby allowing the unpinned knight to mate. Not top-drawer Mansfield, but pretty good nonetheless.

The black king has a flight-move to e5, answered by a triple, 2.Sb7/Sc4/Sf7 (curiously these mates all recur individually in subsequent play). Both the try and the key by the e5-rook remove that flight but grant a new one, besides activating the half-battery on the dark diagonal. The thematic try 1.Rxe3? threatens 2.Qf2 and leads to 1…Kxe3 2.Sdf5, 1…dxe3 2.Sb7, 1…Ra1 2.Sc4, and 1…Sxd3/Se4/Sxe6 2.Re4. But 1…g4! refutes, as the set mate 2.Rf5 for this defence is no longer possible. The key 1.Rxg5!, with the threat of 2.Qxh4, brings about some attractive changes relative to the try play: 1…Kxg5 2.Sf7 (new flight and mate), 1…Sxg5 2.Sb7 (transferred mate), and 1…Ra1 2.Se4 (changed mate).

Andy Sag: The half battery gives a strong clue to the give-and-take key. Very nice changes!
Jacob Hoover: There are three defences after the key, and each one forces the B + S battery to fire in a different way. A proliferation of battery plays (one of which is indirect) and no distracting by-play.
Ian Shanahan: A lovely sacrificial, flight-giving key from the half-battery. There is a symmetrical try and threat, defeated by 1…g4! Grandmaster Lobusov was working on spectacular keys and battery play at the time.

If Black were to begin, every legal move has an immediate mating response set: 1…f2 2.Se2, 1…S~ 2.Qe5, and 1…B~ 2.Qf2/Qh2. With no waiting move that could maintain all of these variations, White must play a key that extends the solution to three moves, making this an example of a pseudo two-mover. The excellent key 1.Sh3! changes the replies to two black defences and also adds two more variations, by granting a flight on h4 and sacrificing the knight. After 1…f2, White answers with the threat-move 2.Sxf2, which leaves Black in zugzwang: 2…B~ 3.Rfg1, 2…Bxe4!? (correction move) 3.Sxe4, and 2…S~ 3.Qe5. Since 2.Sxf2! acts like the key of a two-mover, generating three precise variations, this problem also exemplifies an insert two-mover. The second change is 1…S~ 2.Sf4 and 3.Sxh5, or 1…Sf6 2.Sf4 (waiting) 2…S~ 3.Sxh5, 2…f2 3.Se2, 2…B~ 3.Qf2/Qh2/Rfg1. Black taking the flight leads to 1…Kxh4 2.Sf4+ Kg5 3.Rxh5, 2…Kg3 3.Sxh5. Or if Black accepts the sacrifice: 1…gxh3 2.Rhg1+ Kxh4/Kh2 3.Sxf3. Lastly, the set dual is removed in 1…B~ 2.Qf2. This difficult problem was placed first in a tourney for three-movers that are either pseudo or insert two-movers, but it manages to combine the two ideas.

Andy Sag: Sacrificial flight-giving key with a waiting move threat. First time I've seen that!
George Meldrum: Amazing.

Set mates are prepared for most of Black’s moves in the diagram, except for 1…dxe6 and 1…Se2. The key 1.Bd3! (waiting) completes the block by providing for these two defences and it also adds two variations by unpinning the d4-pawn. If this pawn captures either rook, White exploits the opened d-file: 1…dxe3 2.Bf5 and 1…dxc3 2.Bb5. The key-bishop mates directly after the self-blocks, 1…dxe6 2.Be4 and 1…dxc6 2.Bc4. The remaining defences are mostly unguards: 1…f5 2.Re5, 1…b5 2.Rc5, 1…cxd6 (self-block) 2.Sxb6, 1…S8~ 2.Sxf6, 1…a3 2.Qb3, 1…Sf3 2.Qxf3, and 1…Se2 (line-opening) 2.Qh1. A total of eleven variations, including eight pawn defences.

Andy Sag: The key unpins the d4-pawn, removes the set mate 1…d3 2.Qxd3 but adds four mates making eleven variations including five symmetrical pairs, the highlight being the pair of battery mates after each rook is captured!
Jacob Hoover: Tries 1.Be2/Bb5/Ba6? dxe6! and 1.e7/exd7? Se2! An easy but nonetheless rewarding solve, as the variations display multiple themes (battery plays, self-blocks enabling white self-interference).
George Meldrum: Eleven ways to checkmate, and although many are in set play the new added mates are outstanding.
Ian Shanahan: An incomplete-block. 1…Se2 has no mate set for it, which points to the key piece (if not its destination). A waiter in ye olde style, with a fine sacrificial key that eliminates the set variation 1…d3 2.Qxd3.

The first part is solved by 1.Rb2 Rf3 2.Sb4 Bxb5. The black rook unblocks a flight in order to unguard the eventual mating square b5 (without closing prospective white lines: 1.Rc4/Rb3?). The white rook prepares an attack behind the d3-knight, which then opens lines simultaneously for both white pieces. The knight also blocks the square that was vacated by the black rook and interferes with the latter’s control of b5. The white rook is thus allowed to guard two flights while the white bishop traverses the opened line to give mate. The second part has the black king starting on d6, which changes the solution to 1.e5 Bg4 2.Se7 Rxf6. Now the black pawn creates a flight on e7 and unguards the mating square f6, while also self-blocking e5. After the white bishop is placed behind the f5-knight, the latter opens lines for both white pieces and blocks the square vacated by the e-pawn, besides cutting off the e8-rook. With the white bishop activated to observe the d7-flight, the white rook mates by moving along the opened line.

Jacob Hoover: In each part a black unit moves in order to enable a black knight to perform a necessary self-interference; also, the white rook and bishop exchange functions between the two parts.
George Meldrum: A single black knight move plugs a flight square, blocks a defence, and opens lines for White’s bishop and rook, in both versions.
Andy Sag: Rook and bishop take turns in guarding escape squares while the other piece mates, after a knight clears lines as well as self-blocking. The f6-pawn appears to be unnecessary apart from ensuring the mate involves a pawn capture.
Nigel Nettheim: The exchange of roles of the two white pieces is nice, although only about half the black units take part in each twin. Easy to solve.
Michael McDowell: What is the idea of the problem? A black knight replaces an ineffective self-blocker, while the white rook and bishop exchange functions, taking turns to guard flights by ambushing behind a knight, or mate by moving along a vacated line. Unfortunately the strategy is mismatched. The only task of the b4 rook is to unguard b5, and it chooses b2 to avoid closing a line which White needs open. The e7-pawn must unguard f6, but e5 must be blocked, so its move has a second purpose. The self-block 2.Sb4 happens to interfere with the b2-rook, so the composer added a rook at e8 to create the impression of matching interferences. Helpmate composers call this sort of piece a weasel – the rook is superfluous and is unnecessary for soundness. Because a pawn at b5 is needed to shield the white king the composer added a pawn at f6 simply in order to have matching captures on the mating moves. This pawn is also superfluous. A lighter and more harmonious problem could be created by replacing the black square vacations with self-blocking moves which move across the squares which the knights will then block [see Diagram 429a below].

(a) 1.Ba3 Re5 2.Sb4 Bb3. (b) 1.Rb2 Bh7 2.Sd2 Re1.

Initially, Black’s only mobile unit is the knight and it produces a set variation, 1…Sh6/Sh8 2.Re8. The amazing key 1.Sb2! (waiting) cuts off the two white pieces on the a-file and concedes five flights to the black king. Four of the flight-moves lead to battery mates, though all king moves to the second rank are answered similarly: 1…Kxd4 2.Sbd1 and 1…Kd2/Ke2/Kxf2 2.Sc4. The last king defence admits a queen mate: 1…Kf4 2.Qc1. The black knight’s moves let the f8-rook control f4 and enable the key-piece to deliver an indirect battery mate: 1…S~ 2.Sbd1 (a change from the set play).

Jacob Hoover: The key seems counter-intuitive, since not only does it prepare no threat, it also grants no less than five flights!
Andy Sag: Tries 1.Sxb4? Se5!, 1.Rxf7?? (stalemate). Classic star-flight waiter with pure mates after king moves to the f-file.
Nigel Nettheim: White’s force is so overwhelming that flight-giving was likely; five is generous.
George Meldrum: This problem is hilarious, in a good way.
Ian Shanahan: A spectacular waiting key, creating a double battery to deal with the flights. It's a pity that mating moves are repeated.

The key 1.g4! unpins the e6-rook and threatens 2.Rb6. Black has four pawn defences that unpin the white queen, which then mates in a variety of ways. The en passant captures re-pin the white rook, but open lines for the queen: 1…hxg3 e.p. 2.Qh5 and 1…fxg3 e.p. 2.Qf5. More line-openings occur with 1…e3 2.Qd5 and 1…c3 2.Qe2. The by-play consists of 1…Be3 2.Sc3, 1…Sxe6 2.Bxd7, and 1…Qc6 2.Bxc6/Re5/Sd6. This remarkable task problem – achieving four black pawn unpins of the white queen – came about as an answer to a challenge set by the great Alain C. White, who had produced a similar setting earlier. See J.K. Heydon: Problemist, Solicitor, Businessman, No.46, for the full story, including White’s version of the task.

Andy Sag: A pinned pinner setting! The key unpins the rook on e6. All four pawn defences give different pin-mates by the unpinned queen.
Jacob Hoover: Incidentally, the four white queen mates are all pin-mates, which lend a degree of unity to the problem.
Andrew Buchanan: En passant! Pity that 1…Qc6 allows three new mates.
Nigel Nettheim: The unpin 1…Be3 (and the non-variation 1…Bc3) suggests an e.p. capture in the reverse direction, increasing the appearance of unity, although that unpinning is not essential to the following mate.
Ian Shanahan: The central idea is “pawns unpinning by interference”. The only flaw is the ugly triple after 1…Qc6; otherwise, a fine problem by a composer who died too young.

This difficult three-mover commences with the sacrifice 1.Rxe4! which grants the black king a second diagonal flight, besides the one on g6. Surprisingly the key entails no threat but waits for Black to make a self-weakening move. 1…Kxe4 is met by the brilliant 2.Qxf3+, yielding 2…Kxf3 3.Bd5, 2…Kf5 3.Qd3, and 2…Kd4 3.Sb3 (pin-mate), where the three king moves form the Y-flights pattern. If Black plays 1…Kxg6, then 2.Re7 threatens 3.Bh7, which isn’t stopped by 2…Kf5, thanks to the removal of the g6-pawn. Any black rook move allows the a1-bishop to control e5 and f6, freeing up the g4-knight: 1…R~ 2.Bh7 (threatens 2.g7/Sf6, both battery mates) Kxe4 3.Sf6 (now an indirect battery mate), 2…Rb2 3.g7, and 2…Se5 3.Rxe5. Lastly, 1…S~ prompts 2.Re5+ Kxg6 3.Rg5. Excellent play that combines spectacular sacrifices with subtle white second moves (1…Kxg6 2.Re7 and 1…R~ 2.Bh7) that are hard to find.

Composer: While it is possible to remove the bishop at a1, rook at b2, pawns at c2 and c5, the problem holds up and removes the double threats [after 1…R~ 2.Bh7]. Still I like their inclusion to give that extra complexity.
Andy Sag: The major double sacrifice makes this problem very difficult to solve. Good one George!

The key-move 1.Bh8! is a Bristol clearance (of maximum possible length) that allows the queen to follow the bishop along the long diagonal. The threat of 2.Qf6 is stopped by three of the black king’s four legal moves. Although 1…Kh6 and 1…Kg6 are answered by the same thematic queen move 2.Qg7, these are distinct variations that produce different model mates. Another model occurs with 1…Kf4 2.Qc1. The fourth king move 1…Kh4 doesn’t deal with the threat, but it’s still a pity that a second mate is possible: 2.Qf6/Bf6. Arguably, if Black obligingly plays 1…Bxe4, then the threat 2.Qf6 becomes a model as well! Note the tries 1.Bg7? Kg6!, 1.Qa6? Bc6!, and 1.Qa5+? Bd5! The latter is perhaps the most interesting because it generates two changed mates relative to the actual play: 1…Kh6 2.Qh5 (yet another model!) and 1…Kg6 2.Qh5 (an echo of the post-key threatened mate).

Andy Sag: A miniature with an obvious Bristol clearance key which maintains the four set flights (two unprovided).
Jacob Hoover: All of the mates after the king’s moves are pure mates, and this lends a degree of unity to the problem.
Nigel Nettheim: Although there’s a dual after 1…Kh4 and the black bishop doesn’t take part in the play, the long key-move is nice and partial star-flights are present.
George Meldrum: Predictive key but pleasing, nonetheless. Black’s king is mated on five different squares. Not bad for such a lightweight setting.
Andrew Buchanan: Major dual, and unprovided black half-pin distract from elegant model mates. Instead of the a8-bishop one could economize with a d7-pawn; still get all the tries.
Ian Shanahan: There are unprovided flights, and the white queen is badly out-of-play. The clearance-to-the-corner key veritably leaps to the eye. Some nice mates ensue.

The thematic try 1.Rc2? is a Novotny move that cuts off two black line-pieces to threaten 2.Sdc4 and 2.Qe4. The threats are separated by 1…Bxc2 2.Sdc4 and 1…Rxc2 2.Qe4, and there’s more virtual play with 1…Sf4 2.Qf6, but the try is defeated by 1…Rf4! The key 1.Sc2! is another Novotny double-interference and though it occurs on the same square, one of the generated threats is different: 2.Rc5 and 2.Qe4. The normal mate separation follows with 1…Bxc2 2.Rc5 and 1…Rxc2 2.Qe4. The first-rate key also gives two flights to the black king, leading to 1…Kd5 2.Qd4 and 1…Kf5 2.Qf6. As in the try play, 1…Sf4 answers both threats but a new mate results: 2.Qg5. This fine piece of work was surprisingly unplaced in its Problemist informal tourney.

Andy Sag: A flight-giving Novotny key with unavoidable double-threat, two pin-mates [2.Qe4 and 2.Qg5] and one changed mate.
Jacob Hoover: 1…Kf5 2.Qf6 is a transferred mate [relative to 1…Sf4 2.Qf6 in the try play].
Nigel Nettheim: The key blocks two intersecting lines (Novotny). A thematic try (1.Rc2?) and a changed mate (1…Sf4) are good features. The flights are too, even if their mates are not elegant.
George Meldrum: The queen mates in mirror-like fashion for the black king flights.
Ian Shanahan: A fantastic Novotny key, yielding two flights. There’s also a mate changed after 1…Sf4. Superb problem!

The diagram position is solved by 1.Kd3 Kc1 2.Kc3 Kd1 3.Kb2 Sd4 4.Ka1 Kc2 5.Sa3+ Kb3 6.Sb1 Sc2. The white king traces a curious triangular path to b3, while the black knight avoids the dual 5.Sd2? as it would prevent 5…Kb3. The twin (b) begins with the black king in check, and this fixes the order of Black’s first two moves in the solution: 1.Kd4 Kc2 2.Sc1 Kd1 3.Kc3 Sa5 4.Kb2 Kd2! 5.Ka1 Kc2 6.Sa2 Sb3. Here the white knight must not play 3…Sd2? because that would obstruct the square needed by the white king for the tempo move, 4…Kd2! Good interplay between White and Black in this helpmate showing exact echoes of an ideal-mate.

Andy Sag: Nice twin. The white king must lose two tempos to allow the black king to reach a1 in four moves and the black knight to get to b1 and a2 respectively in two moves to self-block.
Jacob Hoover: Clearly the black king must be mated in a corner, as White doesn't have enough material to achieve mate anywhere else. In part (a) the choice of the square Black moves the knight to must be made carefully (5.Sd2?), while in (b) the white knight must choose its square carefully (3…Sd2?).
Nigel Nettheim: Very nice indeed!
George Meldrum: I really like the solution to the (b) flipside. In vinyl record terms, this is a double A-side hit.

The corner-to-corner key 1.Qh8! threatens 2.Qxb8. Defences by Black’s queen and bishop on the a-file leave each other pinned by the white rook, a weakness exploited by White in the battery variations, 1…Qf8 2.Rf7 and 1…Be8 2.Rd7, where the b7-rook shuts off each defender in turn. The half-pin is utilised again in 1…Qe7+ 2.Rxe7, another battery mate. The by-play 1…Qd6 2.Rxa4 produces a fourth pin-mate.

Jacob Hoover: The black queen and a4-bishop are half-pinned; if one moves the other will be pinned.
Andy Sag: The half-pin on the a-file, the long diagonal battery and the far away queen suggest a long-range pinning key. Most Gamage problems involve pins and unpins.
George Meldrum: Classic corner-to-corner key for a cornered king problem.
Nigel Nettheim: A half-pin is shown very succinctly.
Bob Meadley: Very lightweight for Gamage.
Ian Shanahan: The key is obvious and strong (also because the white queen is initially out-of-play), but it leads to some fine half-pin play involving shut-offs. A good Meredith (8 to 12 units).

If the white bishop controls c3 with either 1.Ba5? or 1.Bd4? to threaten 2.Sc5, the flight-move 1…Ke4! is too strong. The key 1.Bxe3! aims for 2.Bd4 (removing the e4-flight) followed by 3.Sc5, and if the unpinned black knight checks, that prompts two good sub-variations in the threat: 2…Sb6+ 3.Bxb6 (switchback) and 2…Sf6+ 3.Bxf6. Black’s pawns on c6 and e6 can defend by observing d4, but these moves have the drawback of unguarding the d5-knight. After 1…c5, 2.Bh6 surprisingly puts Black in zugzwang: 2…e5 3.Rxd5 and 2…c4 3.Bb1, exploiting a self-block. White answers 1…e5 with the same waiting move 2.Bh6, and while 2…c5 3.Rxd5 repeats a mate, 2…e4 3.Rd2 involves a different self-block with a pleasing break from symmetry. Finally, the flight-move 1…Ke4 permits 2.Bb1+ Ke5 3.Rxe6.

Jacob Hoover: White has no set continuation prepared for 1…Ke4 (or for any other black move, for that matter) in the diagrammed position, so it seems that the key should be a move designed to keep the black king from escaping via f4.
Andy Sag: Black has only five legal moves. The unpin of the black knight on second move allowing checks livens it up.
George Meldrum: The black king should be prevented from reaching the f-file. This makes finding the key a little easier. Did not see Bh6 coming but it did provide a pleasant surprise.

Most of Black’s moves in the diagram are provided with set mates, other than 1…R~file. Two waiting tries prepare for these rook moves. The first 1.g6? vacates g5 for 1…R~ 2.Seg5, but 1…Rh5! keeps an eye on the mating square. The second 1.d7? attacks e5 by discovery, effecting a changed mate, 1…R~file 2.Qxe5, but because the try-pawn has cut off the c8-bishop, 1…Rxg5! cannot be met by 2.Sexg5. The sacrificial key 1.Qc3! (waiting) controls e5 directly. 1…R~ 2.Qxe5, 1…Rxg5 2.Sexg5, 1…B~/Sa~ 2.Sc5, 1…Se~ 2.Sd2, 1…d4 2.Qc6, and 1…d2 2.Qc2. This problem is a precursor to the same composer’s No.248, a twin setting that he considered far superior. Nevertheless, this is a worthwhile version with two good tries and a changed mate.

Jacob Hoover: An incomplete block with some changed mates between the try- and actual phases.
Ian Shanahan: A triply sacrificial waiting key to a problem composed in a 19th-century style.
George Meldrum: This whimsical problem sees the queen being fed to the horses and bishop yet Black can no longer escape via his castle.

Note the set dual after a self-block on g4: 1…g4 2.Sxd5/Sh5. The key 1.Sxd4! threatens 2.Re4 by guarding f5, and though g4 is now attacked by the d1-bishop, neither of the two set mates would work because the key has also granted a flight on e5. Self-blocking defences on e5 bring back the knight mates, with dual avoidance effects: 1…Sxe5 2.Sxd5 (not 2.Sh5?) and 1…dxe5 2.Sh5 (not 2.Sxd5?). A pin-mate results if Black takes the flight: 1…Kxe5 2.Qe3. Now 1…g4 2.Rf5 shows a changed mate; 1…Bf5/Bg2 also permits 2.Rf5. The key-piece is captured in 1…Bxd4 2.Qxd4. There’s by-play with 1…Sxf6 2.Qe3 and 1…g2 2.Qh2.

Jacob Hoover: The key sacrifices both the knight that just moved and the e5-rook to threaten 2.Re4. Accepting either sacrifice leads to mate from the queen.
Andy Sag: The key allows a flight-capture which self-pins the d5-knight. Black’s queen, rook and c3-pawn are there to prevent duals. Well done, Molham!
George Meldrum: Other first move stabs by the f3-knight looked potentially good too. Three queen mates, two rook mates, two knight mates; a somewhat tricky problem.
Ian Shanahan: A fine sacrificial flight-giving key, leading to dual avoidance by line-opening when e5 is captured by non-Royals. Rather heavy for the content, but splendid!

The four solutions are: 1…Sg5 2.e4 Scxe4 3.Ke5 Rc5, 1…Sb5 2.Ke6 Sg5+ 3.Kd5 e4, 1…Sd1 2.exd1=B Rc6 3.Bg4 Sg3, and 1…Sxe2 2.Kg4 Rc4 3.Kh3 Sf2. No apparent theme but the first three solutions all end with elegant model mates. The fourth solution thus could be viewed as extraneous. In fact, it’s possible to adjust the position slightly so that this solution is replaced by another one that also produces a model mate! See Diagram 440v below. The last solution becomes: 1…Rxe2 2.Kg4 Rg2+ 3.Kf3 Rg3.

Andy Sag: Tough to find one solution, let alone four; three of them are pure mates and one uses an indirect battery.
George Meldrum: Brilliant problem and very difficult to solve. Michael Grushko must be a genius, or from outer space!

The white rook on f5 executes two tries and the key. 1.Rd5? (threats: 2.Kf5/Qd3) fails to 1…bxc3! as the set mate for this defence, 2.Ke3, leaves d5 unguarded. 1.Re5? (2.Kf5/Re4) permits a double-check: 1…fxe5+ 2.Kxe5, but 1…f5! refutes because the rook has obstructed 2.Se5. The key 1.Rfg5! (2.Kf5) enables a different double-check, 1…fxg5+, also answered by 2.Ke5 (mate transference). (A second check allowed by the key, 1…hxg5+, doesn’t deal with the threat.) Black’s defences that defeat the tries are handled thus: 1…bxc3 2.Ke3 – a third royal battery mate – and 1…f5 2.Se5. Black self-blocks c3 again with 1…Bxc3 but another mate follows: 2.Qf1. Three subsidiary variations are 1…Qe6 2.Bxe6, 1…Qd5 2.Bxd5, and 1…Rd7/Re7 2.Rxc5.

Jacob Hoover: The square-vacating key 1.Rfg5! threatens to fire the royal battery on the fourth rank with 2.Kf5. This battery still fires with different king discoveries in 1…fxg5+ 2.Ke5 and 1…bxc3 (self-block) 2.Ke3.
Andy Sag: Surprise key gives up the rook with a double-check but the pinned queen is helpless against the cross-check.
George Meldrum: The actual key looked too good to be true. Most variations are from set play but the outstanding double-check on the white king makes it all worthwhile.
Ian Shanahan: A sacrificial key leading to the star variation, a double-check plus Royal cross-check: 1...fxg5+ 2.Ke5. The by-play is rich, and involves further Royal battery mates.

Various queen moves along the first rank would threaten an immediate mate, but they must be played in the right order. Not 1.Qa1? (2.Qd4) Sxf5! 2.Qb1 (3.Qxd3) Sg3, or 1.Qb1? (2.Qxd3) Bxf5 2.Qa1 (3.Qd4) Bh3. Even though the two black minor pieces obstruct each other on f5, they refute the tries convincingly by mating White! To forestall these strong defences, White induces Black to self-obstruct the mating squares as well. The key 1.Qd1! threatens 2.Qxf3, luring each black rook to the third rank. 1…Rg3 2.Qa1 (3.Qd4) Sxf5 3.Qb1 and now that 3…Sg3 is ruled out, 4.Qxd3 is unstoppable. Similarly, 1…Rh3 2.Qb1 (3.Qxd3) Bxf5 3.Qa1 followed by 4.Qd4, since 3…Bh3 is blocked. The queen’s to and fro on the first rank is attractive, though judge Alex Goldstein had misgivings about the short threat after the key move.

Andy Sag: Like a spider, the white queen threatens mates in the correct sequence to render Black powerless. The wrong order exposes White to mates.
Jacob Hoover: It’s quite clear that the self-obstructions are the point of the problem, with no by-play whatsoever to distract the solver.
George Meldrum: Ironically, this position if given to chess players, then a larger majority would find a win for Black. The problem is smooth and subtle requiring little effort or fanfare of play. The same cannot be said of solving it.

The try 1.Bf4? grants a flight on f6, threatening 2.Qc6/Qe5/Qf5, and is refuted by the flight-move, 1…Kf6! A random-try by the bishop on the long diagonal, 1.B~? concedes a flight on d6, threatening 2.Qc6/Qd7/Qe5, and is thwarted by the new flight-move, 1…Kd6! The key 1.Bd4! entails the same triple-threat as the second try, 2.Qc6 [A]/Qd7 [B]/Qe5 [C], and Black’s responses lead to every possible combination of these mating moves. An “imaginary” random move by the knight, 1…S~, permits all three mates: 2.Qc6 [A]/Qd7 [B]/Qe5 [C]. Three defences stop one of the threats but not the other two: 1…c5 2.Qc6 [A]/Qd7 [B], 1…c6 2.Qc6 [A]/Qe5 [C], and 1…Sb4 2.Qd7 [B]/Qe5 [C]. Black’s remaining moves leave only one threat unanswered: 1…Sc5 2.Qc6 [A], 1…Kd6 2.Qd7 [B], and 1…Sb8 2.Qe5 [C]. Such a scheme is known as total primary combinative separation, and it’s rarely accomplished in miniature form and with a flight-giving key, as here.

Andy Sag: A threat separation study of sorts as each of the six black moves eliminates a different threat or pair of threats.
Jacob Hoover: It’s almost total combinative separation, but not quite; there’s no black move that allows all three threats. Still, to achieve such a separation of threats in a miniature setting is impressive.
George Meldrum: An unusual trio of threats yet doused by black responses which moderate the options.

Both the d1-bishop and h4-rook are attacking a4, the black king’s eventual mating square. To give the king access to that square, each side interferes with one of white line-pieces. In part (a), the solution goes 1.Qb3+ Kd4+ 2.Ka4 Kc5. The black queen’s initial move – cutting off the bishop – is thus an anticipatory self-pin, while the white king forms a battery with the rook and fires it to deliver mate. Part (b) presents an analogous solution that swaps the roles of the bishop and the rook: 1.Qg4 Kc2+ 2.Ka4 Kb2. Now the queen cuts off the rook in preparation for a pin along the rank, while the white king closes the bishop’s line and opens it again for a battery mate. The intensive line effects are brought about with exceptional economy.

Andy Sag: In each case, Black sets up a self-pin and White executes a battery pin-mate.
Jacob Hoover: The black queen-side pawn occupies a flight square in both parts, and the h5-pawn is there to prevent cooks. Kudos to Mr. McDowell for another masterpiece!
George Meldrum: The first part, absolutely brilliant, and the second complements.
Ian Shanahan: Lovely masking and pinning effects, with active royal batteries. Gorgeous!

The positions of the two kings and knight suggest that Black’s mating move will be …Sxf3, forced by a queen check on f3. Such a mate would require White to promote all four pawns, three to block flights on g3, h3 and h1. These blocking pieces must not guard f3 or check the black king, and one must also control the king’s remaining flight on e1. Only a bishop on g3 could serve the latter purpose, while a knight is the only suitable piece on h1. Either a knight or a rook would work on h3, but the former necessitates too many moves. The shortest sequence is 1.h6 2.h7 3.h8=R 4.Rb8 5.Rxb3 6.Rh3 7.b4 8.b5 9.b6 10.b7 11.b8=B 12.Bxc7 13.Bg3 14.c7 15.c8=S 16.Sd6 17.Se4 18.Sf2 19.f8=Q 20.Qf3 21.Sh1+ Sxf3. White promotes to four different types of pieces, i.e. the Allumwandlung theme, in a setting with no extraneous white units.

George Meldrum: Placing pieces around the white king is elementary, and even checking with the queen on f3 is easy enough seen. Doing this all in 21 moves is tricky. I love the fact that the queen promotion is done with the f-pawn. Also, the final battery check adds that extra spark.
Andy Sag: The knight shield on f2 is a nice touch, enabling the f-pawn to promote to queen and then reach f3 in one move.
Jacob Hoover: Each promoted piece makes a different number of moves over the course of the solution: the knight makes four moves total, the rook three, the bishop two, and the queen makes only one move.
Ian Shanahan: As soon as I saw the composer’s name and the four white pawns, I immediately guessed “AUW”. It’s economical and elegant, but uses the now hackneyed mechanism of capturing black pawns in order to mobilize the next promoting white pawn. I would make it a SS#19 and start the h5-pawn on h7, to improve economy of time and make the solution less obvious (which pawn promotes on move 1?).

In this complete block position, set mates are prepared for all black moves, including the flight-capture 1…Kxf4 2.Qd4. If Black moves the b4-knight, that opens lines for the two white pieces on the a-file (a4-d4 and a3-d6), leading to a dual in 1…Sa6 2.Qd4/Qe3, but these queen mates are separated with 1…Sc6 2.Qe3 and 1…Sd5 2.Qd4, while 1…Sxd3+ forces 2.exd3. One more set variation is 1…Sf~ 2.Sg6. No white move is available that could preserve all of the set play, e.g. 1.Rf1? Sxd3+!, 1.f3/h5? Kxf4! The key 1.e4! (waiting) involves many effects – such as closing the e3-e5 and d4-f4 lines – that produce some complex changed play. Now 1…Kxf4 enables 2.Qg3, since the e1-rook controls e4. Random moves by the b4-knight still activate the a4-rook, but this is exploited differently: 1…Sa6/Sc6 2.exf5, where the pawn opens both a direct battery on the e-file and an indirect one on the fourth rank. The correction 1…Sd5 generates another battery mate, 2.exd5, while 1…Sxd3+ 2.Sxd3 sees a new recapture by White. The key-pawn gets captured in an added variation, 1…fxe4 2.Rxe4. Only 1…Sf~ 2.Sg6 is retained from the set play in this fine mutate with four changed mates.

Andy Sag: The set position is a complete block; the key maintains the flight capture and introduces four changed mates.
Jacob Hoover: 1…fxe4 is an added defense.
George Meldrum: A fine problem with lots of changed mates. The bishop on h7 is the only elephant in the room as it does not partake in the set play and more or less points to White’s first move.
Ian Shanahan: With the e1-rook being initially out-of-play somewhat, the key veritably leaps to the eye. Regardless of that, what we have here is a rather heavy mutate with nice changed mates. The thematic defensive knight also executes some black corrections.

The diagram position is solved by 1.Bc6 d3+ 2.Kb5 Rh5 and 1.Be4 Rh5 2.Bd3 Bf7; the twinning for part (b) changes the solutions to 1.Bf3 b3+ 2.Kd3 Bg6 and 1.Kb4 Ra3 2.Ka5 Rxa4. In the first solution of each part, Black organises the black bishop to be pinned by one of White’s line-pieces, while the other line-piece delivers a pin-model mate. White’s rook and bishop thus exchange their functions. The second pair of solutions across the twins also involves the two white pieces swapping their roles – now between guarding flights and giving mate – though here the play isn’t as strategically intensive or harmonious (e.g. the black bishop is unused in one solution).

Andy Sag: An economical setting with nice variety of play with rook and bishop taking turns to mate in each case.
George Meldrum: A nice pair of pinned bishop solutions. The other solutions seem random but clever enough. Every solution has the black king mated on a different square.
Paz Einat: In each of the twins there is one nice solution with anticipatory interference, but the other solution seems superfluous to me. I am attaching a possible version with two solutions, no twins, and some additional elements including dual avoidance. A variety of other options exist but I think this one keeps the intended model mates while keeping economy.

1.Bd6 Sf3+ (Sc2+?) 2.Kc5 Rh5. 1.Bg3 Sc6+ (Sxb3+?) 2.Ke3 Bh6.

The key 1.Qf8! abandons the battery on the c-file and threatens 2.Qxf7. In the first pair of thematic variations, the a4-knight blocks a potential flight-square and allows White to fire the R + S battery with a move that cuts off a diagonal line of guard to that square: 1…Sc5 2.Sd6 and 1…Sc3 2.Sd2. The g6-rook defends by opening a bishop-line to f7, and in a second pair of variations, the piece interferes with one diagonal-moving defender controlling the white rook, enabling the R + S battery to fire again with a shut-off of another black defender: 1…Rg5 2.Sg3 and 1…Rg3 2.Sg5. The black rook causes a third self-interference with 1…Rg4 2.Be2. The final variation makes further use of the white rook and knight pair: 1…fxe4 2.Rxe4. This solid piece of work by a GM of composition was originally published with a cook, 1.Qxf5, which I removed by adding the d7-pawn.

Andy Sag: The key adds a second guard to c5, freeing up the e4-knight for battery mates. I like the rook valve on the g-file displaying opening and closing of diagonals. A seventh variation can be incorporated by adding a black rook on b1 and shifting the a5-pawn to b5; then if 1…Rxd1 2.Qb4.
Jacob Hoover: The two knight self-blocks defend by controlling the threat mating line, but each of these self-blocks allows a double-check mate.
George Meldrum: Black’s responses of knight to c3 or c5, and rook to g3 or g5 form the sweet spots of by-play in this composition.
Ian Shanahan: There is an element of symmetry to this problem (most noticeable after the two self-block + white interference variations). Nice valve-play by the g6-rook.

White has two thematic tries that produce similar play: 1.Bxg7? with the double-threat of 2.Sc5 and 2.Sg5, leading to 1…Qxd5 2.Re7 and 1…Bxd7 2.Re5 (1…Rg2/Rf5 2.Bf5), but defeated by 1…Qc1!, and 1.Bc3? with the same double-threat and variations, refuted by 1…Qd4! The key 1.Sb6! threatens 2.Re7 and 2.Re5 – the variation mates seen in the virtual play. Now new thematic defences bring about the knight mates that were threatened after the tries: 1…gxf6 2.Sc5 and 1…Rxf6 2.Sg5. This kind of exchange of a double-threat and variation mates between virtual and actual play is known as the Odessa theme, and it’s presented here clearly and with good unity: the four thematic defences are all capturing self-blocks. The by-play is 1…cxb6 2.R7d6 and 1…Sc6 2.Bf7, plus various ways of separating the threats, including 1…Qxd5 2.Re7 and 1…Bxd7 2.Re5.

Andy Sag: The key gives a double threat albeit separated by rook captures. Captures on f6 allow a symmetrical pair of set knight mates. A few bishop-tries giving the same knight mates as a double threat, notably 1.Bc3? Qd4! and 1.Bxg7? Qc1!!
Nigel Nettheim: Sixth-rank symmetry is the name of the game. The captures on f6 lead to dual-free mates, with the help of the g1-bishop.
George Meldrum: The key move is ordinary; there is an outrageous double threat; defences are all from set play. Maybe it is the tricky tries like 1.Bc3? or 1.Bxg7?, or the fact that Black’s position is so perilous, that I find this problem magical.
Ian Shanahan: The Odessa theme: the try’s threats appear as mates post-key; the key’s threats appear as mates after the try. Sweet reciprocity! The only fly in the ointment here is the unwanted extra try with identical virtual play.