Weekly Problems 2018-A

The waiting key 1.Sg4! prepares for moves by Black’s knight and bishop while preserving the set mates for the pawn moves. Three defences show gate-openings in that they enable a white piece – the queen here – to traverse the line opened by Black and give mate: 1…f6/f5 2.Qxb7, 1…g5 2.Qe4, and 1…B~ 2.Qxh2. A third mate on the long diagonal occurs with 1…b6/b5 2.Bc6. Lastly, 1…S~ 2.Sf2 gives a fifth variation in this Meredith problem.

Composer: The key completes the block, retaining three set mates and introducing two more. Three variations involve opening of different lines for queen mates.
Jacob Hoover: This one was fairly easy, but the line play made it enjoyable nonetheless. To Andy Sag and everyone else at OzProblems.com, Happy New Year!
Nigel Nettheim: Another nice and easy one. And Greetings to Andy!
George Meldrum: Hmm, take away pieces on b7 and e8, and the problem still works. This problem is a bit of fun and a somewhat of a lesson for me on problem building!
Ian Shanahan: A very obvious key to complete the block in this 12-unit Meredith. One can remove the b7-pawn and e8-bishop without any real loss. The theme? Line opening for the white queen in three directions.

The thematic try 1.Qa7?, by controlling c5 and d4, threatens 2.Rxb4 [A] and 2.Se5 [B]. Black has two self-blocking defences that deal with both threats: 1…Sd3 2.Bb3 [C] and 1…Bc3 2.b3 [D]. And 1…Bxd6 permits 2.Sa5, but 1…Bc5! refutes. The key 1.Rh3! guards d3 and c3 to threaten 2.Bb3 [C] and 2.b3 [D] – the variation mates seen in the virtual play. Now another two self-blocking defences handle the double-threats and bring about the mates that were threatened by the try: 1…Sc5 2.Rxb4 [A] and 1…Sd4 2.Se5 [B]. Also, 1…Sxh3 2.Qf1. This curious pattern, in which the pairs of threats and variation mates initiated by the try reappear after key but with their roles reversed, is called the Odessa theme.

Andy Sag: The defences involve one line clearance and two self-blocks.
Jacob Hoover: Solved with a rook sacrifice, 1.Rh3! Two defences self-block and one involves capture of the key-piece.
George Meldrum: The try 1.Qa7? Bc5! is an appealing addition to this problem.
Ian Shanahan: As I wrote when I first published this problem in the column I then edited: The Odessa theme – i.e. pairs of threats in one phase become mates in another, and vice-versa – unified by self-blocking thematic defences. And all black pieces defend. The 2.Qf1 mate is icing on the cake!

If Black is to move, the bishop cannot retain its focus on d3 and a4, so mates follow immediately, e.g. 1…Bd1/Bb3 2.Sd3 and 1…Bb1 2.Sa4. But White has no way of preserving these set mates, and the key 1.Qd7! (waiting) extends the play to three moves. A random move by the bishop unguards a4: 1…B~ 2.Sa4+ Kc4 3.Qb5. The first correction 1…Bd1 leads to 2.Sxd1 Kc4 3.Qb5. A second correction, 1…Bb3, is a distant self-block that admits 2.Sd3+ Kc4 3.Qd4. The try 1.Sc4? with multiple threats (e.g. 2.Sb6, 2.Se5) is defeated by 1…Bf5! This problem was originally published with a twin where all the units are shifted three squares to the right. Now 1.Qg7? fails because the bishop could play further to the top left and still protect d4. And the knight try of the first position becomes the key, 1.Sf4!, since the bishop can no longer refute by attacking the queen. However, I think the post-key play of this twin contains far too many duals to be a worthwhile setting. And little is lost by dispensing with the twin since its variations still occur in the diagram’s virtual play, where duals are a less serious flaw.

Jacob Hoover: There is no white move that leads to mate on the next move; therefore this problem is a pseudo two-mover.
Andy Sag: The key maintains king immobility forcing the bishop to move, allowing the knight to check (or capture the bishop) followed by a queen mate. Try 1.Sc4? If 1…Bb3 2.Qd6+ Kxc4 3.Qd4, and 1…Ba4/Be4 2.Sb6 Bc6 3.Qe7, but 1…Bf5!
George Meldrum: A neat setting.

The key 1.Sd4! threatens 2.Sb5, against which Black has four defences, all played by the f7-bishop and e7-pawn. These two units are half-pinned by the white queen, an arrangement exploited in these variations ending with pin-mates: 1…Bc4 2.Bd6 and 1…exf6 2.Sd5. In the second pair of variations, a Pawn-Grimshaw interference occurs on e6 that allows the white queen to unpin the remaining black unit on the seventh rank and deliver a long-range mate: 1…Be6 2.Qh2 and 1…e6 2.Qc2. Praised by the judge Arthur Mosely as “the most original idea in the tourney, and we think the author has struck an entirely new chord…”

George Meldrum: The key move cleverly opens a line for the white queen and covers the c6-square which in all enables new mates not seen in set play.
Jacob Hoover: There is a half-pin situation on the seventh rank: if either the e7-pawn or the f7-bishop were to move, the other of the two would be pinned by the white queen.
Ian Shanahan: Classic half-pin with the rear white queen mating at a distance after the two defences on e6 (the mutual interferences by Black’s pawn and bishop there constitute a “Pickabish”). The two white queen unpins also show the Gamage theme: the interferences permit harmless unpinning of the interfered-with units, which can no longer close the mating line.
Andy Sag: A tale of two pairs. A fifth variation is possible by adding a white pawn on a6 – 1…bxa6 2.Rc6.

Set mates are provided for all possible black moves: 1…R~ 2.Sd2, 1…Rxd3 2.Qe6, 1…Sb~ 2.Sc5, and 1…Se~ 2.Bxf5. White has no way of retaining all of the set play, e.g. 1.Kb8? Sc6+!, 1.Be6? Rxd3!, while 1.Rc3? (threatening 2.Qe6) fails to 1…Rxd4! The key 1.Qa3! (waiting) grants a flight on d3 but sets up a battery to answer 1…Kxd3 with 2.Sd2. The mate following the correction move 1…Rxd3 is changed to 2.Qxe7. The remaining play is unchanged: 1…R~ 2.Sd2, 1…Sb~ 2.Sc5, and 1…Se~ 2.Bxf5.

Andy Sag: Complete block with one post-key mate change and one added pure mate after flight capture. A try worth mentioning is 1.Kxb7? (2.Sc5) Rb1!, pinning the knight.
George Meldrum: A wonderful key move and after the black king captures the rook, White needs to cover five squares to provide a mating net.
Jacob Hoover: After the key, 1…R~ still allows 2 Sd2 but this time it's an indirect battery play, and the response to the correction 1…Rxd3 (still a self-block) changes to 2.Qxe7. White also has an answer for the flight that the key grants: 1…Kxd3 2 Sd2 (distinct from earlier due to being a direct battery play as opposed to indirect). A rather nice mutate with black correction in both the virtual and actual play.
Ian Shanahan: Fantastic flight-giving zugzwang key. I found this to be most difficult to solve. A concurrent changed-mate after 1…Rxd3. This problem is masterful – just as one would expect from Mosely.

The black king could potentially be mated on many squares, but the shortest sequence involves placing it on e2 for a queen mate on c2. This scheme requires Black to promote various pawns to self-block on f1, e1, and f3. Further, since Black is initially in check, the first move has to be a promotion on c1, and the new piece must not interfere with the eventual mate. 1.c1=S 2.f1=B 3.e1=R 4.Ke2 5.d1=Q 6.Qd5 7.Qf3 Qc2 mate. When first published, this seven-move problem held the economy of length record for a series-helpmate showing the Allumwandlung theme. But subsequently the record of six moves has been achieved, which is the theoretical minimum (given that Black must make four promotion moves plus two queen moves – one diagonal and one orthogonal – to ensure that the queen couldn’t be replaced by another promoted piece). Thanks to Michael McDowell for pointing out the correct source of this problem.

Jacob Hoover: All of the possible promotions (knight, bishop, rook, queen) are seen here, so it's an Allumwandlung.
Andy Sag: A tough one to solve as there are 14 feasible squares for the queen to finish on and c2 was the 8th one I tried. I guess you call it an Allumwandlung as it uses all possible promotions.
Ian Shanahan: Seeing the name above the diagram, one expected the four promotions (AUW, here capture-free). The only blemish is the black king being initially in check, a necessary “trick” to force accurate move-order.

The key 1.Se7! concedes a flight on d4 and threatens a battery mate, 2.Rd6. This B + R battery opens twice more with 1…fxe3 2.Rg4 and 1…Rxd4 2.Re6. The e3-knight fires two batteries at once – directly with the e1-rook and indirectly with the f2-bishop – in 1…Sxe5 2.Sc4, and likewise in 1…Kxd4 2.S3f5 but the roles of the rear battery pieces are now reversed. There’s by-play with 1…Rxe7/Rd5 2.Qd5 and 1…Qxg6/Qf6/Qe6 2.Qxd3.

Jacob Hoover: With 1.Se7! White activates the B + R battery on the e4-h7 line to go with the R + S battery on the e-file.
Andy Sag: The key gives a flight and threatens a battery mate. The set half battery gives a strong clue. Four variations also involve battery mates, two with double-checks. Try 1.Sg7? Sxe5!
George Meldrum: The setting has enough clues for the savvy solver to find the key. Though the stylishness of the variations is just about enough to do your head in.
Ian Shanahan: Tremendous flight-giving key and a stunning variation after 1…Kxd4. Well constructed too. But very anachronistic for 1990: the Good Companions did this sort of thing, with even greater complexity, 70 years earlier.

The black king has two flights on d4 and e4, both unprovided. The sacrificial key 1.Sxf4! threatens 2.Sd3+ Qxd3 3.Qxe6. 1…Bxf4 leads to 2.Qxf6+ Ke4+ 3.Qe5 – a cross-check and pin-mate, and 2…Kd6 3.Qe7 – a switchback mate in which the h8-bishop controls e5 upon the removal of the f6-pawn by the queen. If 1…Qxf4 then 2.Qxe6+ Kd4+ 3.Qd6 – another cross-check and pin-mate, and here the e8-rook guards e4 thanks to the queen’s removal of the e6-bishop. And 1…Qe4 allows 2.Qxe6+ Kd4 3.Qc4, and again the e8-rook is activated, this time to cover e5. The flight moves 1…Kd4/Ke4 are answered by the knight threat but a different mate results: 2.Sd3+ Bf4 3.Rxf4. Three times the white queen captures a blocking unit and then opens a line for a white piece, acting as if it’s the front piece of an indirect battery.

Andy Sag: A great feast of pin-mates, cross-checks and indirect batteries.
Jacob Hoover: Indirect battery play in the threat. Direct battery plays by White and Black in the variations, and the white queen performs clearance moves.

Initially the black king has three flights, only one of which has a set mate (1…Kd4 2.Qd3). The key 1.Rb3! (waiting) grants a fourth flight on e6 and sacrifices the rook. 1…Ke6 2.Qf5, 1…Kc6 2.Qb7, and 1…Kd4 2.Qd3 together form the Y-flights pattern, while 1…Kc4 also permits 2.Qd3. The remaining variations are as set: 1…S~ 2.Qe4 and 1…c4 2.Qd7. There are plenty of plausible tries: 1.Rc3? (threat: 2.Qd7) Kc6!, 1.Re4? (2.Qd7/Qb7) Kc6!, 1.Qg6? (waiting) Kc4!, and 1.Qe7? (2.Qxc5) Kc6!

Jacob Hoover: The sacrificial key 1.Rb3! completes the block. This problem becomes easy to solve when one realizes that the white rook isn't actually needed to perform any of the set mates.
Andy Sag: Neat miniature with sacrificial key providing for two of the three set flights and adding a fourth. All queen mates from five squares.
George Meldrum: The rook move helps provide for the king flights to c4 and c6. Amazingly no extra solutions are found with so many queen moves to try.
Ian Shanahan: The two unprovided flights really flag the key, but the suite of resulting mates are fine. Theme: three-quarters of a star-flight. There are five distinct variations, in miniature – a form Lincoln used to call a “five bagger”! It's a shame the composer passed away recently.

The key 1.Kxe4!, by controlling d4, threatens mate with any opening of the R + S battery: 2.Sf~. Initially in a safe position, the white king has walked into ten possible checks, and all are met by different mates: 1…Qxe2+ 2.Se3, 1…Qd3+ 2.Sxd3, 1…Qc4+ 2.Qxc4, 1…Qxb4+ 2.Sd4, 1…Qxc6+ 2.Rxc6, 1…Sg3+ 2.Sxg3, 1…Sf2+ 2.Bxf2, 1…Sd6+ 2.Sxd6, 1…Re8+ 2.Se7, and 1…gxf5+ 2.Rxf5. Two non-checking defences prompt white mates already seen: 1…Rd1 2.Sd4 and 1…Rd8 2.Sd6. While the key-move provoking ten checks is impressive, the record for such a task is held by a two-mover by J. C. van Gool, in which the key enables 13 checks.

Andy Sag: The key creates an octuplet threat but invites no fewer than ten checks. Five threats are separated by black moves. Another five defend all threats.
Jacob Hoover: Incredibly, the key 1.Kxe4! invites an ungodly number of checks – ten, in fact! – to threaten a knight discovery on the fifth rank. Five of these checks force particular knight discoveries.
George Meldrum: This problem is one to just simply enjoy.
Ian Shanahan: The check-provoking key is ipso facto excellent, inducing many variations. My only regret is that not all eight threats are separately forced.

Andy Sag proposed to adapt the problem to separate all eight knight mates, and the best setting we came up with is diagrammed below. It accomplishes the knight-tour task, but at the cost of one of the thematic checking variations.

The same king move now walks into nine black checks, the missing one being 1…gxf5+. We gain three battery variations to complete the knight-tour: 1…Rg8 2.Sg7, 1…Rh8 2.Sh6, and 1…hxg2 2.Sh4. 

Typically in a series-selfmate, White finishes the sequence with a deflecting check that compels Black’s mating move. But here no such white checking move could be made to work, and instead White sets up a position in which the black mate is forced by zugzwang. First White promotes to a knight with the aim of blocking h7, which will cut off the black queen and give the white king access to h6: 1.e5 2.e6 3.e7 4.e8=S 5.Sc7 6.Se6 7.Sf8 8.Sh7 9.Kh6. White then use the remaining units to self-block on g5 and h5, and at the same time complete the confinement of the black king: 10.Bg5 11.e4 12.e5 13.e6 14.e7 15.e8=B 16.Bh5. And now Black has only two legal moves, either of which mates: 16…Qxg7/Qxh7.

Jacob Hoover: The idea of this problem is to restrict the movement of both kings and the queen as much as possible. The way to do this involves two underpromotions, one of which is an Excelsior.
Andy Sag: Promotions to queen or rook require the bishop to shield on f8, so any checking finale takes too many moves. A non-checking finale must confine the black king forcing the queen to move, so we have to look for a finale where the queen can mate from either g7 or h7. Checking avoidance by the promoted knight leaves only one route to h7, so well done Nigel!
Ian Shanahan: An elegant miniature with well-motivated move order, particularly in regard to the promoted knight’s wanderings. Whilst White’s non-checking final move is subtle, Black’s dualized mate is a weakness.
George Meldrum: Nigel’s problem is neat and concise, requiring a very methodical move order.

Two important set variations are 1…Se5 2.Bxb4 and 1…Sfd4 2.Re3. The thematic key 1.Rxb4! exposes the white king to numerous checks on the long diagonal, and threatens 2.Sd5/Se4 by guarding b3. 1…Se5+ results in a changed mate, 2.Re4, while 1…Scd4+ self-blocks and permits a different opening of the B + R battery: 2.Rb7. The remaining discovered checks by the c6-knight are handled by the threats, and in particular 1…Sxa5+ 2.Sd5 and 1…Sxb4+ 2.Se4 separate them. 1…Sfd4 2.Rb3 shows another change from the set play, and represents a third opening of the white battery. There’s by-play with 1…Sg7 2.Rxg3.

Andy Sag: The key creates a double-threat and sets up an additional battery which comes into play on three occasions, one being a switchback.
Jacob Hoover: Black defends by blocking the c3-h8 line. Two of these defenses (1…Se5 and 1…Scd4) fire the black battery on the long diagonal, a battery play which White counters with more battery play. A third knight defense (1…Sfd4) allows mate by a different double-check.
George Meldrum: The crisscross of play is amazing; the play after 1…Scd4/Se5 is insane.
Ian Shanahan: Cross-checks and batteries à la Mansfield. The key sets up a battery, at the same time opening a black battery directed at the white king. Then… fireworks. Beautiful!

The thematic try 1.Qb4? threatens 2.Qc3 (guarding d3, an unprovided flight). Three variations result: 1…Bd2 (opens the g3-rook’s line) 2.Qc5, 1…Sb5 (self-interference) 2.Qxc4, and 1…Kxd3 2.Qd2 (pin-mate), but 1…Re4! subtly refutes by shutting off the h1-bishop. The key 1.Qf3! threatens 2.Qxe3. A random move by the e3-bishop, 1…B~, enables 2.Qf6 – a changed mate with respect to 1…Bd2 in the virtual play. The correction 1…Bf4 is a self-interference that permits 2.Qe4 (or 1…Re4 2.Qxe4). The flight-move 1…Kxd3 produces a concurrent change, 2.Qd1 – still a pin-mate. Lastly, 1…Re7 is met by 2.Qd5. The correspondence between try and key is striking: the queen on the try-square b4 delivers various mates supported by the a5-bishop and a4-rook, and likewise on the key-square f3 the queen gives mates that require protection by the g3-rook and h1-bishop.

Andy Sag: The key provides for the flight-capture which results in a neat pin-mate.
Jacob Hoover: In all phases of play every mate (including threats) is performed by the queen, so we have the “girl power” theme here too.
Ian Shanahan: The unprovided flight-capture is a blemish, but the idea here – known as the Barnes I theme – is to position the white queen at the intersection point of a white bishop and rook, so it can move along their lines of guard, laterally and diagonally. The try's refutation took time to spot. The pin-mates after the flight are delicious.

The black king on its initial square has too many flights to be covered, so it needs to move to a more confined position. On d4 it could be mated by …Sxe6 – which opens the R + S indirect battery to control the c-file – if e3 is blocked by the queen. But after 1.Kd4?, White lacks a waiting move that would allow this plan to proceed. So Black plays the self-block 1.Qe3 first in order to free the white king to make a tempo move: 1…Kh2!, and then 2.Kd4 Sxe6. Similar tempo strategy occurs in the remaining three parts when the d3-pawn is shifted to other squares: (b) 1.Ra3 Kxf2! 2.Kb4 Sxa6, (c) 1.Rb7 Kg1! 2.Kb6 Sa8, and (d) 1.Se7 Kg3! 2.Kd6 Se8. The four black king moves form a star pattern, while the four white king moves produce a cross.

Andy Sag: Not a twin but a star quadruplet. In each case, Black prepares a self-block and simultaneously allows the white king a tempo move, then the black king moves allowing the c7-knight to mate using an indirect battery to confine the king.
Jacob Hoover: In each solution Black's first move is a distant self-block that also allows White to move the king (because that is the only way White can avoid messing up the configuration of the other pieces). The four white king moves form a king-cross and the four black king moves form a king-star. Very nice. I love it.
Ian Shanahan: Black king star-flight and white king cross. Excellent! Criticism: in each phase, there's a lot of idle ebony.
George Meldrum: The confinement of the white king is not immediately obvious to be part of the main play. The solutions are both amazing and funny at the same time.

In the diagram, Black’s only mobile unit is the d7-knight and any of its moves would allow 2.Qxc5. White has no way of maintaining this block position, however. The key 1.Qd8! (waiting) prepares an ambush behind that knight and unpins the other one on c5. Now 1…Sd~, besides unguarding b6, enables the queen to control d6 for 2.Sb6. The c5-knight yields two variations: the random move 1…Sc~ admits 2.Qg8 and the correction 1…Se6 prompts 2.Be4. Hence this is a mutate that effects one changed and two added mates.

Andy Sag: A complete block in a Meredith setting. The key unpins the c5-knight and changes the set mate.
Jacob Hoover: The c5-knight exhibits correction play; a random move of this knight loses control of the d5-g8 line while the correction move self-blocks.
George Meldrum: A clinical setting requiring a clinical approach to solving. Positives include: all new mates, delivered by queen, bishop, and knight, not just by the queen as in the set play; a nice key.
Ian Shanahan: A sweet mutate (with only one mate changed) after an unpinning key. The unpinned knight shows secondary black correction.

Random moves by the d4-rook, e7-pawn, and a5-queen lead to these respective mates: 2.Qg1, 2.Sf6, and 2.Qf5. Shifting the white bishop from f4 would threaten 2.Rf4, but White must choose its placement carefully. The first try 1.Bc1? is answered by 1…Rd2!, which cuts off the bishop’s control of f4 while still holding off 2.Qg1 (likewise 1.Bd2? Rxd2!). If 1.Be3? to avoid the black rook’s interception, then 1…Rxe4! refutes since the try-piece has obstructed the set 2.Qg1. The bishop’s try-moves along the other diagonal unguard g5, leaving the h7-knight and c5-queen to control that flight. Consequently, 1.Bh2?/Bb8?/Bc7? all fail to 1..e5! when the set 2.Sf6 no longer works. 1.Bg3? carries a second threat of 2.Rxh4, still playable after 1…e5 or 1…Rxe4, but this try is defeated by 1…hxg3! The last try 1.Be5? directly prevents 1…e5 but interferes with the white queen; now 1…Qd2! cannot be met by the set 2.Qf5. The key 1.Bd6! handles 1…e5 in a new way, by shutting off the black rook, so that 2.Qc8 becomes viable (a changed mate). The initial mate for 1…e5 is transferred to 1…exd6 2.Sf6. The remaining play proceeds as set: 1…Rxe4/Rxd6 2.Qg1 and 1…Qd2 2.Qf5.

Jacob Hoover: The key 1.Bd6! [compared with the tries] can be thought of as a “safety play,” even though it doesn't look so safe. XD
Nigel Nettheim: Nice variations, especially with the e7-pawn.
George Meldrum: A form art in the shape of a parallelogram is seen in the path of white queen as it moves to c8 and g1 and back to the black king. Other lines of play are just colouring in.
Ian Shanahan: It took a little while to work out exactly what the key-piece's destination-square was. A fine problem, with masked interferences.

The masked R + B battery on the first rank is only a ruse, and White’s only feasible plan is to use the rook to guard e2 for a bishop mate on that square. A rook try along the b-file, such as 1.Rb8?, is defeated by 1…Bb2!, when 2.Rxb2 stalemates while 2.Re8 fails to 2…Be5. The key 1.Rb4! waits for the black bishop to close a rook-line to e2, whereupon White attacks on that same line, and Black must re-open it due to zugzwang: 1…Bd2 2.Rb2 B~ 3.Be2, and 1…Be3 2.Re4 B~ 3.Be2. After 1…Bb2/Ba3, White plays 2.Re4 again and there’s no defence against 3.Be2. 

Thanks to Bob Meadley who points out that this problem appeared in the Australasian Chess Review in Forsyth notation only, because of its close resemblance to an earlier three-mover by Jan Smutny. See this article by Bob that features the Smutny precursor and an alternative version of the problem by O’Keefe: Languishing in Forsyth.

Jacob Hoover: In each of the main variations, White paradoxically plays to a line that Black has already blocked and such a play puts Black in zugzwang.
Bob Meadley: A nice three-mover showing the advantages of a rook over a bishop.
George Meldrum: The black king cannot be allowed to move which leads to the rook to be appointed to head the task. A neat interplay between the rook and black bishop.

The black king’s flight-moves to e3 and c2 are both provided, albeit with duals after 1…Kc2. Any white king move that unpins the e4-knight would threaten 2.Sf2, but 1.Kb5/Kb6? fails to either check on the b-file, while 1.Kc7/Kd7? is refuted by 1…Qh7+! Only 1.Kd6! solves – an excellent key that invites four checks. 1…Ke3+ 2.Bd2 (as set) and 1…Kc2+ 2.Bd4 (duals removed) activate the black royal battery on the d-file. 1…g2+ interferes with the h1-bishop, permitting another cross-check, 2.Sg3. And 1…Bxc5+ 2.Sxc5 shows a third opening of the B + S battery. The front pieces of the two white batteries are captured in the by-play: 1…Bxe4 2.Qxe4 and 1…bxc3 2.Raxc3.

Andy Sag: The key unpins the e4-knight but walks into four new checks, two answered by double-checks! I like the g-pawn acting like a valve to shut off the h1-bishop.
Jacob Hoover: Solving this one was rather fun for me (read: cross-checks, yay!). I consider the set-up diagram rather beautiful, because the white units are concentrated on one side of the board and the black units on the other.
Nigel Nettheim: Walking into four checks is great fun! The a1-knight prevents 1.Bc-various+, although a black a4-pawn could have been used instead.
George Meldrum: Stepping through the variations was like walking on water. A very high-quality problem but only gaining 5th Hon. Mention??
Ian Shanahan: A spectacular give-and-take key (unpinning a white piece, but walking into four checks) leads to a lot of cross-check fireworks. It's in typical “Good Companions” style. A fine work by a great problemist.

Three thematic defences, aimed at stopping the potential queen mate on f6, generate the set play, 1…Ra6 2.Qe4, 1…Rb6 2.Qd5, and 1…Bf5 2.Qxf5. Various tries threaten the queen mate and lead to the set variations, but are refuted similarly – 1.Rf1? Rf4!, 1.Sh5? Rf4!, and 1.h8=Q? Rf4! The key-move 1.Se4! (same threat) surprisingly disrupts all three set mates and replaces them thus: 1…Ra6 2.Bb2, 1…Rb6 2.Rc5, and 1…Bf5 2.Qg3. Two more variations complete the play: 1…Rxe4 2.Qxe4 and 1…f5 2.h8=Q.

Andy Sag: The key adds a second guard to d6 and shuts off the a4-rook. Three changed mates noted; how good is that!
Jacob Hoover: A plethora of queen mates is featured in the try 1.Sh5? The key disables the strong defense 1…Rf4 and changes most of the play.
George Meldrum: Centre of attention is on f6 with an array of ways White can focus extra pressure and the threat of mate. Black’s 1…Bf5 sets up the nicest of variations.
Ian Shanahan: Three changed-mates after a rather hard-to-spot key.

The diagram is solved by 1.Sd8 Se8 2.Ke6 Ke4 3.Sf7 Bf5. Part (b) with a black knight on e7 instead: 1.Se5+ Kd2 2.Kd4 Bd3 3.Sd5 Se6. And part (c) with a black bishop on c6: 1.Bb4 Kc2 2.Kc4 Se6 3.Bd5 Bd3. The three final positions are all ideal mates. The composer points out that in every solution, the kings make matching moves and each white piece moves exactly once; and further, in (b) and (c) White’s second and third moves are reciprocally changed. A lovely miniature.

Jacob Hoover: A few things each part has in common: (1) one king moves, then the other moves in the same direction; (2) the final position is an ideal mate. Also, in parts (b) and (c) each piece moves exactly once. All this in a very light setting (only six units on the board!). Nice.
Andy Sag: A very economical miniature triplet.

The thematic try 1.Rxc4? sets up a masked Q + R battery and threatens a pin-mate, 2.Rd4. The pinning defence 1…Rc5 allows 2.Rxc5, another pin-mate using the same battery. More virtual play occurs with 1…Rc6 (second pinning defence) 2.Bxc6 and 1…Se6 2.Rxf5, but 1…Sf3! refutes. The key 1.Bxf5! creates a masked R + B battery instead, and similar to the try, both the threat 2.Bxe4 and variation 1…Re6 2.Bxe6 show a pin-mate stemming from the battery. Two knight defences demonstrate dual avoidance: 1…Sc5 2.Qxc4 (not 2.Qd2+?) and 1…Sd2 2.Qxd2 (not 2.Qxc4+?). The try play and post-key play involve completely different defences and mates. Such a scheme is called (1) total change when the theme remains the same across the two phases – here masked batteries with pin-mates – and (2) radical change when the theme changes as well – here pinning defences vs. dual avoidance. So both types are effected in this classy two-mover. Note also how 1.Rxc4? Se6 2.Rxf5 and 1.Bxf5! Sc5 2.Qxc4 show reversed captures of the two black pawns and utilise the thematic queen and h5-rook in the phase where they don’t form the masked battery.

Composer: The masked batteries in the thematic try and solution show the Haring 2 Theme.
Andy Sag: The threat and one variation are pin-mates following the key. There are a number of tries, notably the thematic 1.Rxc4?, where the threat and one variation are also pin-mates.
Jacob Hoover: In the diagram, there are two half-pin setups, but there is no half-pin theme here. After the try 1.Rxc4?, two defenses use the e6 and c5 squares: 1…Se6 and 1…Rc5. After the key, defenses at e6 and c5 also appear, but different pieces move to these squares: 1…Re6 and 1…Sc5.
George Meldrum: First choice draws you to 1.Rxc4 which looks compelling but rebuffed. A smile for the clone solution conscious that Ian is sniggering knowing the trek he contrived.

The square-vacating key 1.Ba3! threatens 2.Rb4. Since the rook-check cuts off the bishop’s control of c5, Black can defend by shifting the knight from that potential flight-square. A random move by the piece self-pins the c6-rook: 1…S~ 2.Sd6. The knight has three correction moves that disable the secondary threat of 2.Sd6, but they provoke other mates: 1…Se4 (interferes with the h4-rook) 2.Qd4, 1…Sb7 (interferes with the queen) 2.Sxb6, and 1…Sd3 (self-block) 2.Qa2. The by-play repeats a queen mate: 1…Rd4 2.Qxd4. A well-constructed problem with no white pawns.

Andy Sag: All variations are set; quite easy to solve. The c6-rook is pinned when the knight moves.
Jacob Hoover: The threat is an anticipatory self-interference, so any move of the c5-knight defends due to giving the king a flight-square.
Ian Shanahan: Three nice corrections by the black knight, in ye olde style. The weakness is that the half-pin mechanism is “incomplete”: there are no variations involving the half-pinned rook, leading to a pin-mate with the knight pinned.
George Meldrum: Some nice variations, even if unconcealed.
Nigel Nettheim: Excellent key, excellent play; bravo!

The solution of part (a) is 1.Be4 Sc7 2.Kc5 Kc3 3.Bc6 Bd4. Replacing the f5-bishop with a black rook for (b) changes the play to 1.Rc5 Bd4 2.Kd5 Kd3 3.Rc6 Sf4. Two ideal-mates are shown in this neat miniature. The three white pieces make one move each per part, reversing the order in which they play in the two solutions. Although both black pieces starting on f5 self-block on c6, each block cannot go with the other mating pattern.

Composer: In each solution the black piece on f5 takes two moves to get to c6.
Andy Sag: In each case, a black piece moves, a white non-mating piece moves, both kings move, a black piece moves a second time to reach self-block position, and White mates.
Jacob Hoover: In (a) the knight guards empty squares in the king's field and the bishop mates, while in (b) the white knight and bishop swap roles. Interestingly enough, the rook in part (b) ends up on the same square that the black bishop in part (a) ended up on.
George Meldrum: OK, Geoff got me. I solved part (b) but spent a long, long time on the diagram position without finding a solution. A nice miniature setting, damn it!

Most initial moves by the white king would threaten 2.Bf4, but its placement must be chosen with care. 1.Ke4? is defeated by 1…Qe7!, which pins the bishop and prevents not only the threat but also 2.Bb2, the set mate for 1…Q~. 1.Kf5/Kg5? is similarly thwarted by 1…Qc5! And 1.Kg3? Qd6! sees a third pin of the bishop, this time on a diagonal. The last try 1.Kf3? obstructs a square needed by the e1-knight, so that the self-block 1…bxc2! cannot be answered by a battery mate. The key 1.Kg4! avoids the pins and obstruction: 1…Qb4/Qc5/Qd6/Qe7 2.Bb2 and 1…bxc2 2.Sf3. The original problem was published with a black rook on b2, which I removed because (1) its variation 1…Rxc2 2.Sf3 merely repeats the mate for 1…bxc2, and (2) either capture on c2 foils 1.Kf3?, which is thus lost as a try.

Andy Sag: All king moves besides the key are defeated, mostly by pins; if 1.Kf3? bxc2! (knight can't go to f3) and of course 1.Ke3? has no threat. Also 1.Bd4? and 1.Bc3? are defeated by 1…Qd6+.
Ian Shanahan: The white king has to be careful in choosing the correct destination.
Ata Karayel: The g2-pawn prevents 2.Sg2 after 1…bxc2. 1.Ke4? is countered with 1...Qe7!, an unsettling move.
George Meldrum: An innocuous looking first move providing clear play. The main complexity is demonstrating that other white king moves are not cooks.

A set line 1…R~ 2.Qxd6 is disrupted by the excellent key 1.Sg3!, which grants two flights and also sacrifices the knight to two black units. The threat is an indirect battery mate, 2.Se2. Captures of the knight permit a pair of queen mates on the long diagonal: 1…Bxg3 2.Qb2 and 1…hxg3 2.Qh8. A third mate on the same diagonal follows one flight-move, 1…Kc3 2.Bf6, while the other king move 1…Ke5 allows 2.Sxc6. All four variations are set up by the key-move (though the non-capturing 1…Bg3 2.Qb2 is prepared) in this clear problem with no by-play.

Andy Sag: The sacrificial key gives two flights. The g6-pawn prevents a dual with the threat if 1…Bc3 but seems to serve no other purpose and could be omitted.
Jacob Hoover: A thematic try is the knight sacrifice 1.Sc3? threatening both 2.Se2 and 2.Sb5. Black can take the knight three ways: 1…Bxc3/bxc3 2.Qf4 and 1…Kxc3 2.Bf6. Unfortunately, 1…Bg3! refutes.
Ata Karayel: Asking about the purpose of h4-pawn solved the problem for me.
George Meldrum: Two flight-squares conceded to the black king; new mates by the knights, bishop, and queen. There is a lot to like in this one.
Ian Shanahan: A sacrificial key giving two flights. Notice too the model mates (after 1…Bxg3 and 1…hxg3). Bravo! A fine problem.

The key 1.Rb8! concedes a flight on d5 and threatens 2.Sf4+ Kd7 3.Be8. Capturing the d5-knight is exploited as a clearance of the fifth rank in 1…Kxd5 2.Rb5+ (switchback) Ke6 3.Bf5, or 2…Kxc6 3.Be8. Taking the second flight leads to 1…Kd7 2.Bf5+ Kxc6 3.Se7, a model mate. The black rook defends by opening a bishop line to f4, but such moves unguard e4: 1…R~ 2.Re8+ Kxd5 3.Bxe4 – this bishop mate echoes the threat – or 2…Kd7 3.Sb8. Six good mid-board mates including the threat, even though only one is a model.

Andy Sag: The key provides for 1…Kd7 and adds a second flight. Nice variety of play. The position can be simplified a bit by omitting the c1-bishop, as 1…Rf3 is still a defence [subsequently the e2-pawn can also be removed since 1…Re2/Re1 no longer defends].
George Meldrum: The black king has a multiple white square bonanza. The heart and soul of this problem, for me, are the lines involving the knight being captured on d5.