Weekly Problems 2024-A

In the set play with White to move, …0-0 mates immediately. This pin-mate employs most of the white pieces, including the two knights on guarding duties, though the a1-rook is redundant. In the actual solution, Black cannot avoid capturing the g2-knight on the first move, thereby spoiling the set mate. Black thus organises another mate, one that utilises the a1-rook along the first rank, and this necessitates the surprising removal of two more white pieces. 1.Kxg2 2.Kxh1 3.Qg2 4.Sc3 5.Se2 6.Sxc1 7.Se2 8.Sd4 for 0-0-0. The change from short to long castling is well accomplished, along with a new pin-mate where a different black piece is immobilised by the white bishop.

Andy Sag: The set king-side castling mate cannot be preserved so Black uses the eight moves to unpin the knight, pin the queen and enable queen-side castling mate instead. Very cunning! Note the d3-pawn stops 1.Kxg2 2.Kxh1 3.Kg1 4.Sf2 Se2.
Nigel Nettheim: Brilliant! 3.Qg2 was, for me, the hard move to find, even though the mate was bound to be 0-0-0. Not 1.d2+? for 0-0 because castling out of check is illegal, a seldom-arising rule.
George Meldrum: An intriguing setting where White can provide mate in one by king-side castling.  Maintaining a castling theme a clear task, the scene does not disappoint.

Two checks by the white knight aren’t mates solely because they would cut off the g7-bishop or the c8-rook. White can threaten mate by shifting one of these line-pieces across the critical square, to avoid the interference. Most such anti-critical moves fail, however, because they cause their own obstructions with another white piece. 1.Bc3? (threat: 2.Sf6) is refuted by 1…Bh4! since 2.Qa5?? is prevented, and 1.Bb2? is countered by 1…Qg5! since 2.Qa2?? is disabled. Similarly, 1.Rc3? (2.Sc7) Bg3! and 1.Rc2? Qg3!, while 1.Rcc6? hinders the a6-rook instead of the queen, enabling 1…Se5! (creating a flight on d4) which cannot be exploited by 2.Rad6?? The key 1.Rc1! (2.Sc7) avoids the self-interferences and leaves the set variations intact. 1…Bg3 2.Qa5, 1…Qg3 2.Qa2, and 1…Se5 2.Rd6. The by-play 1…Bf3 2.Qxd3 gives the white queen an extra purpose.

Andy Sag: The tries show no square works for the bishop so it is a matter of finding a suitable square for the c-rook.
Jacob Hoover: Five tries exist, each of which involves anti-critical play but interferes with another white line-piece.
Nigel Nettheim: A number of good tries.
Andrew Buchanan: Quick to solve, but very clean with lots of nice tries.
Paz Einat: The scheme looks like a well-known Dombrovskis, but what we see is white self-interference tries with unified refutations. A good work of art.

An edge-mate is necessary given this minimal material, so the players coordinate to let the black king reach the first rank in three moves. Part (a) is solved by 1…Re2+ 2.Kd3 Re3+ 3.Kd2 Bf4 4.Kc1 Re1, where White arranges a B + R battery mate. Part (b) steers for a similar ideal-mate, but the roles of the two line-pieces are reversed, to create a R + B battery: 1…Rh2 2.Kd3 Rh1 3.Kd2 Bg1 4.Kc1 Be3. In part (c), the black king heads for the corner while White sets up a R + K battery: 1…Rd1 2.Kf3 Kd2 3.Kg2 Ke1 4.Kh1 Kf2. Hence three different types of battery mates are exemplified in this top-notch Wenigsteiner (a problem with no more than four units).

Andy Sag: In each case a different piece triggers the battery mate. Nice triplet.
Nigel Nettheim: Three different batteries are shown. The Hungarian statistician A. Kalotay (1941-) discusses this helpmate in an article named “Structural Aspects of Chess Problems”.
Jacob Hoover: Three excellent battery-forming maneuvers achieved with only four pieces! Amazing!

If White fires the B + S battery in one of three ways to force the king to d1, the same knight has a potential follow-up mate (currently guarded by a black unit), e.g. 1.Sa4+ Kd1 2.Sc3. Such a device, in which the knight gives a discovered check and then mates from a new direction (avoiding the interference on b2) is called a Siers battery. In the set play, this tactic occurs three times when each black defender – forced by zugzwang – unguards a mating square. 1…Se~ 2.Sa4+ Kd1 3.Sc3, 1…Sf~ 2.Sc4+ Kd1 3.Se3, and 1…g2 2.Sd3+ Kd1 3.Sf2. White aims to preserve these variations by making a pure waiting move with one of the pawns, but three of these moves would block a square needed by the white knight: 1.c3? Se~!, 1.c4? Sf~!, and 1.d3? g2! (although 1.c3? and 1.c4? are refuted by multiple moves, they are tries in spirit!). White therefore must start with 1.d4!, which avoids all the hindrances and keeps the set play unchanged. A very neat combination of Siers battery play and square-obstructing tries, all shown in a Meredith setting.

Andy Sag: There are set mating lines for all black moves with the b2-knight mating on three different squares. In this case White plays a move preserving these lines. An additional try is 1.Ka2? Sc3+!
Nigel Nettheim: We look for a first move that does not harm the set mates. Easy to solve, but nice.
Bob Meadley: Nice little three-mover.

Each of the white knights takes two moves to arrange a check, but most of the eight potential mating squares are well guarded by Black, while a check on f5 would cut off the white rook. Only e6 seems unprotected, except that when either knight moves, it opens a line of defence for the c4-queen or the e3-rook. To offset this effect, Black employs the e6-knight to close the line again, by placing it on the square just vacated by the white piece. 1.Sc7 Sf4 2.Sd5 Se6 and 1.Sc5 Sg5 2.Se4 Se6. Ironically, the mating square becomes doubly protected by Black after White’s first move. The third solution involves a white promotion, and yet it matches the other two parts precisely, with the black knight closing a line of guard to e6 that White has initially opened. 1.Sd8 f8=S 2.Sf7 Se6. A bi-coloured platzwechsel – exchange of places between a white and a black unit – is presented three times.

Andy Sag: The three solutions are thematically coordinated. Each uses a different knight (two original, one promoted) to mate on e6. Also, in each case, the black knight moves twice to interfere with Black’s guard on e6.
Jacob Hoover: In each solution the black knight switches places with a white unit and in doing so interferes with a black line piece. Also, the black knight move is chosen carefully in order to avoid giving check.
Nigel Nettheim: Marvellous. Black uses a jumping piece (S) to interfere with the action of the line pieces (Q, R, B). The d6-pawn prevents White’s 1…f8=Q followed by 2.Qb4 Qxb4.

White’s seventeen moves are largely visible in the diagram, including a 7-move trek by the rook via the h8-corner. This trip involves the sweeping move Rh8-d8, which means that Black will need to clear that line of all pieces at some point, before returning them to their home squares. Black has made three pawn moves, while the h8-rook needs four (Rh6-f6-h6-h8) to open a path for the white rook. The remaining four pieces from d8 to g8 require a minimum of eight moves for each to make a switchback, leaving two spare moves out of the seventeen total. 1.a4 h5 2.Ra3 Rh6 3.Rg3 Rf6 4.Rg6 e6 5.Rh6. Suppose Black develops the bishop to the queen-side with 5…Bc5, then 6.Rh8 Rh6 7.b3 Qg5 8.Bb2 Ke7 9.Bd4 Sf6 10.Rd8 results in a gridlock, because Black is forced to play …d6 soon to allow Rd7+ Ke8, but that leaves the c5-bishop stranded. So Black develops the bishop to the king-side instead, making use of the two spare moves. 5…Be7 6.Rh8 Rh6 7.b3 Bh4 8.Bb2 Qg5 9.Bd4 Ke7 10.Sc3 Sf6 11.Rd8 d6 12.Rd7+ Ke8 13.Sd5 Sg8 14.c3 Qd8 15.Qc2 Be7 16.h4 Bf8 17.Se7 Rh8. Five switchback manoeuvres arise from an attractive problem position (homebase set-up for the black pieces), with the unusual feature that no captures occur at all.

Andy Sag: The white rook takes seven moves to get from a1 to d7 leaving no spare moves. However Black has two spare moves; the trick is to find out how to use them.
Jacob Hoover: The sequence features a bi-colored Turton between the rooks and a Bristol maneuver with the black bishop and queen.
Nigel Nettheim: Each side’s moves were fairly clear, but the intertwining of them had many nuances. It seems amazing to me that the whole scheme works soundly. Back-rank switchbacks are shown here on the K-side, raising the question whether something similar could be shown on the Q-side.

Black’s queen and a5-bishop are preventing a pair of knight mates on c5 and c3, while the black rooks are stopping another pair on f2 and g3. White induces Black to weaken these guards after the key 1.Rd5!, which threatens 2.Re5+ fxe5 3.Qxe5. This queen mate relies on the pins of both black knights, so Black can defend by unpinning either piece. After 1…Qb4, the queen keeps protecting c5 but by taking over the bishop’s duty in observing c3, it becomes overloaded: 2.Sc3+ Qxc3 3.Sxc5. Similarly, 1…Bb4 maintains control of c3 but interferes with the queen’s guard of c5: 2.Sxc5+ Bxc5 3.Sc3. Such a mutual interference between two defenders that act on the same kind of line (diagonal or orthogonal), and becoming overloaded in turn, is termed a Wurzburg-Plachutta. The two black rooks bring about the same idea on g2 when they try to free the other knight. 1…Rhg2 2.Sg3+ Rxg3 3.Sxf2, and 1…Rgg2 2.Sxf2+ Rxf2 3.Sg3. A doubling of the Wurzburg-Plachutta theme is complemented by matching unpins on diagonal/orthogonal lines and two pairs of knight mates, all of which combine to create a harmonious, helpmate-like impression.

Andy Sag: The pinned black knights give a strong clue. Unpinning defences lead to four different knight mates.
George Meldrum: Nice problem with lots of tries.
Nigel Nettheim: The theme is the triple-negative “unsuccessful unpinning defence” x 4.
Jacob Hoover: Four unpinning defenses exist in two Wurzburg-Plachutta pairs. This was an easy solve, but a rewarding one nonetheless.

The four white squares next to the black king are not defended and the white queen can potentially mate on any of them. Three thematic tries and the key by the queen threaten different pairs of mates on these squares. After 1.Qa6? (2.Qc4 [A], 2.Qd3 [B]), both threats are stoppable by 1…Sb2, but this move interferes with the b1-rook and enables 2.Sxb3. Black defeats the try with 1…Qf1! The second try 1.Qh7? (2.Qd3 [B], 2.Qe4 [C]) provokes another knight defence, 1…Sf2, which cuts off the h2-rook and allows 2.Se2. The black queen now refutes by 1…Qe3! The last try 1.Qb7? (2.Qe4 [C], 2.Qd5 [D]) leads to 1…Sc3 2.Qb4, when the knight obstructs the d2-bishop. Yet another queen defence defuses the threats, however: 1…Qg2! Correct is 1.Qf7! (2.Qd5 [D], 2.Qc4 [A]), and here the knight closes a different line controlled by the d2-bishop: 1…Se3 2.Qf4. The black queen can only separate the threats with 1…Qf1 2.Qd5 and 1…Qg2 2.Qc4. The active white queen produces an AB-BC-CD-DA cycle of threats in four phases, while the black knight causes a different interference in every part. That’s already a lovely blend of themes, but we also see a white queen vs black queen duel in how the tries are handled.

Andy Sag: I was almost fooled by the try 1.Qh7 until I realised that 1…Qe3 pins the e5-rook to stop 2.Rd5 mate.
George Meldrum: Particularly nice is the mirror image to the actual solution with 1.Qb7, again with a double threat and a mirror response to 1…Sc3: 2.Qb4. Other tries of 1.Qa6 and 1.Qh7 are worthy of note. (The knight on h1 is needed for 1.Qb7 to be listed as a ‘try’).
Paz Einat: Quadruple cycle of double threats, nicely done.

Two strong checks by Black in the initial position are provided with knight responses: 1…Ra2+ 2.Sa4+ Rxa4 and 1…Qh1+ 2.Sd5+ Qxd5. White needs to create a threat and a plausible one is 2.Rb8+, which would force 2…Rxb8 if not for 2…Kc7. So White starts by covering c7 with the queen, though 1.Qc4? is too direct and it’s refuted by 1…Rxc8+! or 1…Qh1+! The key 1.Qf7! observes not only c7 but also a7 and b7 (besides unguarding b5), with the result that the set knight replies to the black checks no longer work. White counters these defences in new ways with 1…Ra2+ 2.Qa7+ Rxa7 and 1…Qh1+ Qb7+ Qxb7. If 1…Rg~file, the threat move 2.Rb8+ is still effective to induce 2…Qxb8. One pair of cross-checks by the knight in the set play is deftly changed to another pair by the queen after the key.

Andy Sag: Easy enough to solve with technically three “variations” and a short mate (1…Rxc8).
Andrew Buchanan: Well I solved it very quickly. Two changed mates.
Nigel Nettheim: The long moves are attractive.
Jacob Hoover: Very nice. Changed mates across two phases, with no distracting by-play. Now, if only there were a try which featured even more changed mates…

The very light position suggests uncomplicated play, but it’s tricky to find a suitable mating square for the black king. In one solution, the king heads for g8 to prepare for a rook mate on the top rank, a plan that requires removing the h5-bishop and self-blocking f7 with the rook. 1.Rxh5 2.Rf5 3.Rf3 4.Kb3 5.Kc4 6.Kd5 7.Ke6 8.Kf7 9.Kg8 10.Rf7 Rh8. In the other solution, the king goes to h7 to enable a battery mate on the h-file. After 1.Rg5 2.Rg3, the king would take eight moves to reach h7 via g5, but that’s too slow since another move is needed by the rook to unguard the mating piece. Instead, the king takes a shorter route by capturing the d4-bishop, which makes g7 accessible; then that square can be blocked by the rook as it makes the unguarding move. 3.Kb3 4.Kc4 5.Kxd4 6.Ke5 7.Kf6  8.Kg7 9.Kh7 10.Rg7 Bf7. The captures of the bishops are especially devious in view of the slender white force, and both parts finish with model mates.

Andy Sag: In each case a bishop must be removed before the black rook moves to a self-block position, but it took me a while to see that the king, not the rook, must capture the d4-bishop to avoid losing a tempo.
George Meldrum: The solution with the black king on h7 was the easy one, then being frustrated with finding a second solution I finally worked on the assumption that the answer must include the other bishop capture to create a theme. At that point, the pathway fell into place. Very nice problem.

The white queen can threaten a few short mates along various lines, but such attempts fail: 1.Qd4? (2.Qe3) Ba7!, 1.Qc3? (2.d3/d4) d4/Bd3!, and 1.d3? (2.Qc3) d4! The key 1.Qa1! unpins the e4-bishop and involves a full-length threat, 2.Bc2+ Ke2 3.Qd1. Black’s main defence 1…Bb1 is a critical move that passes over d3, a potential interference square. Now 2.d3? would threaten both 3.Qc3 and 3.Qe5 – the latter because the black bishop is cut off from the e-file – but 2…d4! refutes again. White plays 2.d4 instead with a single threat, 3.Qc3, after blocking the queen from e5. Black’s only counter is 2…cxd3 e.p., which carries two weaknesses; the move interferes with the black bishop and re-opens the long diagonal for the queen, permitting 3.Qe5. Here the en passant move demonstrates two peculiar line-effects that are not possible in any other types of captures: (1) the capturer lands on an empty square and closes a line that’s previously open, and (2) the captive’s removal immediately opens a line that isn’t blocked by the capturer. There’s by-play with 1…Ra7/Rb7 2.Sxh4 (threat: 3.Sg2) Bxf3 3.Sxf3.

This version of a three-mover by Weenink was sent by Rauf Aliovsadzade, who found the original in Brian Harley’s Mate in Three Moves. He writes: “In the main variation, a black interference caused by an en passant capture leads to a switchback mate. Somehow, a second threat [2.fxe4 followed by a Q + B battery mate] isn’t mentioned in the book, and there is only one variation. In the offered version, the threat is unique, and another variation is added.”

Andy Sag: If Black uses the e.p. defence, the bishop is blocked from returning to e4 after the queen switchback to e5. I like that!
Nigel Nettheim: The key is quite good. The theme is “crossing a critical square”, the white queen crossing d4 (avoiding 1.d3? d4!), and similarly the black bishop crossing d3 (1…Bb1 2.d4 cxd3 3.Qe5).
Karel Hursky: The trickiest ever switchback I have ever seen.
George Meldrum: For me, this problem rotates around the superb en passant line.

Each white grasshopper needs two moves to travel to a mating square, one that exploits a pawn on the third rank as a hurdle. Meanwhile the black grasshoppers must block two squares that are accessible to their king, e1 and f1. The two solutions are 1.Gxe1 Gh3 2.Gf1 Gf5 and 1.Gxf1 Gb4 2.Ge1 Gh4. Since the white grasshoppers exchange their roles as the mating piece and the captive, the Zilahi theme is realised. Besides an AB-BA reversal of black moves in the two parts, we also see the Umnov effect, when a black piece occupies a square that was just vacated by a white one. Excellent analogy between the two phases, including a nice touch in geometry: each white grasshopper ends up on the opposite side of the black king, forming an orthogonal/diagonal line with its initial square. This fairy problem represents a significant improvement on Jacob’s own Weekly Problem No.422.

Composer: I took another look at my fairy helpmate-in-2 and changed it a little so that the thematic content is more exciting.
George Meldrum: Easy to solve but fascinating how Black’s moves are swapped around in the two solutions.

Black has three line-pieces targeting the e4-pawn, and if any of them captures it, the piece would become pinned by the white rook. Such immediate captures produce the set play, 1…Qxe4 2.Sc6, 1…Rxe4 2.Se6, and 1…Bxe4 2.Sc2, where each white mate exploits the pin. The key 1.Sc4! attacks e3 and e5 so that 2.Qe3 is threatened, but the knight has also removed the white bishop’s control of d5, such that capturing the e4-pawn would give the king an escape square and stop the threat. The set replies to these captures no longer function, however, again because of the d5-flight (in two cases). White must find new ways to take advantage of the self-pins: 1…Qxe4 2.Qd6, 1…Rxe4 2.Qe5, and 1…Bxe4 2.Qd3. Three prepared pin-mates carried out by the knights are superbly changed to another three executed by the queen. The by-play 1…Qb8 2.Sc6 cleverly ensures that the d8-knight, which is essential for the set play, doesn’t become idle after the key.

Andy Sag: Theme is pin mates after various pieces capture the e4-pawn.
Nigel Nettheim: The theme is self-pinning defence. The key gives up control of d5 (after e4 is captured), but takes control of e3 and e5.
Jacob Hoover: The thematic set mates involve the e4-pawn and pin-mates. The key 1.Sc4! completely abandons this play; then the black self-pinning moves recur as defenses, with queen mates as the white responses this time.
George Meldrum: Cool changed mates, nice.

The black king has two escape routes, Ke3-f2 and Kc4-b3, besides the option of returning to d3 after each initial move. Handling all of these possibilities will require white queening, though which pawn to promote depends on the route chosen by Black. The key 1.f4! (waiting) enables a long-range move by the a8-bishop, one that will clear a path for the prospective queen. 1…Ke3 2.Bh1 Kf2 3.a8=Q Kg1/Kf1 4.Qg2, or 3…Ke3 4.Qf3. An immediate king switchback yields 2…Kd3 3.a8=Q Kc4 4.Qd5, or 3…Ke3 4.Qf3. After 1…Kc4, it is the other bishop’s turn to make a clearance move. 2.Ba1 Kb3 3.h8=Q Kxa3/Ka2 4.Qb2, or 3…Kc4 4.Qc3. A king switchback now brings 2…Kd3 3.h8=Q Ke3 4.Qd4, or 3…Kc4 4.Qc3; compared with the earlier 2…Kd3 variation, two pairs of changed mates (delivered by different queens) effectively occur against 3…Ke3 and 3…Kc4. Overall, two maximum-length Bristol clearances lead to a splendid variety of non-symmetrical queen mates.

Bob Meadley writes that he owns a copy of Problemkunst im 20. Jahrhundert: Ausgewählte Schachaufgaben (1957) [Problem Art in the 20th Century: Selected Chess Problems], authored by the two composers of the present four-mover. Found in this book is their own comment on the problem (Google Translated from German): “The double setting of the bishop-queen opening with the two promoting pawns on a7 and h7 is a theme that we only succeeded in resolving after years of effort.”

Andy Sag: The key leaves both white bishops clear long diagonals and two legal moves for Black. Depending on Black’s move White does a Bristol with the correct bishop followed by promotion to queen which mates next. No escape for Black.
George Meldrum: Amazing how there are no short mates (that I noticed). Remarkable overall.

In this complete block position, queen mates are arranged for all possible black moves, 1…Bf~ 2.Qa2, 1…Bh~ 2.Qh7, and 1…cP~ 2.Qb8. Two aggressive tries by the queen threaten one of the set mates immediately, but fail to a subtle defence: 1.Qxf2? (2.Qa2) c5! and 1.Qxh3? (2.Qh7) Bh4! Two other tries involve knight threats: 1.Kxf6? guards g7 (2.Sh6/Se7) Bh4+! and 1.Sf7? (2.S7h6) Be3! In the latter, Black exploits how the knight on f7 closes the queen’s mating diagonal. Alternatively, White may aim to preserve the block position by making a waiting move with the king, but three such attempts similarly shut a queen mating line: 1.Ke6? Bf~! and 1.Kd8/Ke8? cP~! Only the key 1.Kd7! succeeds in not disturbing the set play. Besides an abundance of tries, the three variations are well unified by the gate-opening defences (Black opens a line traversed by the mating piece) and the long-range queen mates.

Composer: After all threats fail, there is one move that preserves all set mates resulting in a waiter with three widely separated queen mate variations and nine tries (four significant) threatening the set mates, five additional queen mates on the same lines and three knight mates.
Andrew Buchanan: I think it’s a fun problem with the white king having a unique square for a tempo move.
Bob Meadley: It is clear that the waiter mustn’t disturb the mates and the white king, so useless in most games, retreats after saying hello to his rival.

To help achieve stalemate, the black knights need to be captured, as they can’t be immobilised. Their removal will release two pairs of rook-and-pawn, and the most efficient way to confine them again is to shift each rook to the knight’s starting square followed by a bishop promotion in the corner. This scheme uses up four moves, leaving just one spare for a knight. The other knight must be captured on its initial square, and it would take the white knight three moves to reach b1 (faster than g1), meaning the g1-knight should sacrifice itself on f3 to the white king. 1.Sf3 Se4 2.Rg1 Sc3 3.h1=B Sxb1 4.Rxb1 Ke4 5.a1=B Kxf3. Surprisingly, the white knight gets captured as well. The charming “pseudo-homebase” diagram also exemplifies Dark Doings, a setting that comprises maximum black and minimum white forces.

Andy Sag: Immobilising the rooks and sub-promoting the outside pawns needs four moves so one black knight must be captured in-situ. Not difficult once you realise that the black pieces are not in their original positions!
Jacob Hoover: As more-mover helpstalemates go, this one was pretty easy.
Andrew Buchanan: Very simple but fun composition by a composer who I have a lot of affection for.

White has to provide for 1…Kg7, and if the king on f4 gets out of the way, a queen mate on h6 would follow the flight-move. Thus 1.Ke5! (threat: 2.Qxh6), a brilliant key that not only unpins the d4-knight but also exposes the white king to multiple checks. After 1…f6+, 2.Kxf6 threatens 3.Qxh6 again, leading to 2…Sf5 3.Kxf5. If 1…cxd6+, then not 2.Kf6? Sf5!, but 2.Kxd6 re-pins the knight and 3.Qxh6 is unstoppable. The knight checks 1…Sf3/Sc6+ enable White to fire the B + K battery immediately: 2.Kd5+ Sd4/Se5 3.Qxh6, or 2…f6 3.Qxh6/Bxf6. There’s a subtle difference between 1…Sf3+ and 1…Sc6+ in how Black punishes the wrong continuations by White. After 1…Sf3+, not 2.Kf6? Sd2? 3.Kxf7, but 2…Sg5!, whereas after 1…Sc6+, not 2.Kf6? Sd8! The refutations are the same, though, in 1…Sf3/Sc6+ 2.Kf5+? Sd4+! The black knight has one non-checking defence, 1…Sf5, which allows 2.Kxf5+ f6 3.Qxh6/Bxf6. The hard-working white king makes the thematic key, plays four different second moves (each chosen precisely), and even delivers a battery mate or two.

Andy Sag: The key unpins the d4-knight and invites four checks but threatens a short mate. Easier than usual for LM problems.
Jacob Hoover: The key invites four checks. Quite easy to solve.

Black’s king has two legal moves only, both capturing white pieces, while the b1-bishop wants to stay put to avoid giving a disruptive check. In the set plays, White starts by attacking d4, a potential flight-square for the king after its move. 1…Bc3+ [A] 2.Kxc4 Rc7 [B] and 1…Rf4+ [C] 2.Kxe5 Bc7 [D]. In the actual solutions, Black has no waiting move capable of preserving the set lines, and must capture immediately. White answers by checking Black, similarly to control a potential flight when the king moves again. 1.Kxc4 Rc7+ [B] 2.Kd4 Bc3 [A] and 1.Kxe5 Bc7+ [D] 2.Ke4 Rf4 [C]. Curiously, White plays the same two pairs of moves as those seen in the set lines, but their orders are reversed (AB-BA and CD-DC). Thus every move by the a5-bishop and f7-rook recurs while changing its functions between guarding and mating. The four mating configurations show pleasing diagonal-orthogonal echoes, with the king finishing on different squares throughout.

Andy Sag: Strange pattern where flight captures in the solutions are followed by checks from c7 then mates from f4 and c3, but are preceded in set play by checks from f4 and c3 and followed by mates from c7.
George Meldrum: It is mind blowing how White’s moves are transversed between set play and solution.

Black’s pawns on the middle files, regardless of where they originated, made a minimum of five moves, including two captures. The other black units used up the remaining nine moves to reach their diagram squares, so the two missing pawns were captured without moving at all. White is missing the a- and h-pawns, which must have promoted in order to be captured near the centre; consistent with the removal of two stationary black pawns, these white ones played axb7 and hxg7. Black therefore cannot start with the obstructive …a5/h5?; closing the sixth rank with an early …d6/e6/Sf6? would also fail, by blocking the h-rook’s path to c6. 1.h4 e5 2.h5 e4 3.h6 e3 4.hxg7 h5 5.a4 Rh6 6.a5 Rc6 7.a6 Sf6 8.axb7 a5. Both white pawns must promote to a queen, the only type of piece able to sacrifice itself on d6 or e6 in just two moves. 9.g8=Q a4 10.Qg3. Not 10.Qg4? Ra5 11.Qe6+ dxe6 and White cannot proceed. 10…Ra5 11.Qd6 Sa6 12.b8=Q cxd6 13.Qb3 Qc7 14.Qe6+ dxe6. The second solution begins with 1.a4 and it leads to plenty of changes. 1…e5 2.a5 e4 3.a6 e3 4.axb7 a5 5.h4 a4 6.h5 Ra5 7.h6 Sa6 8.hxg7 h5 9.b8=Q Rh6. Thus far, the changes consist of switching the order of many moves, and so we might expect the b8-queen to be captured on e6 as in the first solution, but 10.Qb3? Rc6 11.Qe6+ dxe6 and White is stuck. Instead, a new move is needed – 10.Qb4, which allows Black to (again) capture on d6 first. 10…Rc6 11.Qd6 Sf6 12.g8=Q cxd6 13.Qg4 Qc7 14.Qe6+ dxe6. The Ceriani-Frolkin theme is brought about when a promoted piece gets captured, and here it’s not only shown twice in each solution, but the two parts produce a reciprocal change of capture squares for the two queens involved.

Andy Sag: The main issue is to figure out where the e3-pawn came from. In any case at least three moves are needed to get it there. It is soon clear that the white a- and h-pawns must promote and then be captured and that neither side has any spare moves.
Jacob Hoover: I really loved the great analogy between the two solutions, as well as the interesting way in which the move orders were forced. No wonder this problem tied for first prize!

The key 1.Bf2!, by unguarding f4, threatens 2.Rxf4+ Rxf4, a triple pin-mate – i.e. a mate that depends on the pins of the e5-queen, d3-bishop, and c3-knight. Black can defuse the threat by unpinning any of these pieces, though the knight can’t be released and so it’s not a thematic piece as such. If the black queen frees the white one with a random move, 1…Q~, then White takes advantage of the unpin with 2.Qe2+ Sxe2. The correction move 1…Qe8 prepares for 2.Qe2+? Qxe2!, but now 2.Qe4+ provokes 2…Qxe4. One more defence by the queen, 1…Qf6, avoids unpinning the white piece altogether; however, by cutting off the f7-rook, it enables 2.Rg3+ fxg3, a triple pin-mate similar to the threat. If Black releases the d3-bishop with a random 1…Rd~, then 2.Be2+ Sxe2 likewise exploits the unpin. The correction 1…Re1 ensures that 2.Be2+? would fail to 2…Rxe2!, but 2.Be4+ brings 2…Rxe4. The four main variations demonstrate black correction play, along with an exchange of functions between the white queen and bishop, which alternate between sacrificing themselves on e2/e4 and staying pinned for the double pin-mates.

Andy Sag: Unusual to see so many variations in a selfmate.

In the initial position, three black units are preventing mates as follows: the c2-knight stops a knight mate on d4, the d3-pawn ensures that Rxe3 is not a double-check, and the queen controls the B + R battery directly. The white queen has five plausible moves that threaten mate on d5, but four of them interfere with another white piece – a weakness that’s exploited by each of the aforementioned defenders as well as the black king itself. 1.Qd4? obstructs the knight’s mating square and it's thwarted by 1…Sb4! After 1.Qe4?, which blocks the rook along the e-file, Black can safely play 1…d2! to open a diagonal for the f1-bishop. 1.Qd6? creates a flight on c4 that’s handled by 1..Kc4 2.Re4, but since the rook is denied access to c6, there’s no answer to 1…Qa8! (1…Qd8 2.Re~). The last try 1.Qe5? closes the e-file again, and it leads to a changed mate, 1…d2 2.Qc3; but now 1…Kc4! refutes. Only 1.Qg5! – a fine withdrawal key – manages to avoid all of the interferences. 1…Sb4 2.Sd4, 1…d2 2.Rxe3, 1…Qa8 2.Rc6, 1…Qd8 2.Rd6, and 1…Kc4 2.Re4. While multiple self-obstructing tries by a white unit are a well-known theme, it’s rarely implemented with the strongest piece, a queen.

Andy Sag: Flight-giving key with threat, five defensive variations and many thematic tries. Very nice!

A non-thematic try, 1.fxe7? with multiple threats, is refuted by 1…Bg7! The key 1.Qh1! sets up a half-battery on the long diagonal and threatens 2.Rxe3+ fxe3 3.Kxg3. Only the black knight is able to stop this threat, and each of its two defences results in an anticipatory interference with the b5-rook. After 1…Se5, 2.Qh5 entails a double-threat, 3.Qxe5/Qf5, that cannot be handled by 2…Rxd5, since the knight has cut off the fifth rank and 3.Qf5 remains viable. The threats are also separated in 2…S~ 3.Qf5 and 2…e6/Be6/Bh7 3.Qxe5. Black prevents both threats with 2…Sxg4, but that permits 3.Qg6 instead. White avoids 2.Qd1?, which is defeated by 2…Rxd5! Analogous play follows 1…Sd4 when 2.Qd1 threatens 3.Qxd4/Qd3, and since the knight has closed the d-file, 2…Rxd5 doesn’t cover 3.Qd3. 2…e5 is also met by 3.Qd3, though 3.Qxd4 is not uniquely forced by any black move. The knight again has a counter against both threats, 2…Sxe2, which is answered by 3.Qc2. This time, 2.Qh5? fails to 2…Rxd5! The white queen starts with a corner-to-corner key and proceeds to mate on seven different squares (including the main threat), while carefully exploiting Black’s subtle interferences.

Andy Sag: Key sets up a deadly diagonal half-battery threat line. The two defensive lines feature matching play, double threats and diagonal queen mates. Quite artistic!
George Meldrum: Nice solution with an appealing pair of matching variations.

The black king has four flight-squares on e4, c2, d2, and c4, of which the first two will be covered by the eventual B + K battery mate. White’s knights and c5-bishop control three more squares next to the king, and these officers are able to make a two-move manoeuvre to observe d2 while unguarding and re-guarding their respective squares. When White executes each of these manoeuvres, that opens a line for a different black piece – the queen, a7-rook, or d6-rook – to reach and block the remaining flight on c4. Finally, the self-blocking black piece relinquishes control of a square accessible to the white king, which then fires the battery accordingly. 1…Se3 2.Qe6 Sf1 3.Qc4 Kxh5, 1…Sc3 2.Ra4 Sb1 3.Rc4 Kxf7, and 1…Bb4 2.Rxc6 Bc3 3.Rc4 Kxf6. An attractive problem with three harmonious parts that involve good interplay between the two sides.

Andy Sag: In each case a white piece moves twice to ensure all four black squares adjacent to the black king are guarded. Meanwhile a black piece also moves twice to block c4 and leave a piece adjacent to the white king unguarded, enabling a battery mate by the h7-bishop. First prize well deserved for good coordination of solutions.
Jacob Hoover: The three solutions all involve a different way for White to “clear the path” for Black. Nice one, indeed.
George Meldrum: A very nice set of solutions.

The key 1.Be1! (waiting) releases the queen from the task of protecting the c3-pawn. Since White cannot afford to let the king escape to the d-file, the queen still needs to maintain control of d3 and d5 while navigating to a mating square. Two such manoeuvres are possible, both aiming for a mate on e4, but depending on where the f7-pawn goes, only one is viable. 1…f6 2.Qd1 f5 3.Qf3 f4 4.Qe4; not 2.Qd7? f5 3.Qxf5 stalemate. 1…f5 2.Qd7 f4 3.Qf5 f3 4.Qe4; not 2.Qd1? f4 3.Qf3 stalemate. A fine differentiation of the two queen routes, based on stalemate avoidance. On a technical note, the key is a pure waiting move that does not threaten 2.Qd1?, because of 2…f6! 3.Qf3 f5 when the humble black pawn defuses the threat on e4.

Andy Sag: The key provides a guard on c3, freeing up the queen who must then find a way to get to e4 whilst keeping the black king immobile and avoiding capturing or blocking the f-pawn in this miniature two-liner.
George Meldrum: Neat in structure but somewhat easy to solve.
Bob Meadley: My my, what a composer is VC; clever fellow who can make such a beautiful problem with few pieces.
Jacob Hoover: To think that such a great stalemate-avoidance problem could be achieved with only seven units. Amazing!

To force the eventual selfmate, the limited white force must not only self-block the white king but also restrict the mobility of the black one. For instance, White might promote the b- and c-pawns, using one promotee to block a2 and the other (a queen) to capture the black units on e5, e4, and h3, to aim for Qc3+ Qxc3; but the mate isn’t forced as the black king could escape to d1 or e2. The solution involves a similar plan, the main differences being that the white king is mated on b4 and three promotions are needed, with two promotees blocking a4 and b5 while also serving to guard d1 and e2. 1.b6 2.b7 3.b8=Q 4.Qxe5 5.Qxa5 6.Qb5 7.a5 8.a6 9.a7 10.a8=Q 11.Qxe4 12.Qea4 13.Kb4 14.c4 15.c5 16.c6 17.c7 18. c8=Q 19.Qxh3 20.Qc3+ Qxc3. All three pawns promote to a queen and, remarkably, execute a rundlauf by returning to their starting squares in the diagram.

Andy Sag: The mating scenario is easy enough to identify but all three pawns had to be promoted to queens to get it down to 20 moves. Clever how the king move has to be delayed until after one queen gets to a4 but must move before the c-pawn can go.
Jacob Hoover: The final position, an ideal mate (what else would you expect from a publication called Ideal-Mate Review?), is the diagonal analogue of the epaulette mate. Very stylish.
George Meldrum: Exquisite set of moves.

For the White-to-mate part, it’s tempting to prepare for a direct battery mate on the long diagonal, but the b3-pawn cannot be protected. Rather, the two sides organise the king to be mated on d3, and the B + S battery is utilised indirectly to control flights on c3 and d4. 1.Sxf4+ Sd5+ 2.Kd3 Sxf4. Black begins by removing the knight guarding d3, and the discovered check on the d-file forces the other white knight to d5 (not the alternative h5). The black king’s move effectively unpins the same knight, which then mates on its counterpart’s starting square, f4. The Black-to-mate solution shows matching strategies that are colour-reversed and entail an orthogonal-diagonal transformation. Here a direct battery mate on the d-file cannot be arranged, but opening this R + S battery ensures that all flights on that line are guarded, upon the king’s arrival on e5. 1.Sxd7+ Sf6+ 2.Ke5 Sxd7. Now White first captures the knight that’s attacking e5, and the discovered check on the diagonal forces the other black knight to f6 (avoiding b6). Then the white king’s move to e5 unpins that knight, which gives mate on d7, its counterpart’s original square.

Andy Sag: The white pawns give a strong clue that the black king ends up on the d-file. Once the white mate is solved, the duplex is easy because a similar pattern of play with exchange of knights and cross checks is immediately suspected.
George Meldrum: So many checks! Well worth checking out.
Andrew Buchanan: Beautiful symmetry.