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.