Weekly Problems 2025-B

Both white knights will need to move in each twin – to guard flights and to give mate respectively – but one gets pinned if Black shifts the f7-rook or the e7-bishop to self-block on f6. In part (a), the thematic try 1.Rf6? Sf7 (unpinning the other knight) followed by 2…Sh4 fails only because Black lacks a waiting move (e.g. 2.Be~? checks). The solution switches the two knights’ roles and moves the black king to the square where it will begin in (b): 1.Bf6 Se7+ (unpinning the other knight) 2.Kg5 Sf3. In part (b), the solution of (a) becomes the thematic try, with 1.Bf6? Se7 and 2…Sf3 failing as there is no waiting move for Black (e.g. 2.Rf~? checks). The try from (a) now works as the solution, because the king starting on the “wrong” square allows a tempo to be spent on returning it to the “right” one: 1.Rf6 Sf7+ 2.Kf5 Sh4. Black’s tempo play is enhanced by the paradoxical twinning of the king. The self-blocking moves to f6 are also Grimshaw interferences that enable mates on f3 and h4, anticipating that the king’s move will unmask a line of defence.

Andy Sag: Looks easy at first glance but great care is necessary to avoid checks on the white king.
Satanick Mukhuty: A lovely juxtaposition of Grimshaw and Umnov! Funny how, when you place the black king on f5, it’s mated on g5 – and conversely, when you put it on g5, it’s mated on f5.

The out-of-play c8-knight has two natural tries that threaten 2.Rxd5. 1.Se7? handles 1…Bg2 with 2.Sxf5, but 1…Ra5! refutes, while 1.Sb6? meets 1…Ra5 with 2.Qc4, but 1…Bg2! refutes. The key 1.Rd7! threatens 2.Qe5+ Kc4/Kc5 3.Qxd5, against which the main defences seen in the try phases are playable. 1…Bg2 enables 2.Se7 with the threat of 3.Sxf5, which leads to either the self-block 2…Be4 3.Se6 or the switchback 2…Bh3 3.Rxd5. 1…Ra5 similarly allows 2.Sb6, threatening 3.Qc4, and this branches into the self-block 2…Rc5 3.Qe5 or the switchback 2…Ra4 3.Rxd5 (2…Rxb6/Rb4/Rc3 3.Qc3). Two elegantly matching variations illustrate the Swiss theme, a logical style idea that involves changing White’s threat. Initially, the thematic tries 1.Se7? and 1.Sb6? carry the threat of 2.Rxd5. But after the preparatory key 1.Rd7! enticing 1…Bg2 or 1…Ra5, the respective knight moves 2.Se7 and 2.Sb6 entail new threats – 3.Sxf5 and 3.Qc4 – that Black cannot parry without creating more weaknesses.

Andy Sag: Giving the queen access to e5 looks attractive but precise placement of the rook is required (1.Rd8? Rb7!). The need to delay correct use of the c8-knight to the second move (in the two main variations) is not so obvious.
Satanick Mukhuty: Interesting logical problem showing self-block decoys! Note that 1.Rd8? with the same threat fails to 1…Rb7!, pinning the white queen.
George Meldrum: The key rids Black’s annoying pin on the white queen with …Rb7.  The variety of possibilities the setting holds makes it more difficult to solve.

The starting position is a complete block where all possible black moves are given set mates: 1…e2 2.Qxe2, 1…B~ 2.Qc4 (1…Bc5/Bb6/Ba7 result in a dual, 2.Qc4/Rc3), 1…Bc3 2.Rxc3, 1…g5 2.Qf5, and 1…h6/h5 2.Qxg6. White has no waiting move capable of preserving the zugzwang, however; e.g. 1.Qe6? Bc3! The key 1.Rc4! grants a flight to the black king and threatens 2.Rxd4. Taking the flight with 1…Kxc4 permits 2.Qe2, which shows a transferred mate relative to the set variation 1…e2 2.Qxe2, while 1…e2 now produces a changed mate, 2.Qxd4. Another change follows a random move of the black bishop: 1…B~ 2.Bc2, exploiting the key-move’s vacation of c2 and obstruction of c4 (a dual still occurs in 1…Bc5/Bb6/Ba7 2.Bc2/Rc3). The correction move 1…Bc3 again forces 2.Rxc3. The uncommon block-threat type is demonstrated with a fine key, two changed mates, and one added variation.

Andy Sag: Nearly fell for one of the tries. The key grants a flight capture and initiates a few changed mates. Unfortunately, a few duals in both true play and set play noted.
Jacob Hoover: A rather easy solve. One try 1.Qe6? (waiting) removes the set duals and otherwise seems to preserve the block, but 1…Bc3! refutes.
Satanick Mukhuty: For Black’s every response, there is a mate prepared. Yet, surprisingly, the key is not a waiting move. A fine example – with an active sacrifice – of what, I believe, is known as the Block-Threat idea!
Bob Meadley: The try 1.Bxa5? is defeated by 1…Bc3. An unusual position with six black pawns and no white pawns. Lovely two-mover by J. J. O’K.
George Meldrum: Elegance in a lightweight setting by J. J. O’Keefe.

The black king has to relocate to a dark square, to be mated by either the bishop or the pawn supported by the bishop (a third option where the pawn mates while guarded by the king takes too long to organise). In the first solution, the king heads for c7 to prepare for a pawn mate on b6, meaning the white pawn must capture the four black pawns placed diagonally one by one. 1.Kc6 fxe3 2.Kc7 exd4 3.Bc6 dxc5 4.Sb7 cxb6. In the second solution, the king aims for f4 so that the bishop could mate on e3, and this time the four black pawns must be removed by the bishop in the opposite order. 1.Ke4 Bxb6 2.Kf4 Bxc5 3.Bf3 Bxd4 4.Se4 Bxe3. An amusing problem in which the thematic black pawns serve contrasting roles – first assisting with the white pawn’s moves, then hindering the bishop, but needing to be captured all the same.

Andy Sag: The two white units take turns in gobbling up the b- to e-pawn chain; meanwhile the black king moves twice and the a8-bishop and d6-knight set up self-blocks. Nice twin!
Satanick Mukhuty: Delightfully funny!
George Meldrum: A problem to put a smile on your dial.

White wants to force Black to fire the B + R battery, but an immediate 1.Sf4+? Rxf4+ isn’t mate because of the e8-rook. Two non-thematic tries threaten 2.Sf4+ by withdrawing the rook from the e-file: 1.Rd8? pins the d6-pawn but 1…Sxb4! creates a flight on c5, while 1.Rc8? pre-empts the knight defence but 1…dxc5! creates a flight on e4. The key 1.Se4! closes the e-file to threaten 2.Sf4+ again, and Black defends by also cutting off the white rook – 1…Se5/Se7 2.Sf4+? Kxe4. However, these black interferences with the rook are exploitable, since White can now move the key-piece on e4 without activating that rook. After 1…Se5, which also cuts off the h8-bishop’s access to d4, White avoids a self-interference with the queen, 2.Sc3+? Kd4; instead, 2.Sf6+ forces 2…Rxf6. Analogously, after 1…Se7, which cuts off the e8-rook’s access to e6, White avoids interfering with the other rook, 2.Sf6+? Ke6; instead, 2.Sc3+ forces 2…Rxc3. These two variations demonstrate a dual avoidance effect called the Java theme. By-play: 1…Sxb3 2.Qxb3+ Rxb3. Additionally, the set play of this problem involves a paradoxical element; at first 1…Se5 and 1…Se7 enable 2.Sf4+ Rxf4, yet after the key, these knight defences disable the 2.Sf4+ threat.

Andy Sag: The key must accomplish two objectives: (1) guard c5 in case of 1…Sxb4, and (2) prevent the e-rook from moving to e2. Took a long time to see that 1…Sxb3 is a variation, not a try refutation!
George Meldrum: The key move is not hard to find. The three extra variations are tricky.
Satanick Mukhuty: Interesting dual avoidance!
Bob Meadley: The key allows Black to play 1…Sxb4 as c5 is covered by the key-piece. I wouldn’t like to solve one of Edgar’s 3-move selfmates!

Shifting the white king to release the d5-rook will threaten two double-checking mates, 2.Rd8/Ra5, but Black refutes with various checks, e.g. 1.Ke8? Qa4+!, 1.Ke7/Kf8? Qb4+!, 1.Kg6? Qb6+! Alternatively, White may aim for a zugzwang by preparing for the queen defences that maintain the pin; 1.Rg4? Qc4/Qa2 2.Rg8, but 1…Qf3+! (likewise 1.Rh4? Qf3+!), 1.Ke6? Qc4/Qa2 2.Rf8, but 1…Qb6+! The key 1.Kg8! (waiting) does leave the rook pinned and again answers 1…Qc4/Qa2 with 2.Rf8. A random queen move that unpins the rook leads to 1…Q~ 2.Rd8/Ra5. These dual mates are separated in 1…Qb8+ 2.Rd8 and 1…Qb7 2.Ra5, but here the white moves are not double-checks but pin-mates where the rook and bishop exchange functions as the pinner and mating piece. Two more checking defences are handled precisely, 1…Qg3+ 2.Rg5 and 1…Qxd5+ 2.Bxd5. An aristocrat miniature with a subtle key, plausible tries, and intriguing battery variations.

Andy Sag: The key does not remove the pin and allows two additional checks, but for a miniature waiter there are many duals.
Jacob Hoover: Thematic content: Avoidance of self-injury, unpins, battery plays.
Satanick Mukhuty: Interesting miniature with good content.

The black rooks are holding off a bishop mate on b1 and a queen mate on b2. White can try to draw the defenders away from their ranks by threatening a bishop mate on the a2-g8 diagonal, but 1.Bf5? Re1!, 1.Bg6? Rf1!, or 1.Bh7? Rg1!, and Black hangs on. The key 1.Be4! keeps the d1-rook tied up protecting d5 and b1, and remarkably puts Black in zugzwang. In the three main variations, the h2-rook causes an anticipatory interference with its partner along various files. 1…Re2 2.Bf5 – White paradoxically attacks e6 only when it’s guarded, to threaten 3.Be6+ Rxe6 4.Qb2, 3…Rd5 4.Bxd5, against which 2…Rde1 is now ineffective; 2…Red2 still allows 3.Be6+ Rd5 4.Qb2. Similarly after 1…Rf2, 2.Bg6 threatens 3.Bf7+ Rxf7 4.Qb2, 3…Rd5 4.Bxd5, since 2…Rdf1 has been neutralised. And if 1…Rg2, 2.Bh7 threatens 3.Bg8+ Rxg8 4.Qb2, 3…Rd5 4.Bxd5, given that 2…Rdg1 fails to defend. Other moves by either rook result in short mates, except for 1…Rd3 2.Bxd3 (3.Bb1) Rc2 3.Bxc2 S~ 4.Bb1/Qb2. The knight blocks the g-file with 1…Sg3 (like one of the main lines), then 2.Bh7 threatens 3.Bg8+ Rd5 4.Bxd5, while 1…Sf2 enables 2.Qb2.

Andy Sag: The potential mates Qb2, Bb1 and by the bishop on the a2 to g8 diagonal make it easy to overload the rooks.
Satanick Mukhuty: Overall, an excellent lightweight problem on anticipatory interference. The solution is not that obvious either.
George Meldrum: Really hard to solve. Had Black been able to skip a move then it would not have worked but as it was then the two black rooks got in each other’s way. Found no problem with the short mates as the concept of the problem was clear.

The six solutions are divided into three pairs where each couplet contains identical strategies. In the first pair, queen mates on d3 and e3 are arranged after removals of their rear guards and bishop self-blocks. 1.Bf8 Qxf1 2.Bc5 Qd3 and 1.Bb7 Qxe1 2.Bd5 Qe3. In the second pair, the bishops’ annihilations of the knights clear their squares for the queen and also give the king access to d3 and e3. 1.Bxe5+ Qxe5+ 2.Kd3 Sb2 and 1.Bxc4 Qxc4+ 2.Ke3 Sg4 – here the Zilahi theme is also shown since the knights exchange roles in getting sacrificed and giving mate. In the third pair, the king and queen make two-move trips to set up analogous mating configurations, which involve a diagonal-orthogonal echo. 1.Kd5 Qxf3+ 2.Ke6 Qf7 and 1.Kc5 Qxd2 2.Kb5 Qa5. The Helpmate of the Future scheme, in which at least two pairs of matching solutions are displayed, demands great technical skills, and here three pairs are achieved with perfect white economy and no twinning necessary.

Andy Sag: Three pairs with widely different play but each pair well matched.
Satanick Mukhuty: Neat helpmate of the future.

Every possible black move in the initial position is provided with a set mate. In particular, four thematic variations are: 1…Qc4 [a] 2.Sxb1 [A], 1…Bd3 [b] 2.Sxa2 [B], 1…Qb3 [c] 2.Qxb3, and 1…Bc2 [d] 2.Qxc2. White has no neutral move capable of preserving all of the set lines, and the key is 1.Qf1! (waiting), which places the queen in control of c4 and d3 instead of b3 and c2. Now 1…Qc4 [a] 2.Qxc4 and 1…Bd3 [b] 2.Qxd3 bring changed mates for [a] and [b] compared with the set play, while 1…Qb3 [c] 2.Sxb1 [A] and 1…Bc2 [d] 2.Sxa2 [B] show not only changed mates for [c] and [d], but also a pair of transferred mates in [A] and [B] – knight mates which were originally effective against [a] and [b]. This combination of changed and transferred mates is called an Ideal Rukhlis. Other variations are 1…Qa1 2.Qc4 (a change from 2.Qb3), 1…Qxd5+ 2.Kxd5, 1…Bxe4 2.Kxe4, 1…c6/c5 2.Kd6, and 1…g4 2.Kf4. The symmetrical play is perhaps the only weakness in this otherwise impeccable mutate, which demonstrates the Ideal Rukhlis theme at a remarkably early date.

Andy Sag: A waiter with nine variations, five changed mates and no duals. How good is that!
Bob Meadley: Not easy.
Satanick Mukhuty: Perfect mutate with five changed mates.
Paz Einat: An excellent mutate showcasing what would be known as “Ideal Rukhlis.”

Preparing a rook mate on the top rank seems plausible with the given material, but such a plan just fails, e.g. 1.Kf7 Rxb2 2.Ra7 Bxc2 3.Kg8 Bg6 4.Rg7 and 4…Rb8?? is obstructed, or 1.Kf7 Kh2 2.Kg8 Bxc2 3.Rg1 Bg6 4.Rg7?? Ra8. The black king stays put in the solution, and to arrange the blocks and guards around the piece, the two pairs of bishops and rooks execute matching clearance manoeuvres. 1.Bh7 Ra8 2.Ra7 Bg6 3.Re7 Be8 4.Bf5 Ra6. The attractive sequence finishes with a great touch, when both the black bishop and the white rook travel back in the direction from which they came.

Andy Sag: The black bishop and white rook both perform Bristol clearance type manoeuvres to allow all pieces to legally reach their final positions in two moves.
George Meldrum: Precise move order required with both Black and White needing to make way for each other.
Satanick Mukhuty: Double bicolour Bristol clearance! Exquisite problem!

Although the black pawns on f2 and g2 are half-pinned by the h2-rook, attempts to create a threat with 1.Bh4? (2.Sg3) and 1.Kf4? (2.Bxf3) are easily refuted by various promotions of these pawns. After the key 1.d7!, which threatens 2.d8=Q and 3.Qd3, black queening defences are not effective, e.g. 1…f1=Q 2.d8=Q Qxd1 3.Qxd1. Black has four underpromotion defences that can be divided into two pairs. In the first pair, Black makes use of the possible pins on the second rank to threaten stalemate. 1…g1=S leaves the new knight trapped and self-pins the f2-pawn, but 2.Bd6 releases the stalemate and forces 2…cxd6 3.Sg3. 1…f1=B immobilises the new bishop and self-pins the g2-pawn, but 2.Bxh3 sets up a zugzwang, 2…f2 3.Bg4. In the second pair of defences, Black promotes to a knight to threaten a check on g3. 1…f1=S 2.Be1 – keeps a guard on f2 and brings about another zugzwang – 2…S~ 3.Sg3. If 1…gxh1=S, 2.Kf4 carries an unstoppable threat, 2…Sxg3 3.Bxf3. White exploits the half-pin in all four variations, though a special feature of this problem is how the half-pin is also advantageously used by Black (not possible in a two-mover), as a means to produce stalemate.

Andy Sag: Promoting either of the 2nd rank pawns self-pins the other leaving Black hopelessly defenceless. Sacrificing a bishop to avoid stalemate is a diabolically clever twist, as is the pawn unpin and switchback mate.
George Meldrum: Some tricky and very nice lines in the solution.
Satanick Mukhuty: An interesting take on stalemate avoidance motif.

The arrangement of the kings and knight suggests that White will use a promoted queen to check on c3 (after the removal of the b4-pawn), to compel a knight mate. The scheme requires self-blocking pieces on a1, a3, and b3, none of which should guard c3 or attack the black king. Only a knight works on a1, and a bishop on b3 (where it controls the d1-flight); a rook or knight can block a3, but we may assume that the former is faster. That the correct sequence of moves must be unique provides some clues. For instance, to force a single path of a promoted knight to a1, the piece may be tasked with capturing the b4-pawn, and if the d-pawn is knighted on d8, it would have a precise route to b4. There are many tries that take 31 moves, such as starting with 1.hxg3 followed by a rook promotion, which costs an extra pawn move. The solution does begin by promoting the h-pawn to a rook, but leaves the g3-pawn to be captured by a promoted queen from b8. 1.h4 2.h5 3.h6 4.h7 5.h8=R 6.Rd8 7.Rxd3 8.Ra3 9.d4 10.d5 11.d6 12.d7 13.d8=S 14.Sc6 15.Sxb4 16.Sc2 17.b4 18.b5 19.b6 20.b7 21.b8=Q 22.Qxg3 23.Qc3 24.g4 25.g5 26.g6 27.g7 28.g8=B 29.Bb3 30.Sa1+ Sxc3. The Allumwandlung theme is impressively merged with four-fold Excelsiors, in which the promoting pawns commence from their initial rank. This ten-unit setting holds the economy record for the task combination.

Andy Sag: Easy to see that all four white pawns must promote and that a knight must end up on a1 after capturing the b-pawn. Harder to see that the final move of the knight must be delayed leaving it temporarily on c2 so the queen can get to c3 in one move after being promoted on b8 and capturing the g3-pawn.
Satanick Mukhuty: I saw the name Unto Heinonen and the four white pawns and knew it was going to be an AUW. However, it was still not easy to see the trick involving Q + S battery creation on c3-c1. Fantastic problem!

Since 1.Se2+ would interfere with the f2-rook and allow 1…Kd2, White begins with a bishop move, which will threaten 2.Se2 by preparing to open the d-file for the d6-rook. Four black pieces can counter by playing to d5, prospectively cutting off the white rook. All of these defences have been provided with a mating reply, but the wrong choice of move by the bishop will disrupt one such set mate. 1.Bxe4? Rd5!, 1.Bc4? Sbd5!, 1.Bb6? Scd5!, and 1.Ba6? Qd5! Only the key 1.Bf1! manages to avoid all of the self-obstructions. 1…Rd5 2.Sxe4, 1…Sbd5 2.Qc5, 1…Scd5 2.Sb5, and 1…Qd5 2.Qa1. White safety play by the bishop is blended with subtle line-opening/closing effects and unified defences on the same square.

Andy Sag: It’s all about maintaining a guard on d2 so the black king can’t escape.
Jacob Hoover: The key avoids all of the errors committed by the tries. Themes: Avoidance of self-injury, line closures, line openings.
Satanick Mukhuty: White combination meets defences on the same square. Neat!
Bob Meadley: Lovely.
George Meldrum: This one really had me going. No new play other than the threat but somehow the key and threat were covered like a magician’s illusion.

White has two pairs of line-pieces trained on the black king, pinning the knights, while the d3-queen and e6-rook are themselves pinned. Planning to capture either knight as the mating move proves impractical, e.g. 1.Rb3 Qxb3 2.Qg8 and neither 2…Bxc4 nor 2…Rxd6 works because of the flight on a7. In the two solutions, the black king surprisingly steps away from the board edge, keeping one knight pinned but releasing the other. After 1.Kb5 Bd1, the freed d6-knight unpins its own former pinner with 2.Sf5 to enable 2…Rb6, a pin-mate. Likewise, after 1.Kb6 Rf7, the c4-knight unpins its former pinner with 2.Se3 to allow 2…Qb5, another pin-mate. A well-executed orthogonal-diagonal transformation across the two phases, with exchange-of-functions between three pairs of pieces. As an extra effect, White alternately mates on b6 and b5, the same squares that are visited by the black king.

Andy Sag: A pair of solutions with well-matched guarding and unpinning play and both ending with pin-mates.
Jacob Hoover: In each solution the black king unpins one of the black knights while keeping the other one pinned, then Black’s second move unpins the mating piece. Not too difficult, but not too easy either.
Satanick Mukhuty: Perfectly harmonious combination of direct and indirect unpinnings.

Ostensibly White has castled on the queen-side as one of the few visible moves, with many left to facilitate the captures of the missing queen, bishops, and knights. The c1-bishop was captured at home (blocked by the b2/d2-pawns), and the nearby black queen is a clear candidate for taking that piece. The other black units made a total of six visible moves, leaving six for the queen, but a route like Qd5xa2xb1xc1-b1-a2 wouldn’t work because the remaining white units to be removed – d1-queen, f1-bishop, and g1-knight – have insufficient time to sacrifice themselves on the paths of the black pieces. The black queen could alternatively reach c1 from the king-side, which proves more efficient, partly because this allows the white queen to be captured without moving at all. Such a black queen capture on d1, however, will dislodge the white king, meaning we need to rethink our original assumption that White castled queen-side. 1.e3 d5 2.Bc4 d4 3.Bd5 Qxd5 4.Sf3 Qxf3 5.0-0 Qxd1 6.f3 Qxc1 7.Kf2 Qxb1 8.Ke2 Qxa2 9.Rae1 e6 10.Kd1 Bd6 11.Kc1 Se7 12.Rd1 0-0. White sets up a queen-side castling position by hand, a manoeuvre that is even more paradoxical when it begins with a real king-side castling.

Andy Sag: Found this difficult… White king-side castling keeps the white king out of the way while the black queen cleans up the queen-side pieces, then White has enough spare moves to get the king back to the queen-side. A truly amazing manoeuvre.
Jacob Hoover: This one taunted me for two days before I found the solution.
Andrew Buchanan: I think 3.Bd5! is the trick then hidden and fake castling for White.
Satanick Mukhuty: This took me a long time to solve. I don’t think it’s easy to see that the white king castled king-side. Incredible problem!

The black king has a flight to f3, which has no mating reply prepared, but there’s a set mate for any move by the d6-knight, 2.Qd5. The key 1.Re2! (waiting) grants two more flights to the king. Now with the rook guarding e3, 1…Kf3 2.Sf6 and 1…Kd3 2.Sf2 are possible – respectively direct and indirect B + S battery mates. The third flight gives the star variation, 1…Kd5 2.e4, a double pin-mate where both black knights are immobilised. A changed mate from the set play follows moves by the d6-knight, 1…Sd-any (opening a queen-line to d5 and d3) 2.Sd2. Finally, the c5-knight carries out correction play; its random placement 1…Sc~ (opening a rook-line to d5 and e5) permits 2.Sf2, while the correction move 1…Sd3 blocks a flight and allows 2.Sd2. The splendid key and six variations present a fine assortment of traditional ideas.

Andy Sag: The key adds two flights but guards the e3-pawn and vacates d2, leaving both white knights free to move to decisive squares.
Jacob Hoover: Interesting problem for the number of different things it shows: a pin-mate, direct and indirect battery plays, black correction.

In the initial position, Black’s rook and bishop are respectively preventing Rxf6 and Qh5 mate. The key 1.Kd7! guards e8 to generate a threat, 2.Rg8+ Kf7 3.Rg7 (not 2.Ke8? Ba4+). Black’s only defences are to check with the line-pieces. After 1…Rd2+, not 2.Kc8? Rf2, but 2.Sd3 draws the rook to the third rank, 2…Rxd3+ 3.Kc8 Rf3 4.Qh5 – the decoyed rook is forced to interfere with the bishop (2…Ba4+ 3.Kc7 and Black cannot handle the double-threat of 4.Rxf6/Qh5). Similarly, after 1...Ba4+, not 2.Kc7? Bd1, but another knight sacrifice 2.Sc6 entices 2…Bxc6+ 3.Kc7 Bf3 4.Rxf6 – the decoyed bishop cuts off the rook (2…Rd2+ 3.Kc8 again creates an unstoppable double-threat, 4.Qh5/Rxf6). In four instances on the third move, the white king must choose its square accurately. Two wonderful Roman decoy variations culminate in a mutual interference on f3.

Andy Sag: The white king invites checks from the black rook and bishop. The white b4-knight interposes and if captured this leads to a Grimshaw on f3 thus undermining Black’s defences.
Jacob Hoover: White invites two checks and induces a Roman decoy in each case.
Satanick Mukhuty: A pair of perfectly matched variations showing peri-critical decoy.

The black king is confined by the three white minor pieces, so that any check by the two major pieces is a potential mate. The obvious plan to organise a queen mate on the f-file doesn’t work, however, because of the impeding black pawns. Instead, the two sides collaborate to open the second rank for the rook to deliver mate on that file. 1.fxe2 Kb3 (not 1…Kc1?) 2.e1=R Rxf2. In the second solution, the two sides again clear the second rank, but this time to allow the queen to mate on the a2-g8 diagonal. 1.cxb2 Kd1 (not 1…Kb3?) 2.b1=S Qxa2. In this witty example of the Zilahi theme – the queen and rook exchange functions in getting sacrificed and giving mate – the two thematic pieces travel through each other’s starting squares. Two dual avoidance effects are presented as well: in each part, the white king must choose between two line-opening moves, and the black pawn must select the right type of underpromotion.

Andy Sag: The rook (or queen) is captured by a pawn, king vacates 2nd rank, the same black pawn sub-promotes leaving the 2nd rank clear for the queen (or rook) to capture a pawn and mate. Where the king moves and what the pawn promotes to must be chosen with care in each case.
Jacob Hoover: We see the Zilahi theme and, in addition, line clearance in both solutions.
Bob Meadley: Not often we see two brothers collaborating. I like these problems with simplicity and humour. The white king as usual is in the way.

Black has five possible pawn moves, of which three are given set white responses. The unprovided defences are 1…b4 and 1…exf6, and two good tries prepare for one of them. 1.Ra2? (waiting) b4 2.Rxa5 (threat: 3.Rc5) bxc3 3.Ra4, but 1…exf6! refutes. 1.Kd7? (waiting) exf6 2.Se8 ~ 3.Sd6, but 1…b4! refutes. The key 1.Rc2! (waiting) deals with both defences in new ways. 1…b4 2.Rd4+ exd4 3.cxd4 and 1…exf6 2.Rd6 ~ 3.Rc6. The other three pawn moves are countered as in the set play, though in one case the variation is shortened. 1…a4 2.Rb2 ~ 3.Rb4, 1…f4 2.Re2 ~ 3.Re4, and 1…e4 2.Rd4 (set 2.Rd4+ Kxc3 3.Sxb5). The four main lines all finish with a rook mate, where each final attack on the king comes from a different direction.

Andy Sag: The key poses no threat and ensures either rook can move leaving the other to guard the c3-pawn. The second-move rook sacrifice is hard to see; the remaining variations are reasonably straightforward.
Satanick Mukhuty: Neat zugzwang! It took me some time to spot the reply to 1…b4.
Bob Meadley: Lovely. Leonid is Israel’s answer to smug solvers.

The diagram is a complete block position in which all possible black moves are provided with set mates: 1…Kg7 2.Qh6, 1…B~ 2.Qh6, and 1…Bg7 2.Se7. If White aims to preserve the set play with 1.Kxh2? (waiting), then Black escapes with a check, 1…Bd6+! Another try, 1.Qf4? (waiting), answers 1…Kh5 with 2.Qg4/Bf7, but it’s spoiled by 1…Kh7! The waiting key 1.Qh3! grants a flight on g5, and thus adds the variation 1…Kg5 2.Qg4. Two of the set lines are retained, with 1…Kg7 2.Qh6 and 1…B~ 2.Qh6. However, the self-blocking 1…Bg7 is met by a new mate, 2.Qf5. The miniature mutate form limits how much content is achievable, but this first-rate example manages to show four variations including one added line and one changed mate.

Andy Sag: A neat miniature waiter featuring a complete block, a withdrawal key adding a second flight, four variations, one changed mate and a few nice tries.
Jacob Hoover: The key prepares no threat and actually gives Black g5 as a flight.
George Meldrum: Nice key move.
Bob Meadley: A lovely little thing that shows again how beautiful chess is.

A discovered check by the d5-knight (except Sc3+/Se3+) could force …Rxd1 mate, but the flight on e7 needs to be covered first. Four thematic tries and the key guard e7 in different ways. 1.Qg5? is refuted by 1…Qxg6!, when 2.Sf6+ to prevent 2…Qd6 also interferes with the white queen, allowing 2…Kxe7. 1.Qa3? is handled by 1…Rxa4!; now 2.Sb4+ stops 2…Rd4 but cuts off the queen too and permits 2…Kxe7. 1.Rb7? fails to 1…Bb8!, then 2.Sc7+ to disable 2…Bd6 also interferes with the white rook and enables 2…Ke7. 1.Re6? (or 1.Rc7?) unguards c7 and it’s defeated by 1…Qh6!, since 2.Sf4+ preventing 2…Qd2 also cuts off the white queen, allowing 2…Kc7. The key 1.Qe5! avoids all the potential white line-closures and it entails four threats, 2.Sf6+/Sb4+/Sc7+/Sf4+. Black has four defences that force these knight checks individually, thereby producing the Fleck theme. 1…Qxg6 2.Sf6+ Rxd1, 1…Rxa4 2.Sb4+ Rxd1, 1…Bb8 2.Sc7+ Rxd1, and 1…Qh6 2.Sf4+ Rxd1. These thematic black defences are the same moves that serve as the refutations to the four main tries. Byplay: 1…Rxb6/Bxb6 2.Sxb6+ Rxd1. An extra try, 1.f8=B?, is answered by 1…Qg8! The Fleck theme is combined with outstanding try play where Black provokes various white self-interferences.

Andy Sag: Attempts to move the e-rook or use a pawn or promoted bishop to guard it all fail. So it is up to the queen to find the right square to guard it to free up the d-knight to perform a battery check and simultaneously block all “defence” attempts.
Andrew Buchanan: 5/8 white knight’s wheel after 1.Qe5! with various thematic tries.
Jacob Hoover: The key seemed obvious to me (the queen’s barely contributing from g3). However, the numerous primary Flecks in the try- and actual play are the reason why this problem got a 4th prize.