Weekly Problems 2026-A

All three white line-pieces may be expected to contribute to the mates, even though each one seems passively placed away from the black king at first. White activates a pair of them in two moves, while the third piece is utilised as a guard when it’s approached by the king (which on e4 has too many flights). After 1.Kd3, Black can block the sole flight on e4 with various pieces, but the rook is selected as the move simultaneously opens a line for the white bishop to give mate – as long as the rook is stopped from returning to e2 by a pin. 1…Qg6+ 2.Re4 Bf1. The other two solutions follow the same pattern, with different black pieces blocking e4 to open other mating lines. 1.Kd5 Bg2+ 2.Sce4 Ra5. 1.Kf4 Ra4+ 2.Sfe4 Qf7. The three white pieces cyclically switch their functions to (1) guard flights, (2) pin the e4-piece, and (3) deliver mate.

Andy Sag: In each case, Black moves king, White checks, Black self-pins a piece on e4, White executes a pin-mate. Well-coordinated solutions.
Jacob Hoover: Not only is there a pin-mate in each of the three solutions, but also across the solutions the three white line-pieces exchange roles in a cyclic fashion between guarding, pinning, and mating.

Since checking is forbidden, White cannot move the rook or bishop in part (a), and stalemate is achieved by using the king to mop up most of the black units. 1.Ka2 2.Ka3 3.Ka4 4.Ka5 5.Kxb6 6.Kc7 7.Kxd7 8.Ke8 9.Kxf7 10.Kxg8 11.Kxh7 12.Kg6 13.Kf5 14.Kxe4. In part (b), the white king can release the other two pieces by interposing on c3/d4; however, the number of viable stalemate configurations remains limited. Akin to the first solution, the rook aims for e5 where it restricts the black king while being protected by the bishop. 1.Kc2 2.Kc3 3.Re2 4.Rxe4 5.Re5 6.Kxc4 7.Kc5 8.Kxb6 9.Kc7 10.Kxd7 11.Ke8 12.Kf8 13.Kxg8 14.Kxh7. The two ideal-stalemate positions are near-exact echoes, placed well apart – an uncommon theme in series-movers.

Andy Sag: Both parts end with the same configuration in different locations. Apart from check avoidance, the black rook dictates the move sequence as it must be captured to allow the white king access to the 7th and 8th ranks.
Jacob Hoover: The two final positions are echoes of each other. This one was quite easy as series-movers go.
Satanick Mukhuty: Neat!

In the set play, Black captures the d5-pawn with four different pieces, which become pinned by the rook. White takes advantage of the pin in each case, while also covering the (unprovided) flight on d4: 1…Qxd5 2.Sf3, 1…Rxd5 2.Bb2, 1…Bxd5 2.Sc6, and 1…Sxd5 2.h8=Q. The key 1.Rc4! removes the d4-flight but grants a new one on d5, to threaten 2.Qxe6. The four capturing defences are playable, but their set replies no longer work without the pins. Instead, White exploits these moves to d5 as self-blocks, along with the fact that d4 is already guarded: 1…Qxd5 2.Sxg6, 1…Rxd5 2.Bxf4, 1…Bxd5 2.Qc7, and 1…Sxd5 2.Sd7. The white queen is further employed in 1…Kxd5 2.Qc5. A top-notch free change problem where four black self-pins are converted to self-blocks.

Andy Sag: The key takes a flight but gives a flight-capture. Each of the five captures of the d5-pawn requires a different mate, four of which are changed mates.
Jacob Hoover: The defenses at d5 recur from the set play but have different white responses this time around. I like this problem a lot.

Black has a strong defence, 1…Bh6, for which White has no prepared response. The key 1.h6! (waiting) is a type of clearance move that aims to open the h-file for the queen by provoking the capture, 1…Bxh6. Now 2.Rg5 leaves Black in zugzwang again – 2…B~ 3.Qh3, or specifically 2…Bxg5 3.Qh3 produces a model mate; 2…Ke3 3.Rg3 shows another model, one that involves all three white line-pieces; and 2…e3 3.Qa8. If 1…Bg7 then 2.Rxg7 leads to two sub-variations that are similar to those seen before, 2…Ke3 3.Rg3 and 2…e3 3.Qa8. A distinct line is 1…e3 2.Qe5 (threat: 3.Qd5) e2 3.Qxe2. Lastly, 1…Ke3 permits a short mate, 2.Rg3. Sacrificing a unit purely to clear a line is termed an annihilation, and here the idea is combined with model mates.

Andy Sag: If Black captures the h-pawn, White offers up the rook to prevent 2…Bxf4. Took a while to see that!
George Meldrum: An unlikely looking key move which is designed to clear the way for the white queen on the h-file. An even more surprising Rg5 move after the black bishop captures the pawn.

The white units shifted from their initial squares have used up all 18 available moves, so the missing e- and g-pawns were captured at home. Black’s missing d- and f-pawns must sacrifice themselves on squares that could be visited by White, and this is possible only if they promote. 1.h4 d5 2.Rh3 d4 3.Rc3 d3 4.Sh3 dxe2 5.d4 f5 6.Sd2 f4 7.Sb3 f3 8.Bd2 fxg2 9.f4 g1=R 10.Kf2 e1=R. Seemingly Black could promote either pawn to a knight too without disturbing the white king. However, the promoted rooks are necessary for a special manoeuvre, designed to cater for White’s largely fixed move order. Firstly, the g1-rook neutralises a queen check. 11.Qh5+ Rg6 12.Qa5 Sd7 13.h5 Sb6 14.Bb5+ Bd7 15.Ba4. Secondly, since the next white move Rg1 is forced, the e1-rook must clear the rank, but a simple switchback like 15…Re3? 16.Rg1 Re1 17.Bxe1 leaves the other black rook uncaptured. Only 15…Reg1 16.Rxg1 Re6 17.Sc1 Re1 18.Bxe1 succeeds in removing both rooks. The two promoted pieces have remarkably switched places, each sacrificing itself on the other’s promotion square, g1 and e1.

Jacob Hoover: This was hard!
Andrew Buchanan: A beautiful proof game, which looks deceptively easy to create.

The key 1.Sh5!, by observing f4, threatens 2.g4. Black’s c4-knight defends by opening a line for the a4-rook, but wherever it goes, the knight cuts off two black line-pieces simultaneously. The pair of self-interferences seems to permit dual mates, but each knight defence has a compensating effect that forces a unique reply. 1…Sb2 (cuts off a1-bishop and b8-queen) 2.Rxf7 [A] (not 2.d4+? [B] Sd3), 1…S4b6 (cuts off b8-queen and a6-rook) 2.d4 [B] (not 2.Qd7+? [C] Sxd7), 1…S4d6 (cuts off a6-rook and b8-queen) 2.Qd7 [C] (not 2.Sg3+? [D] Kf6), and 1…Se5 (cuts off b8-queen and a1-bishop) 2.Sg3 [D] (not 2.Rxf7+? [A] Sxf7). There’s by-play with 1…gxh5 2.Rg5, 1…Qf4 2.Rxf4, and 1…Qg3 2.Sxg3/d4/dxc4. A 4x2 cycle of white dual avoidances based on an unusual geometry – a black piece landing on the intersections of four defensive lines.

Andy Sag: Quite a lot of play on this one.
Jacob Hoover: Every move of the black knight blocks a guarding line and a controlling line while mitigating one of those blocks, thus forcing a particular white response.

The black king has access to g6/g8 only, which hints at a rook mate on the g-file. White’s rooks are half-pinned on the 2nd rank, while Black’s b2-rook and e5-knight are half-pinned on the long diagonal. That black knight is liable to give a discovered check if it moves to unguard the g-file. If Black tries to self-pin the piece with 1.Rb3, then 1…Rd4 and 2…Rxg4 fails because the c6-rook cannot hide away. The solution does shift the e5-knight, but only after the arrival of the white rook on d6, which cuts off both Black’s queen and rook (besides guarding f6). 1.Bc8 Rd6 2.Sd7 Rg2. The black bishop crosses over d7 to prepare for the knight’s interference, and the latter’s move also self-pins the b2-rook, allowing the second white rook to execute a pin-mate by sliding along its own pin-line.

Part (b) starts with the black bishop on e3, which in controlling the g-file serves a similar function as the c6-rook in (a). After 1.Rb3 Rd6, the bishop cannot hide away to enable 2…Rg2. In the solution, the white rook’s arrival on f4 cuts off both Black’s queen and bishop, freeing the e5-knight to move without checking. 1.Rb6 Rf4 2.Sc6 Rg2. The black rook vacates c6 to prepare for the knight’s interference, and again the latter’s move self-pins the b2-rook, which permits a different white rook to move along its own pin-line and give a pin-mate. Intricate line strategy where the black and white half-pins are utilised but not in the standard ways.

Andy Sag: Tricky well-matched twins leading to similar pin-mates with the two white rooks exchanging roles.
George Meldrum: The white rooks swap roles in the solutions of the pair. Found solving a task with all the blocking lines and pinning of pieces. Enjoyable problem.

A random move by White’s c3-knight (such as 1.Sa4?) unguards e4 and threatens 2.Bxe4+ Qxe4. Black counters by removing the queen from the long diagonal, but a random defence (like 1…Qb8) also unguards d5 and permits 2.Qd5+ Sxd5. The black queen has two correction moves that protect d5 from another direction, the first of which is 1…Qg8, but that enables 2.Sxg3+ Qxg3. The second queen move 1…Qd8! defeats the knight’s random try. The knight has two correction moves that prepare against this strong queen defence, which inadvertently attacks d4. The first is 1.Se2? and if 1…Qd8 then 2.Sd4+ cxd4/Qxd4; however, since the try-piece has placed an unwanted guard on g3, 1…Qg8! now refutes. The second specific knight move 1.Sb5! is the key. As seen previously, the threat of 2.Bxe4+ Qxe4 provokes 1…Q~ 2.Qd5+ Sxd5, and the queen corrections lead to 1…Qg8 2.Sxg3+ Qxg3 and 1…Qd8 2.Sd4+ cxd4/Qxd4. Both Black and White execute correction plays that intertwine as these random and specific moves thwart one another.

Jacob Hoover: After the key, 1…Qd8 and 1…Qg8 are correction moves. There are four thematic tries: 1.Sa4/Sa2/Sd1? all put the knight on a square from which it cannot move to d4 – 1…Qd8!, and 1.Se2? corrects the error that the above tries commit, but it does add a guard to g3, allowing 1…Qg8!
George Meldrum: Somewhat easy to solve but includes a nice array of play.

The key 1.d3! is aimed at avoiding an en passant capture in the threat, 2.Sf3+ Bxf3 3.d4. Black has three defences that commit various types of errors. 1…cxd3 enables the queen to guard d5 from another angle – 2.Qa2, which threatens 3.Sc6, and if 2…Bxd5 then 3.Qh2. 1…Bxd5 serves as an annihilation of the white pawn, clearing the long diagonal for the queen in 2.Re4+ Bxe4 3.Qxe4. And 1…Bc5 is a distant self-block, allowing 2.Sc6+ Kxd5 3.Bf7. No clear theme, but we find good strategies throughout, such as (in the first variation) two line-openings by Black that are exploited by the sweeping queen.

Andy Sag: The initial pawn move negates the en passant defence.

The black king has four flight-moves, of which two are provided with set mates: 1…Kf5 2.Qf6 and 1…Kd5 2.Qd6. Two strong tries remove different pairs of these flights: 1.Kc4? threatens 2.Qf6 [A], but 1…Kf4! [a] refutes, while 1.Rf2? threatens 2.Qd6 [B], but 1…Kd4! [b] refutes. The key 1.Rg3! controls the prospective flight on e3 and creates a zugzwang. Now 1…Kf4 [a] induces 2.Qf6 [A], the very mate that was thwarted by 1…Kf4! [a] after the first try. Similarly, 1…Kd4 [b] induces 2.Qd6 [B], the very mate that was thwarted by 1…Kd4! [b] after the second try. This paradoxical pattern of a black defence that alternately disables and enables the same mating move is called the Dombrovskis theme, and here it’s shown cleanly in a light position with two alluring tries. The by-play follows the set variations, 1…Kf5 2.Qf6 and 1…Kd5 2.Qd6.

Andy Sag: The key preserves all four flights including two unprovided ones making this miniature easy to solve.
George Meldrum: Admirable with four king-flights in a miniature setting.

The four capturing moves by the black bishop assist White in various ways. In three cases, they clear mating squares for a knight, thus the set plays, 1…Sa4 2.Bxc3 Sxc3, 1…Sd7 2.Bxf6 Sxf6, and 1…Sd3 2.Bxc5 Sxc5. The fourth capture acts as a self-block that frees the f2-pawn: 1…Bxg4 2.Bxe3 f3. When Black begins in the actual solutions, the bishop still captures the four pawns, but each expected follow-up fails because Black lacks a tempo move. After 1.Bxc3, if 1…Sa4? then any bishop move inevitably disturbs the mate on c3, so instead 1…Sd7 2.Bxf6 Sxf6. Likewise, after 1.Bxf6, not 1…Sd7? 2.B-any Sf6+, but 1…Sa4 2.Bxc3 Sxc3. The other two captures lead to a similar reciprocal effect. 1.Bxc5 – not 1…Sd3? 2.B-any Sc5+ – Bxg4 2.Bxe3 f3, and 1.Bxe3 – not 1…Bxg4? 2.B-any (unblocks e3) f3+ – Sd3 2.Bxc5 Sxc5. Each set-play sequence returns after a familiar bishop move which, however, has changed its function to a pure waiting move.

Andy Sag: The four set plays are each closely related to one of the solutions.
Jacob Hoover: Black tempo moves and two pairs of black move reversal (AB-BA and CD-DC) in the four solutions. I found the fact that the four mates seen in the set play were repeated in the solutions to be rather pleasant.
Satanick Mukhuty: Each of the four solutions is paired with a corresponding set play, both ending in an identical mate. Brilliant!

The diagram position seems mostly symmetrical, but White must force the black king toward its nearest corner on the right-hand side. Thus not 1.Rf8? Kd1! 2.Rf2 Kc1 3.Sd3+ Kb1! After 1.Rc8! Kf1 2.Sf3, White threatens both 3.Rc2 ~ 4.Rf2 and 3.Rc1+ Kg2 4.Rg1. 2…h2 deters 3.Rc2? with 3…h1=S!, but White exploits the distant self-block on h2 with 3.Sxh4 Kg1/Ke1 4.Rc1. If 2…Kg2 then not 3.Rc2+? Kg3! but 3.Rg8+ Kh1/Kf1 4.Rg1. A short mate follows 1…Kd1 2.Sd3 ~ 3.Rc1. The non-thematic 1.Rd8? fails to 1…Kf1 2.Sf3 h2 3.Sxh4 Ke1!

In position (b), the black king is closer to the left-hand corner and White switches plans accordingly. The solution of (a) thus becomes a thematic try (when shifted left): 1.Rb8? Ke1! 2.Se3 Kf2 3.Rf8+ Kg1!, while the main try from (a) becomes the solution here (shifted). 1.Re8! threatens 2.Sc3+ Kc1 3.Re2 ~ 4.Rc2 as well as 2.Re2, with 1…Kc1 compelling 2.Re2 Kb1 3.Sc3+ Ka1 4.Ra2, 3…Kc1 4.Rc2. Two difficult and pleasantly distinct solutions, differentiated by board asymmetry and the presence of the h3-pawn.

Andy Sag: In each case a different edge of the board enables a mate if the black king ventures into a corner square. Nice miniature twin.
George Meldrum: Amazingly tricky to solve for a problem with so few pieces. The solutions are different to prevent the black king from running off the edge of the board (so to speak).
Satanick Mukhuty: The idea is to drive the enemy king to the side that is one file shorter. Clever use of the chessboard asymmetry!