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.