Weekly Problems 2025-A

White has two apparent tactics or “tries”: 1.Sxf3+? forces 1…Rxf3+ which isn’t mate because of the b3-rook, and 1.Bxe5+? forces 1…Rxe5+ which isn’t mate because of the e1-rook. The key 1.Ba6! unguards d7 and threatens 2.Qxd7+ Bxd7. Since this mate depends on Black’s d2-bishop (or c1-queen) controlling the g5-flight, Black responds by cutting off the piece with a rook on e3. These defences cause a mutual interference between the rooks – this is called the Wurzburg-Plachutta theme – enabling the try-moves to work. 1…Ree3 2.Sxf3+ Rxf3 and 1…R3e3 2.Bxe5+ Rxe5 (Black’s mating moves open an indirect B + R battery that re-guards g5 and f4 respectively). In directmate problems, a Wurzburg-Plachutta requires at least three moves to be implemented (see Weekly Problem No.691), but this example demonstrates how in a selfmate the theme can be realised in two moves.

Andy Sag: Obvious key unguards the pinned knight. The variations were a bit harder to spot.
George Meldrum: Very neat.

The black king is almost totally confined for a diagonal battery mate, 1…Ra2, but the d2-flight cannot be guarded or blocked in time. Alternative mating squares for the king – the most plausible being a4 for a rook mate on a5 (supported by the bishop) – also fail to work within four moves. The surprising solution involves setting up another diagonal battery aimed at the king on c3, but from the opposite direction. 1.Kxd4 Rb5+ 2.Ke3 Bxf6 3.Kd2 Re5 4.Kc3 Re2. The black king carries out a 4-move round-trip (rundlauf) in the shape of a diamond, while White dismantles the B + R battery and re-forms it on another part of the board. The final position is also a model mate with only the white king not taking part.

Andy Sag: The black king does a circular switch-back!
Satanick Mukhuty: Nice round-trip of the black monarch!
George Meldrum: Very tricky problem.

The white knight on d5 has eight possible moves, seven of which are thematic tries. These tries generate various threats that are countered by the black knight on d3. 1.Sc3? (2.Se2) bxc3 2.bxc3, but 1…Sxc1! refutes, and similarly 1.Se3? (2.Sc2) fxe3 2.fxe3, but 1…Se1! refutes. A second pair of symmetrical tries are 1.Sc7? (2.Se6) Sc5! and 1.Se7? (2.Sc6) Se5! A third pair contains multiple threats, and these are handled somewhat drastically by capturing the try-piece: 1.Sxb4? (2.Sc2/Sc6/Qxd3) Sxb4! and 1.Sxf4? (2.Se2/Se6/Qxd3/Qe3) Sxf4! The last try is 1.S5xb6? (2.Qd5) Sxf2!, where it’s a slight pity that White brutally captures a black officer. The white knight’s eighth move is the key, 1.S5xf6!, which in contrast carries no threat. 1…Sd~ 2.Be5 and 1…Sb~ 2.Qd5. White executes a knight tour consisting of the key and seven tries, while Black employs one knight to defeat these tries with seven different moves. A fine task problem demonstrating a knight vs knight duel.

Andy Sag: Post key, only the knights can move. The try 1.S5xb6? is brutal but I thought the refutation was subtle. First prize deserved.
Jacob Hoover: Each try is refuted by a different defense. Since all eight possible moves of the d5-knight are seen here, we have a white knight-wheel.

In two of the solutions, the black king remains on e6, meaning the flights on e5, e7, and f7 need to be dealt with. For the first part, a knight promotion mate on d8 occurs after the c8-rook unguards the mating square and simultaneously blocks e7. 1.Re8 Rd5 2.Rxe7 d8=S. White aims for a rook mate on the e-file for the second part, forcing the black queen to find a unique hideaway square. 1.Qa4 e8=B 2.Qxd7 Re1. In the third solution, White arranges a queen promotion mate on e8, which is viable only if the black king goes to d7 (because of the impeding black pieces on g8 and h8). 1.Qxd1 dxc8=R 2.Kd7 e8=Q. Four different types of promotion, or the Allumwandlung theme, are spread over three phases of play. Furthermore, White’s three units rotate their functions to (1) be sacrificed, (2) control flights, and (3) give mate. Hence we see a full 3x3 cycle of function changes, which incorporates a cyclic Zilahi.

Andy Sag: The three solutions are check free and feature all four possible promotions. All three white units take turns to get captured and participate in delivering mate. Difficult to solve.
Jacob Hoover: We have a cyclic change of roles for the three non-royal white units. In addition, since all four possible pawn promotions take place, we have an AUW.
Satanick Mukhuty: Interesting AUW. Excluding the king, White has three units; each of them gets captured in exactly one of the three solutions – perfection!

Black has two legal moves only and set play is prepared for them: 1…Kc5 2.Rc1+ Kd4 3.Rc4 and 1…d5 2.Rh8 dxe4 3.Rd8. Yet White has no pure waiting move capable of preserving both variations, e.g. 1.Rh3? Kc5!, 1.Re1? d5!, 1.Bf8? d5! The fabulous key 1.Rh6! (waiting) changes the reply to 1…Kc5, and it’s aimed at forestalling stalemate – 2.Ke3 gxh6 3.d4. The other set line is retained, 1…d5 2.Rh8 dxe4 3.Rd8. A third variation is added when Black accepts the offered rook, 1…gxh6 2.Bf6+ Kc5 3.d4. The three-move mutate was one of Whyatt’s specialties, and here he demonstrates the form with a first-rate key.

Andy Sag: The 1…Kc5 variation is all about stalemate avoidance. A stroke of genius!
George Meldrum: You’ve got to love White’s first move.
Satanick Mukhuty: Attractive mutate!

Black’s d-pawn clearly has captured one of White’s missing knights on the c-file. If the b-knight is sacrificed on c4, that leaves three moves for the g-knight to reach d5. All this makes the first solution straightforward: 1.Sa3 d5 2.Sc4 dxc4 3.Sh3 Qd5 4.Sf4 Kd8 5.Sxd5. Part (b), requiring the same position to be reached after White’s 6th move, is trickier. Both sides must “waste” a move somehow, but White cannot lose a tempo with either knight. Suppose the b-knight tries to be captured on c5 instead, to use up three moves; that would be compatible with the d-pawn spending an extra tempo to reach c4 via c5. However, after 1.Sc3? d6 2.Sa4/Se4, Black is stuck since 2…Qd5 is unplayable. The solution utilises the d-pawn route just mentioned, but here the plan is to sacrifice the g-knight instead on the c-file. 1.Sf3 d6 2.Se5 Qd7 3.Sxd7 Kd8 4.Sc5 dxc5 5.Sc3 c4 6.Sd5. The identity of the knight on d5 is thus changed, and the black queen gets captured on a different square. Other than …Kd8, no moves are repeated across the two solutions.

Andy Sag: In (b), to get six white moves, one knight must be captured on a black square.
Jacob Hoover: In part (a) both white knights move toward the edge of the board initially and in part (b) they both move toward the center.
Satanick Mukhuty: The d7-pawn captures the b1-knight in one line and the g1-knight in the other. Enjoyed the unusual twinning.

The whole white force has to contribute to corral the black king, and if the strong defence 1…Kb5 is allowed, the distant white king becomes a bystander. The key 1.Sd6! begins a knight manoeuvre that pushes the black king in the opposite direction, all the way to the right edge. 1…Kd5 2.Se4 Ke5 3.Sf6 Kf5 4.Sg4 Kg5 5.Sh6 Kh5 6.Sf7 Kh4 7.Rh6, or 5…Kh4 6.Sf7 Kh5/Kh3 7.Rh6. The knight completes a rundlauf by returning to its initial square f7, and two variations finish with similar model mates.

Andy Sag: A miniature one-liner where the knight makes six moves ending where it started after forcing the black king all the way to h-file. Nice!
George Meldrum: Simple idea but really cool, and White duplicates its starting setting on move six.
Satanick Mukhuty: A cunning, systematic knight manoeuvre that seals the black monarch’s inescapable fate, one square at a time.

After the key 1.Qb4!, the threat of 2.Qxd4 is parried by all possible moves of either black knight. The d4-knight is controlling White’s R + S battery on the e-file, and a random move by this piece, 1…Sd~ (e.g. 1…Sc2), permits 2.Sxf4. Three specific moves of this knight prevent the 2.Sxf4 secondary threat – such defences are called correction moves – but they commit new errors that White can exploit. 1…Sdxe6 (self-pin) 2.Qc3, 1…Sf5 (interference) 2.Qe4, and 1…Sc6 (interference) 2.Qxd6. The f4-knight also controls the R + S battery, and its random placement 1…Sf~ (e.g. 1…Sg2) enables 2.Sxd4. This knight likewise has three correction moves that preclude 2.Sxd4, but their own errors lead to other mates. 1…Sfxe6 (self-pin) 2.gxh4, 1…Sg6 (interference) 2.Sd3, and 1…Sd5 (self-block) 2.Sc4. By-play: 1…Ra4 2.Qxd6. There are no less than eight thematic variations in this highly intensive rendition of correction play.

Andy Sag: Lots of interesting play with threat and nine variations. A pity that 1…g4 2.gxf4 does not defend the threat.
Jacob Hoover: With no less than nine distinct mates (including the threat) there is a high degree of variety to be seen here. This solver heartily approves of this.
Satanick Mukhuty: Beautiful combination of black correction and Mackenzie theme.

In two solutions, Black begins by blocking one of the king’s flights on d3 and e3 with the queen, a move that simultaneously unpins the white queen. To cover the other flight, the latter piece prepares to mate on e5 or f5, each an occupied square that must be cleared by a black bishop. 1.Qd3 Qe7 2.Bxe5 Qxe5 and 1.Qe3 Qxg6 2.Bxf5 Qxf5. The other two solutions are more difficult, as they involve shifting the black king to an initially guarded square. The e2-knight first cuts off either the white bishop or rook, to grant the king access to e5 or f5. White then unpins the queen by moving the king to the g-file, carefully choosing a square that’s compatible with the subsequent queen play. Finally the black king’s move leaves the knight pinned, which is essential for the mate delivered by the queen. 1.Sd4 Kg8 2.Kxe5 Qe7 and 1.Sf4 Kg7 2.Kxf5 Qxg6. Each of the two pairs of solutions shares plenty of strategic effects – such a scheme is known as Helpmate of the Future. Curiously, some connecting elements are also found across the two couplets: the pawns on e5/f5 are captured, once by the bishops, then again by the king, and …Qe7/Qxg6 recur as White’s first moves and mating moves.

Andy Sag: There are two sets of “twins” here; in one set the black queen unpins the white one and blocks a flight, and a pawn is captured by a black bishop only to be taken by the white queen in the mating move. In the other set, the e-knight unguards a white pawn, the white king moves to unpin the queen who delivers a pin-mate after the black king takes the unguarded pawn.
Satanick Mukhuty: In one pair of solutions, the black queen acts as a self-blocker; in another, the black knight from e2 gets pinned (anticipatory self-pin). Since the solutions are pairwise homostrategic, I believe this qualifies as a Helpmate of the Future.

There are three set variations where White’s b8-bishop plays an active part. 1…e6 2.Be5+ Kxe5 3.Qxf4; 1…e5 2.Bd6 (threats: 3.Bc5/Ra4) Sc2 3.Bc5, 2…Sb3/e4 3.Ra4; and 1…Bg1 2.gxf4 any 3.Be5. In two of these set lines, White exploits the e7-pawn’s self-blocks on different squares. The key 1.Rc7! surprisingly interferes with the bishop and thus abolishes the set play, besides granting a flight on e5. The threat is to sacrifice the key-piece with 2.Rc4+ dxc4 3.Be5. If Black takes the flight, the king walks into the B + R battery: 1…Ke5 2.Rc6+ Kf5 3.Qxf4, 2…Kd4 3.Ra4. The two mating moves here – plus 3.Be5 in the threat line – all occurred previously in the set variations, but against other defences, so a sort of mate transference is effected. Black’s f4-rook can foil the threat by guarding e5, but both ways of doing so result in self-blocks. 1…Re4 2.Qc3+ Ke3 3.d4 and 1…Rf5 2.Ra4+ Ke5 3.Rc6 – two battery mates. The fine post-key play is further enhanced by the set play, in that the two phases exhibit transferred mates and a change of self-blocking units.

Andy Sag: The key poses a tricky threat and gives a flight which turns out to be a nasty battery ambush. The two rook defences are also tricky because the resultant self-blocks are not immediately evident.
Rauf Aliovsadzade: Nice key.
Satanick Mukhuty: Black’s defences with the rook (in two variations) result in self-block weaknesses, while 1…Ke5 is neatly handled by the battery created via the fine flight-giving key. Satisfying!
George Meldrum: Nice problem by Makaronez. Especially like the extra lines of play where the black king gets mated on four different squares.

It’s not feasible to organise any mid-board mate by the knight where the king is placed on a white square like c4 or d5, mostly because four black pieces are not enough to block all flights. The solution shifts the king to the edge square d1 for a knight mate on e3. The self-blocking units must avoid guarding e3, hence a rook is allocated to d2 while the b5-bishop targets e2, leaving the b2-bishop to access c1 in one step and the other rook to obstruct e1. Even with the mating configuration determined, the move sequence proves difficult to uncover, as Black must take care not to give any check, e.g. 1.Re3 2.Re1 3.Rb3 4.Kc3 5.Kd2 6.Kd1 7.Rd3 8.Rd2 9.Bc1 10.Be2 is too long. The trick is to use the king to remove the c2-pawn, thereby clearing the second rank for the b4-rook to reach d2 in just two moves. 1.Re3 2.Bc1 3.Rb2 4.Kc3 5.Kxc2 6.Kd1 7.Rd2 8.Re1 9.Be2 for Se3. The diagram shows a linear arrangement of black rooks and bishops called “organ pipes” as a visual feature (see Weekly Problem No.715). Curiously, in the mating position the black pieces on d2/e2 cut off defenders on c1/e1, which otherwise would prevent the mate; this echoes the self-interference effects associated with the organ pipes, as if the four pieces had begun on the first rank.

Andy Sag: Only the knight can mate and there are six squares that the black king can be mated on but only one (d1) can be done in nine moves and then only if the white pawn is captured by the black king en route.
Satanick Mukhuty: A beautifully well-concealed solution. For the longest time I didn’t realise how the c2-pawn fit into the picture!

The black king seems unlikely to be mated on its initial square, given its many flights. White’s rook and bishop are both pinned, and if either is released by Black, we may anticipate a further mutual unpinning effect with …Bd6 and …Rf5 in the two phases. Black has numerous ways of freeing each white piece, such as by withdrawing the pinner on f1 or a3; for each first move to be forced, then, it needs an additional motive. The interpositions Bf3 and Sb4 work by serving as prospective self-blocks for the approaching black king, which heads for each white piece’s starting square. 1.Bf3 Bd6 2.Ke4 Re5+ 3.Kf4 dxe3 and 1.Sb4 Rf5 2.Kd4 Be5+ 3.Kc5 d4. White’s first move in each case, besides acting as an unpin as mentioned, shifts a line-piece across the critical square, e5. The unpinned piece then lands on this square, causing a self-interference that enables the king to reach its final spot. The batteries formed by the critical play don’t fire as one might expect, and instead White mates with the d2-pawn on different squares.

Andy Sag: Black unpins a white piece which then unpins the other white piece which then checks. Finally the king moves a second time allowing the d-pawn to mate. Nicely matched solutions.
Satanick Mukhuty: Perfectly harmonious solutions!

Two prominent captures by the black knight are provided with set mates: 1…Sxd3 2.Rxd3 and 1…Sxd5 2.Rxd5. The thematic try 1.Bf3? threatens 2.Qg4. When Black defends with the knight captures, the set replies no longer work (for non-symmetrical reasons); instead White exploits these defences as self-blocks – 1…Sxd3 2.R3e4 and 1…Sxd5 2.R5e4. This try is defeated by 1…gxf5!, however. The key 1.Qg4! concedes two flights by unguarding the rooks, and threatens 2.Bf3. The two knight defences are still playable and White answers them with yet another pair of mates: 1…Sxd3 2.Bxd3 and 1…Sxd5 2.Bxd5. The three pairs of changed mates (across set, try, and actual play) against the same two black moves produce the Zagoruiko theme. If Black takes the offered rooks, White activates the dark-squared bishop: 1…Kxe3 2.Bc5 and 1…Kxe5 2.Bg7. Lastly, 1…gxf5 permits a fourth battery opening (including the threat), 2.Bxf5.

Andy Sag: The key grants two flight captures. Threat and five variations all bishop moves to mate including four batteries and two changed mates.
George Meldrum: Changed mates from set play after 1…Sxd5/Sxd3. The try 1.Bf3 has changed mates after 1…Sxd5/Sxd3; however, 1…gxf5 stops the mate threat. All mate lines are new after the key.
Jacob Hoover: A bit easy but enjoyable because of the rich thematic content: a 3x2 Zagoruiko, battery plays, and a white bishop-star.

The set play 1…Sc3 2.Bf6 g4 3.Bxc3 highlights the g-pawn’s role in preventing stalemate. The position is in fact a complete block with a full-length variation prepared for 1…g4 – 2.Bg5 g3 3.Bh6 Sc3/Sf6 4.Bg7 g2 5.Bxc3/Bxf6. The main try 1.Bxg5? gives Black stalemating opportunities by removing the pawn, and it’s one move too slow: 1…Sc3 2.Be3 Se2+ (2…Sb5 3.Bd2) 3.Kc2 Sc3 4.Bf4 (or 4.Bh6) S~ 5.Be5+ Sc3 6.Bxc3. The key 1.Ba5! eyes c3 and keeps the knight paralysed; 1…g4 2.Bd2 g3. Now 3.Kc2? to vacate c1 for the bishop seems tempting, as both knight checks are covered, but 3…g2! 4.Bc1 Sb4+/Se3+ refutes. Instead, White plays the sweeping 3.Bh6 to transpose back to the set variation, 3…Sc3/Sf6 4.Bg7 g2 5.Bxc3/Bxf6, or similarly 3…g2 4.Bg7+ Sc3/Sf6 5.Bxc3/Bxf6. Five-move trip by the bishop with attractive long-range play.

Andy Sag: To take or not to take (g5); that is the question.
Satanick Mukhuty: You have to keep the g-pawn alive to avoid stalemate.
Thomas Thannheiser: Long bishop circuit.
George Meldrum: Tricky, but expect nothing less from a Shinkman problem.
Bob Meadley: 3.Bh6!! Very, very good and what a master he was.

Initially the R + S battery on the f-file is restricted by a diagonal pin of the f5-knight. The situation is reversed in the twin, where a black knight on f5 forms a B + S battery but is pinned by the rook. This suggests that the white-black analogous effects associated with duplex helpmates may occur across the twins, rather than within the two duplex solutions of each position. In (a) for the White-to-mate part, the bishop blocks e8 and when both kings shuffle into place, the unpinned knight delivers a battery mate: 1.Be8 Kd5 2.Kf7 Sfe7. For the Black-to-mate solution, the rook steps back to block f3, the f5-knight gets captured by its black pinner, and the white king occupies the vacated f4-square: 1.Rf3 Bxf5+ 2.Kf4 g5. In (b) for the White-to-mate part, the bishop steps back to block h7, the f5-knight gets captured by its white pinner, and the black king occupies the vacated g6-square: 1.Bh7 Rxf5+ 2.Kg6 Se7. For the Black-to-mate solution, the two kings shuffle into place and after the rook blocks c4, the unpinned knight delivers a battery mate: 1.Kd3 Ke5 2.Rc4 Sd4. Two pairs of matching solutions are rarely accomplished in duplex helpmates, especially when the strategies involved are reasonably complex as here.

Satanick Mukhuty: In each part, we get a battery mate in one instance, and in another, the front piece of the said battery is captured.

Two half-batteries on the second rank are aimed at the black king, each employing two pawns coupled with a major piece. If White moves any of these pawns, that will threaten a battery mate delivered by its counterpart. The four pawns have eight possible (non-capturing) moves, seven of which serve as tries that are refuted in different ways. 1.f4? (2.e3/e4) Qh5!, 1.f3? (2.e3/e4) Qc7!, 1.e4? (2.f3/f4) Qa7!, 1.e3? (2.f3/f4) Sf4+! In the first three king-side tries, Black exploits how the pawn that has already moved can’t be used to shut off the black queen, while the fourth try interferes with a queen mate on f4. 1.c4? (2.b3/b4/bxa3) Qg7!, 1.b4? (2.c3/c4) Ba4!, 1.b3? (2.c3/c4) Sc4! On the queen-side, the first two tries likewise fail because the pawn that has just moved can’t shut off the enemy queen or bishop, while the third try obstructs a knight mate on b3. The eighth pawn move is the key – 1.c3! (2.b3/b4/bxa3), which neutralises 1…Qg7 and prepares to meet 1…Ba4 with 2.b3. The mates set for the two knights’ defences are unhindered: 1…Sc4 2.Sb3 and 1…Sf4+ 2.Qxf4. Lastly, 1…axb2 forces 2.Rxb2. The tries are harmonious and unmissable when the solver is faced with eight analogous first moves.

Andy Sag: The dual threat is a minor blemish but some tries on the king-side are especially interesting.
Satanick Mukhuty: Rich try play executed through the use of two half-batteries. It is always instructive to solve a Mansfield two-mover!