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!

In two solutions, the queen mates with the support of the rook: 1.Kf4 Rf5+ 2.Ke4 Qf3 and 1.Rf4 Rd5 2.Ke4 Qd3. These mating configurations are the same but reflected, to bring about a pair of echo mates. In the other two solutions, the queen and rook swap functions: 1.Rc4 Qf3+ 2.Kd4 Rd5 and 1.Rg4 Qd3+ 2.Kf4 Rf5. Another pair of reflection echo mates is displayed. While such precise echoes are common in helpmates, this example is exceptional in adding a formal theme that connects all four parts. If the white moves are labelled – 1.Kf4 Rf5+ [A] 2.Ke4 Qf3 [B], 1.Rc4 Qf3+ [B] 2.Kd4 Rd5 [C], 1.Rf4 Rd5 [C] 2.Ke4 Qd3 [D], 1.Rg4 Qd3+ [D] 2.Kf4 Rf5 [A] – we see how they all recur as initial and mating moves to produce a cyclic pattern, AB-BC-CD-DA.

Andy Sag: A pair of queen mates and a pair of rook mates.
Rauf Aliovsadzade: Nice cycle!

White has two potential ways to force Black to mate, both knight checks on f2 that are answerable only by opening the R + P battery. However, after 1.Sdf2+? gxf2+, the e4-knight can block on g3, and after 1.Sef2+? gxf2+, the king gains a flight on e4. In the set play, all possible moves by Black enable White to execute one of these knight checks. 1…S~ pins the e4-knight, allowing 2.Sdf2+ gxf2; and 1…Rxa4 guards e4, allowing 2.Sef2+ gxf2. But White has no pure waiting move that could preserve these set variations; e.g. 1.a5? Rxa5! The unexpected key 1.Kf4! (waiting) places the king in line with the Q + P battery instead. Now neither knight check is threatened (for similar reasons as before), while the set replies to the two black defences no longer work, due to the king’s placement. These two defences have in fact switched their weaknesses, and to exploit them White accordingly reverses the two responses. 1…S~ guards e4, permitting 2.Sef2+ gxf2; and 1…Rxa4 pins the e4-knight, permitting 2.Sdf2+ gxf2. The reciprocal change of white continuations against a pair of black defences is achieved with attractive orthogonal-diagonal conversions.

Andy Sag: 1.bxa3? b2!, 1.a5? Rxa5! The key changes which knight checks on f2 from set position.
Satanick Mukhuty: Beautiful mutate with reciprocal change of play!

To get out of check, White has to either give a discovered check with the king, or capture the c3-knight with check. So this must be an unconventional problem with a checking key. 1.Kd4+? and other king moves fail to 1…Qe4+! The key 1.Bxc3+! also breaks the convention against capturing a piece on the first move, but Black is granted four checking replies. 1…Sf7+ 2.Be5+ Qd3+ 3.Ke6 or 2…Qb3+ 3.Kd4 – the king delivers a pair of battery pin-mates; also 2…Be3+/Bc3+ 3.Sxd1. If 1…Bf4+ then 2.Bd2+ leads to more pin-mates, 2…Qd3+ 3.Rxd3 and 2…Qb3+ 3.Rxb3; these two queen checks result in changed mates when compared with the 1…Sf7+ variation (such a scheme is known as Visserman type). An unfortunate dual follows 1…Qf5+ with both 2.Be5+ Be3+/Bc3+ 3.Sxd1 and 2.Rxf5+ Bf4+ 3.Bd2, 2…Kg3 3.Sxh1 working. Lastly 1…Kg3+ enables a short mate, 2.Sxh1. Spectacular cross-check problem where the main defences 1…Sf7+ and 1…Bf4+ branch into five sub-variations where every single move by Black and White is a check. Indeed, even the flawed variations beginning with 1…Qf5+ and 1…Kg3+ consist of checking moves throughout. Given this theme, White being in check initially and the checking key seem to be congruous features.

Remarkably, the composer has produced an improved version of this three-mover that not only removes the white dual but also extends the short variation. See diagram below.

Composer: A fun mate-in-3 with all moves by White and Black being a check. The key move is outrageous being a check, a capture, and covering one of Black’s flight squares. Still, I hope there is enough variety in play to keep the solver interested.
Andy Sag: One good battery deserves another.
Satanick Mukhuty: An unusual problem, no doubt. At first, I was quite puzzled by all the batteries and the lurking possibilities of cross-checks and pin-mates.
Bob Meadley: Compared to George’s previous 3-mover the difference is like chalk and cheese. Of course the cross checks are an old theme but not shown in this very game-like wild position. This seems a new area to me and I like it as it brings chess play and chess problems closer.

With only three moves available to paralyse the strong black force, the solution is likely to involve capturing some black units and pinning other ones. A plausible plan consists of using the h3-bishop to pin the knight on g6, and that will open the h-file for the rook to pin the e7-bishop on h4. However, after 1.Sg6 Bf5 2.d1=B (this self-locking promotion also enables the c1-bishop to guard the flight on h6) f7 3.Bh4 fxg8=R, the black bishop on b7 remains mobile. The solution is similar but aims to pin that bishop by removing the g7-pawn. Once …fxg7 is chosen, though, the black rook seems to block the pawn’s promotion. Hence we switch to promoting on h8 by capturing the knight, a move that also permits the black rook to reach g6 and be the pinned piece instead. 1.d1=B fxg7 2.Bh4 gxh8=B 3.Rg6 Bf5. A fairly challenging sequence with good interplay between the two sides that forces the move order.

Andy Sag: Took a while to spot this one! Both sides must sub-promote to bishop.
Satanick Mukhuty: Simple but enjoyable!

The key 1.Kd7! cuts off the white rook, granting a flight on d4, and threatens 2.Sxc6 by attacking e6. Black has six defences, each employing a different type of piece. Taking the king’s flight results in a royal battery mate, 1…Kxd4 2.Ke6. Black’s queen and rook may pin the threat-piece but they unguard the same mating square from behind: 1…Qd1 2.Qxe4 and 1…Rd1 2.Rxe4. The black knight weakens White’s control of f5 with 1…Sxg4, but that unguards another mate – 2.Sgf3. The black bishop commits a self-block in 1…Bxd4 2.Bb8. Lastly the f6-pawn creates a flight-square with 1…f5, and that permits 2.h8=Q. In every variation, White’s mating unit matches the black defender in type. At least three instances of such corresponding pieces are required to fulfil this idea known as the Balbo theme, and this is a record demonstration with six variations. The excellent key is unusual for a task problem.

Andy Sag: The key must add a guard to e6 to provide for 1…Bxd4, so is easy enough to spot. However, it grants a flight capture self-pinning the bishop and is answered by a king-triggered battery mate. Nice play!
Satanick Mukhuty: A pleasant two-mover with a first-rate key that grants the black king a capture-flight!
Jacob Hoover: Each defense is answered by a unit of the same type as the unit which just moved – the Balbo theme.
George Meldrum: Any problem that brings a smile on discovery, like this one, is a winner.

Two batteries are aimed at the black king, but neither could fire as the knights are on guarding duties. The king is in fact totally confined; hence we activate one of the outlying white pawns on the verge of promotion. 1.e5 gxf8=Q 2.e6 Qa3. Twinning by removing a white unit is slightly paradoxical in that such a piece on the mating side must have somehow prevented a solution in the previous part. In this helpmate, each new solution becomes viable when the vanished white unit unguards a flight-square, which the king then accesses. (b) 1.Kxd4 cxb8=Q 2.Kd5 Qe5, (c) 1.Kxc4 c8=Q+ 2.Kd3 Qc3, (d) 1.Kc2 cxd8=Q 2.Kb1 Qd1, and (e) 1.Ke3 g8=Q 2.Kf4 Qg5. Thus the white batteries are a camouflage and the Striptease twinning removes the four officers involved one by one. White arranges various queen mates instead after promotions on five different squares.

Andy Sag: Each of the five settings promotes to a queen on a different square, utilising all five possible set promotion squares. In each case the promoted queen goes on to deliver mate.

Of the 20 moves available to Black, at least 16 are taken up by pieces to reach their diagram squares, plus three are used by the h-rook to get captured on f3, leaving one spare move. White made nine visible moves with the king, queen, and pawns, so many remain for capturing the two missing black pawns. Three difficult, interconnected questions are: (1) which black unit should be allocated the spare move and its purpose, (2) how to steer the white king to d5 through a minefield of black units, and (3) which white pieces should be utilised to remove the two pawns. Consider this sample try that demonstrates the issues; here Black’s g-pawn uses the extra move to sacrifice itself to the g-knight, while the white king aims to access d5 via c4. 1.Sf3 g5 2.Sxg5 Sf6 3.Se6 Rg8 4.Sc5 Rg3 5.Sxd7 Rf3 6.Sc5 Qd6 7.h4 Qh2 8.exf3 Sc6 9.Ke2 Bf5 10.Se4 Rd8 11.g3 Rd5 12.b3 Rb5 13.Kd3 e5 14.Kc4 Bb4 15.Qe1 Sd8 16.Sg5 c5 17.Sh3; now 17…Bd3+? dislodges the king or 17…Se4? blocks the f5-bishop.

In the solution, Black’s c-bishop is given the extra move to reach d3 in three steps, which allows …Se4 to be played early without impeding that bishop. Both black pawns are therefore captured unmoved, and White employs the long-range bishops for that task. 1.b3 Sf6 2.Bb2 Se4 3.Bxg7 Rg8 4.Bb2 Rg3 5.h4 Rf3 6.exf3 f6 7.Bb5 Kf7 8.Bxd7 Sc6 9.Bh3 Qd6 10.Bc1 Qh2. At this point, it seems that the black bishop’s route must be …Be6-c4-d3, since …Bd7 and …Rd8 would entangle these pieces with the c6-knight. But this scheme again hampers the white king, regardless of the spare tempi available to White: 11.Ke2 Be6 12.Qe1 Rd8 13.g3 Rd5 14.Bf1 Rb5 15.Ke3 Sd8 16.Kd4 Bc4 17.Qd1 Bd3 18.Qe1; here 18…e5+? disturbs the king or 18…c5+? obstructs the f8-bishop. The actual route of the c-bishop is the surprising …Bh3-f1-d3, which leaves a safe passage for the king. 11.g3 e5 12.Bf1 Bh3 13.Bb5 Rd8 14.Ke2 Rd5 15.Qe1 Sd8 16.Bd7 Rb5 17.Kd3 Bb4 18.Kc4 c5 19.Kd5 Bf1 20.Bh3 Bd3 21.Bf1. White’s f-bishop makes two round-trips along the same path, first to capture the d7-pawn, then again to make way for its black counterpart, as a pure clearance manoeuvre. Extremely tough to solve!

Andy Sag: After working out that one black rook must be captured on f3, it can be concluded that Black has only one spare move. Fortunately White has plenty of spare moves which allows the white-squared bishops to follow each other clockwise round in a circle, so the black one can use the spare move to get to d3 via f1.
Satanick Mukhuty: Astounding proof game featuring a double rundlauf by the f1-bishop and a switchback by the c1-bishop. The idea of the c8-bishop taking the h3-f1-d3 route seemed exciting, and that in turn led me to uncover the double rundlauf. Took me quite some time to unravel this.
Jacob Hoover: Whew. That one was sadistically difficult!