Weekly Problems 2017-A

The key 1.Bb8! creates three threats, all rook mates: 2.Rc5/Rd6/Re5. Black’s play allows these mates to occur in every possible combination. Only one black move does not disable any threat – 1…Bg7 2.Rc5/Rd6/Re5. Three defences allow different dual mates by preventing one of the threats: 1…Se6 2.Rd6/Re5, 1…c3 2.Rc5/Re5, and 1…Bxf6 2.Rc5/Rd6. Another three defences force each of the rook mates individually: 1…Sf7 2.Rc5, 1…d3 2.Rd6, and 1…Sb7 2.Re5. Lastly, one move eliminates all of the threats but provokes a new mate, 1…Sxc6 2.Be6. This unusual theme, in which dual mates appear by design, is known as total combinative separation.

Nigel Nettheim: The pattern of black moves and white mates, including duals, is evidently considered to be the point of interest. Eccentric.

The diagram part is solved by 1.cxd5 Ba7 2.Kf4 Bb8 3.Qg4 Sxd5. The initial capture of the bishop on d5 is aimed at giving the white knight access to that square in the eventual mate. White sets up a B + S battery with the remaining bishop, while Black positions the king and finishes with a self-block by the queen. Part (b) is solved by 1.Rxe3 Bxc6 2.Kg2 Sd5 3.Sg3 Sxe3. Now it’s the bishop on e3 that gets captured but for a similar purpose – to clear that square for the knight’s mating move. The other white bishop is employed to form a B + S battery, which fires after a black king move and a self-block by the e4-knight. The two solutions vary in interesting ways – e.g. their move orders are forced using different techniques – but overall there’s great unity in the battery play rendered along two diagonal lines.

Andy Sag: Twin double-checks from batteries set up on move 2. Had a tough time until I realised that in each case one white bishop must be removed to allow the white knight to end up on that square. Note that the g6-pawn is a cook-stopper in (a) involving the knight mating on f5, and the d2-pawn is a cook-stopper in (b) involving the rook self-blocking on f1.
Nigel Nettheim: A celebration of the power of the double-check. The white knight had to be brought into play, which assisted solving, and the d2-pawn is needed for (b) only. But each first move is a surprising capture, and the perfect twinning seems amazing.

The key 1.e6!, which threatens 2.Qf4, thematically opens the fifth rank and enables the f5-bishop to give a number of discovered checks. Indeed Black has no defence other than to check with this bishop, and four variations result. 1…Bxe6+/Bxd3+ – an unguard and a self-pin respectively – 2.Qe5. 1…Bxg4+ is also an unguard and by creating a flight on f3, it induces the cross-check, 2.Sc5. 1…Be4+ is a self-block that leads to another cross-check, 2.Sf5. And 1…Bg6+ interferes with the g7-rook and permits 2.Bxg5. A black bishop-star is produced, an idea not commonly seen in directmates.

Nigel Nettheim: The latent cross-checks suggest the key, after which the play is clever with a mixture of (self-)pins and batteries. The h7-pawn prevents 1…Bh7, and the c6-pawn prevents 1.Sxf5+ Ke4 2.Qc6.
Andy Sag: Key allows discovered checks all answered by cross-checks as the f5-bishop provides line interference, self-block, self-pin, etc. The white pawn on c6 can be omitted if the black pawn is shifted from f7 to d7.
Jacob Hoover: A nice black correction theme with cross-checks thrown in for good measure. An old problem, but a good one.
Thomas Thannheiser: The threat 2.Qf4 also works on 1...Bxg3 because the bishop is pinned. Nice cross-check problem.

Two self-blocking pawn moves produce important set play: 1…e5 2.Sc5 and 1…cxd5 2.Re6. The key 1.Qh5! controls e5 and threatens 2.Sc5. Paradoxically 1…e5, which initially enables 2.Sc5, now defends against it (by cutting the queen’s line to d5), and a changed mate results: 2.S7f6. Another change occurs with 1…cxd5 2.Qg4. The original answer to 1…cxd5 is transferred to another defence: 1…c5 2.Re6. Such a combination of changed and transferred mates (with respect to the 1…cxd5 defence) creates a Rukhlis pattern, though the proper Rukhlis theme requires the idea to be doubled. Black commits two more self-blocks with 1…Bf5 2.Qh1 and 1…Sd3 2.Bg2. Lastly, 1…Sa4 allows 2.Rxa4. Whether the Dombrovskis-type paradox and the Rukhlis effect shown were intended or not, this century-old problem seems ahead of its time!

Nigel Nettheim: A wonderful collection of tries, so not easy to solve. 1…Bf5 2.Qh1 is very nice.
Andy Sag: Hard to solve until you realise that the key frees up the d7-knight whereas in set position the d5-knight is free to move. Three defences are diagonal self-blocks.
Jacob Hoover: Very nice.

The waiting key 1.Re2! completes the block. Each of the two black pawns has the maximum possible four legal moves, and they all generate different white responses. 1…c6 2.Sc7, 1…c5 2.Qc6, 1…cxb6 2.Sxb6, and 1…cxd6 2.Qxd6 involve two interferences with the black rook and two square-clearances. 1…f6 2.Se7, 1…f5 2.Re5, 1…fxe6 2.Bxe6, and 1…fxg6 2.Rxg5 show two interferences with the black queen, one square-clearance, and one unguard. The BP4 theme is therefore brought about twice. The by-play consists of simple unguards by three black pieces. 1…S~ 2.Qd4. The black rook is preventing three mates on the c-file, two of which are forced by 1…Rc6 2.Qxc6 and 1…Rc5 2.Qxc5; duals follow 1…Rc4 2.bxc4/dxc4 and 1…R-else 2.Sxc7/Qc6/Qc5. The black queen is also stopping three mates, with two separated by 1…Qf6 2.Bg2 and 1…Qf5/Qh5 2.Se7; other queen moves allow various combinations of 2.Bg2/Se7/Re5, except for 1…Qxf4 2.Se7/Sxf4. The try 1.Re1? is defeated by 1…Qf6!

Andy Sag: Waiter with countless variations. The main point appears to be the eight variations involving all possible moves of the two pawns and these are dual-free, and arguably one – 1…fxg6 2.Rxg5 – is a changed mate (different rook).
Jacob Hoover: The main theme seems to be shown with the two black pawns, with the black corrections being almost an afterthought in my opinion.
Nigel Nettheim: Quite elaborate, but spoiled by the duals – one in the set play and many (including three triples) in the actual play.

If the two white bishops were allowed to cover the knights standing next to the black king, the queen would be freed to mate on the seventh rank. But three black pieces are in the way, two of which if moved could check the white king by discovery. Dealing with these hurdles, the white queen captures one of the three black pieces (self-pinning itself) on its way to the seventh rank, while the other two black pieces open the white bishop lines and, simultaneously, close black lines to avoid checking White and to unpin the white queen. 1.Rg3 Qxe4 2.Sg4 Qh7. Part (b) has a black bishop starting on f3, and it’s solved by 1.Bg4 Qxf2 2.Sg3 Qf7. Two perfectly matched solutions with terrific line-play.

George Meldrum: The twin position gave away the key move somewhat. Clearing the lines for the two white bishops seemed to baffle me for quite some time. Neatly done.
Andy Sag: An accurate twin comprising a tale of two batteries: the f3-piece deactivates one battery, the queen self-pins by capturing a knight, and the remaining knight unpins the queen which then mates.
Jacob Hoover: This wasn't too difficult for a helpmate.

The key 1.Rg4! protects e4 to create the threat, 2.Sb4. The variations 1…Re5 2.Sf6 and 1…Bc6 2.Sc7 show excellent, analogous play. In each case Black shuts off a white piece – the h8-bishop or the c8-rook – so that the threat-move, which interferes with the white queen, would give a flight on the fourth rank; but each defence also self-blocks, enabling a knight mating move that disrupts a line controlled by the same white piece cut off by Black. In 1…Rxh8 2.Rg5 and 1…Bxc8 2.Qxb5, Black removes the white line-pieces altogether but exposes the king to orthogonal mates on the fifth rank. 1…Sc2 2.Qxb3 and 1…Sd3 2.Qd4 see the black knight interfering with the queen on d1 twice to permit queen mates. The problem hence presents three pairs of corresponding variations. There’s by-play with 1…Ba3 2.Sxc3, 1…Rxe4 2.Qxe4, and 1…Qd4 2.Qxd4.

Andy Sag: The key guards the e4-knight threatening 2.Sb4 and leaves the queen en prise but frees it up to mate in four variations.
Jacob Hoover: In the diagram, the white queen – the only piece guarding the e4-knight – is threatened with capture by the b5-pawn. Of the squares near the black king that the white queen guards, all of them, with the sole exception of e4, are guarded by other white units. So the solution seems to be to put another guard on e4, and doing so also threatens 2.Sb4.

The black knight has four legal moves including two checks, all with set play prepared: 1…Sb6+ 2.Qxb6 and 3.Qb1/Qb2/Qc5/Qc7; 1…Sc5+ 2.Qxc5; 1…Sb2 2.Qc5+ Sc4 3.Qxc4; and 1…Sc3 2.Qc5 and 3.Qa3/Qxc3. The key 1.Qg4! entails a short threat, 2.Qd1, and completely changes White’s answers to these defences. 1…Sb6+ 2.Kd6 (threat: 3.Qd1) Sc8+ 3.Qxc8, or 2…Sc4+ 3.Qxc4. 1…Sc5+ 2.Kc8 and 3.Qd1/Qc4. 1…Sb2 2.Qe2 and 3.Rc2. After 1…Sc3, not 2.Qc4? Qxg7! but 2.Qb4 (threats: 3.Qa3/Qb2/Qxc3) Sa4/Sd1 3.Qb1. In response to the knight checks, White makes a leisurely king move and, in the case of the first variation, invites two further checks!

Andy Sag: The threat is a short mate but we have all four possible knight moves providing a defence; the first variation involving successive checks is the highlight.
Jacob Hoover: After 1..Sb6+ and 1…Sc5+, if White moves the king anywhere other than the noted squares Black has a delaying check.

Set mates have been arranged for every possible black move: 1…d3 2.Qxd3, 1…e4 2.Qd6, 1…Ke4 2.Qf3/Qg2, 1…B~ 2.Bxb7, and 1…S~ 2.Sxf6. But White has no way of preserving all of these variations, e.g. 1.Qh2? d3!, 1.Qh3? e4! The withdrawal key 1.Qe1! (waiting) yields three new mates: 1…d3 2.e4 (nice en passant avoidance), 1…e4 2.Qxa5, and 1…Ke4 2.Qh1. The remaining play is unchanged: 1…B~ 2.Bxb7 and 1…S~ 2.Sxf6. The only flaw of this well-keyed mutate is the set dual, 1…Ke4 2.Qf3/Qg2, fixable by adding a white pawn on h2 and a black one on h3.

Andy Sag: Looks like an old classic; complete block with five variations including three changed mates.
George Meldrum: The range of tries, and the changed mates, combined with the innocuous looking key move make this a pleasing problem.

After the key 1.Qb2!, White threatens 2.Qg7/Qh8. Black has three defences on c3 that interfere with the b3-rook and unpin the white bishop on the third rank. This bishop is thus allowed to fire the R + B battery, playing to a different square each time to shut off a black line-piece. 1…Sc3 2.Be1, 1…c3 2.Bf4, and 1…Bc3 2.Be5. The direct unpin 1…Rxb2 enables the battery to fire one more time – 2.Bf2. A fourth defence on c3 sees the black rook closing one white queen line and opening another: 1…Rc3 2.Qb8. Lastly, 1…Rxg3+ permits 2.Rxg3.

Andy Sag: Sacrificial key and six variations, four involving different placements of the unpinned battery trigger bishop.
Jacob Hoover: A nice presentation of a line-effect theme. We also see a "defences on same square" thing going on.
Nigel Nettheim: Nice handling of the four defences on c3.
George Meldrum: An alluring setting with a wicked key move that provides threats by the double. But it is all in the variations, most of which centre around blocking the queen’s path on c3. My favourite is 1…Rc3 2.Qb8.

This tough helpmate is solved by 1.d5 a3 2.d4 axb4 3.d3 b5 4.dxe2 b6 5.e1=B bxa7 6.e2 a8=Q 7.e3 Qf3. Both thematic pawns depart from their initial ranks and eventually promote, so the Excelsior idea is doubled. The unusual motive for the black promotion accounts for the difficulty. Black promotes not for the purpose of employing the new piece (e.g. to self-block), but solely to clear e2 for the e3-pawn. A bishop promotion is required since another piece on e1 would either check White or control the mating square f3.

Andy Sag: Not hard to see that the promoted queen could get to f3 in seven moves but only if the e4-pawn was not there. Working out how to deal with the e4-pawn took forever. A number of near misses in eight moves make this a very difficult and tantalizing problem.
George Meldrum: I can personally vouch that there are about 20 other ways to do this in eight moves. It took most of my Saturday, and it was only in the freshness of Sunday morning when it came into view. There is only one was to describe this problem: frustratingly good.

The key 1.Se4! threatens 2.Sd6. The two black knights defend by capturing the white queen, to create a flight on e7. But each knight move also opens a white line to an eighth-rank square controlled by the e7-pawn, enabling White to promote on that square and give a pin-mate: 1…Sfxe6 2.exf8=Q and 1…Scxe6 2.exd8=Q. The knight defences are thus anticipatory self-pins, and there’s a paradoxical element as well in that the white mates on f8 and d8 occur only after they have been guarded by the black knights. Two more thematic defences yield a flight by capturing the e7-pawn, and again they lead to pin-mates: 1…Qxe7 2.Qg8 and 1…Bxe7 2.Qc8. The impressive pinning strategy shown on the e-file also entails an exchange of functions between the white queen and pawn. One by-play variation is 1…Rc6 2.Qd7.

Andy Sag: All five defences have set mates including two pairs of pin-mates. The knight defences open white lines aimed at the promotion mating squares.
Nigel Nettheim: The capturing promotions make a nice symmetrical matrix, causing any black knight that ventures onto e6 to be pinned. The c3-rook and d3-pawn are not needed, but provide the minor variation; I’d vote to remove them.

A plausible mating scheme involves placing the black king on a8 and two pieces on a7 and b8 to self-block, and this would enable the white bishop to mate by capturing an interposing piece on the long diagonal. The self-blocking pieces must be bishops to avoid interfering with the mate, so Black promotes both pawns to this type of unit. And since to check during the move sequence is forbidden, Black uses the knights to shield the white king from the promoted bishops. 1.Sf6 2.Se4 3.Sf2 4.g1=B 5.Bh2 6.Se4 7.Sd2 8.c1=B 9.Ba3 10.Sb3 11.Sd4 12.Bc5 13.Ba7 14.Sb6 15.Sc6 16.Ka8 17.Bhb8 Bxc6.

Andy Sag: The final scenario with the black king on a8 is fairly obvious but how to get there in 17 moves without checks is the task.
Nigel Nettheim: The series of tasks in logic is elegant, though not difficult. For instance, a knight must occupy b6, for on c5 or d4 it would prevent mate.
George Meldrum: Another try was to get the black king to f1 and mate with Be2 but it just fails the 17 moves stipulation. The problem would have been much easier if the white king were on another square!
Andrew Buchanan: Not complicated but it was fun to follow the false trails and eventually see all the constraints that led to a unique story solution. Fun to see the knight and bishops dancing round the white king.

The initial position is a complete block, with set mates prepared for all of Black’s moves: 1…B~ 2.Qb2 and 1…g4 2.Qh4. The key 1.Qh2! (waiting) preserves the set play but also unpins the black knight. A random move by the piece opens a white queen line for 1…S~ 2.Qe5. Two correction moves disable the queen mate but they cause self-blocks that are exploited by the rooks: 1…Sg6 2.Rgf7 and 1…Se6 2.Ref7. A third correction interferes with the black bishop and permits yet another queen mate: 1…Sd3 2.Qh6.

Andy Sag: The key unpins the black knight to add four variations to the two already set in an economical eleven-piece setting.
Ian Shanahan: Three excellent corrections by the black knight.
George Meldrum: Quite a cute problem that frees the black knight to add to the set play with four new mates.
Nigel Nettheim: The black knight comes into play with 1…S~ 2.Qe5 and three nice corrections. Very economical.
Andrew Buchanan: 1.Ka2? gets checked and 1.Kb2? amusingly occupies a key square that White would need. 1.Qg3? (threat: 2.Qxg5) was promising but 1…Bg6! controls f7. Still the idea of pinning the black knight along a new line looks cool, and 1.Qh2! covers e5 indirectly. It's an obvious idea to have lots of black knight defences, to break the woodenness of the white symmetry. Perfectly dual-free.
Brian Stephenson: Clean, elegant setting with the c7-pawn being needed to stop the dual 2.Qd6 after some black knight moves. Much enjoyed.
Jacob Hoover: This problem had a lot of things for me to like: black correction, line effects, a complete block, and a proliferation of queen mates.

The thematic set play consists of two pairs of variations that involve reversals of White’s second and third moves (as the A-B-C-D labels indicate): 1…Rxe4+ 2.fxe4+ [A] Bxe4 3.g8=Q [B], 1…Bxe4 2. g8=Q+ [B] Rxg8 3.fxe4 [A], 1…Rxd4 2.Sc7+ [C] Bxc7 3.Qxd4 [D], and 1…Bxd4+ 2.Qxd4+ [D] Rxd4 3.Sc7 [C]. After the key 1.Kd3!, Black’s four initial captures in the above variations all stop the threat of 2.Se3, but thanks to the white king’s new position, the continuations are all changed: 1…Rxe4 2.g8=Q+ [B] Bxg8 3.fxe4 [A], 1…Bxe4+ 2.fxe4+ [A] Rxe4 3.g8=Q [B], 1…Rxd4+ 2.Qxd4+ [D] Bxd4 3.Sc7 [C], and 1…Bxd4 2.Sc7+ [C] Rxc7 3.Qxd4 [D]. Again we see two reversals of White’s second and third moves. And further, an elaborate form of reciprocal change is rendered with respect to the set play, in that after each pair of defences, White swap not only the two second moves around but the two mating moves as well. There’s by-play with 1…Rc3+ 2.Sxc3+ Sxc3 3.Qb3. A dense pattern yet crisply shown.

Andy Sag: Short threat swaps bishop and rook checks and adds four changed mating plays to one preserved set play.
Brian Stephenson: The short threat of 2.Se3 just had to be investigated, which meant only one possible candidate for key, which I tried and so very quickly solved this. It was only after I finished writing down the variations that I realised that there might be a double reciprocal change. And there was!
Nigel Nettheim: A thematic key. The respective black rooks and bishops cannot both continue to guard the vital squares g8 and c7. A heroic doubling (or quadrupling) of the theme: alternated white second and third moves respond to alternated black bishop and rook captures. The d7-pawn avoids a dual 1…Rxe4 2.Bxc4+ Kc6 3.d5.
Jacob Hoover: A whole lot of reciprocal changes occur between the set and actual play, and the black rooks and bishops interchange roles. A very interesting theme here; and I enjoyed it immensely.
George Meldrum: A heavily engineered setting with full military precision. The battlefield contains diligent distraction tactics. A medal should go to General Onkoud.

The key 1.Qh3! threatens a pin-mate, 2.Qe6. Any black move to b4 or c4 would unpin the d4-knight and thwart the threat, and four such defences result in two pairs of mutual interferences between the rooks and bishops. 1…Bb4 2.Rc4, 1…Rb4 2.Sxc5, 1…Bc4 2.Sc3, and 1…Rc4 2.Qd3. Hence the problem exhibits a double Grimshaw, which is additionally unified by the common unpinning motive. Four other variations make up the by-play: 1…Qh2/Qh1 2.Sf2, 1…Bxe2 2.Rxe2, 1…e5 2.Sd6, and 1…f5 2.Qf3.

Brian Stephenson: With 1…Qxd1! taking a flight at e3 and unprovided, one is encouraged to look for a threat on the e-file to cover e3. That's going to be by the queen, so 1.Qh3! (2.Qe6) is soon found.
Andy Sag: The key sets up a pin-mate threat with four unpin defences including two already set, all creating interferences to allow different mates. Removal of the e2-pawn is answered by a required double-check mate and finally there are three set plays involving two unguards and a self-block making eight variations in total.
Nigel Nettheim: The main play is the pair of rook-bishop (Grimshaw) interferences on b4 and c4.
Jacob Hoover: Four moves unpin the knight and these occur in two Grimshaw pairs.
George Meldrum: Not much in new play after the key, but the problem forces you to work through some very nice variations. My choice one is 1…Bb4 2.Rc4.

A great key, 1.Bb6! (threat: 2.Qc5), concedes two flights to the black king, enabling it to execute a pair of discovered checks: 1…Kb4+ 2.Sfd5 and 1…Kc3+ 2.Scd5. The key also opens the a-file and permits a third discovered check: 1…axb5+ 2.Sa6. The three cross-check variations are supplemented by 1…Bd4 2.Qxd4.

Andy Sag: The key allows three discovered checks answered by battery mates. Two of these are flights and the mates are double-checks, required in the 1…Kc3 variation. The black rook and a- and b-pawns can be removed if the h8-bishop is relocated to g7, reducing the setting to eleven pieces albeit with one less variation.
Ian Shanahan: A rather tricky flight-giving key to find. The cross-check plus self-block is delicious. Clearly, though, the two batteries must be activated somehow.
Brian Stephenson: Solved on the “Wouldn't it be nice if…” principle. The d2-pawn stops 1.Sfd5+ cooking. A high-class traditional two-mover and much enjoyed.
Thomas Thannheiser: Cross-check problem from good old Good Companions time with the relatively obvious key.
George Meldrum: After the key move the black king is given two flight squares – wow. After the key move Black can check the white king three ways – wow. In summary… wow!

The diagram position is solved by 1.Rec3 Rh7 2.Bd3 Bf2. Black’s initial rook move, besides interfering with the b2-bishop, crosses over the critical square d3. After White covers a potential flight with the rook, Black plays the g6-bishop to the critical square to cut off the black rook, allowing a long-range mate by the white bishop. The twinning, by shifting the c4-pawn to d4, opens the c-file but closes the long diagonal. The resulting solution is 1.Bc2 Bb8 2.Rd3 Rh6. Now the first bishop move involves an interference with the c1-rook as well as critical play over the d3-square. White uses the bishop to guard another flight, then the e3-rook moves to the critical square to cut off the black bishop, enabling the white rook to give a long-range mate.

Thomas Thannheiser: Exchange of functions between g6-bishop/e3-rook and g3-bishop/h3-rook on the other side.
Jacob Hoover: In each part, both black self-interferences are necessary for a valid mate.
Andy Sag: I found it easier to solve (b) first. Nice twin where rooks and bishops swap preparation, mating and interference roles.
Brian Stephenson: All the interesting play is by Black, with White just moving into position.
Nigel Nettheim: Neat twins.
Andrew Buchanan: Quite fun.
George Meldrum: Poetry in motion.

Set mates are arranged initially for every possible black move: 1…Be5 2.Be4, 1…Bd6 2.Sb6, 1…Bc7 2.Sxc7, 1…Sa~ 2.Qc6, 1…Sf~ 2.Qe6, 1…b4 2.Bc4, and 1…c4 2.Sb6. Tries that attempt to preserve the set play include 1.Qb6? Bd6! and 1.Bb2? c4!, while 1.Re8? threatening 2.Be4 is spoiled by 1…Be5! After 1.Sc4! (waiting), the key-piece loses control of c4 and c6 but observes e5 and d6, leading to these changed mates: 1…Be5 2.Rxe5, 1…Bd6 2.Qxd6, 1…Sc6 2.Sab6, 1…Sc8 2.Qb7, and 1…b4 2.Be4. A new defence 1…bxc4 allows 2.Bxc4. The rest of the play is as set: 1…Bc7 2.Sxc7, 1…Sf~ 2.Qe6. This terrific mutate achieves an Ideal Rukhlis (long before the composer Rukhlis was born!), which combines changed and transferred mates in a pattern as indicated by the following move labels: set 1…Be5 [a] 2.Be4 [A], 1…Bd6 [b] 2.Sb6 [B], 1…b4 [c] 2.Bc4, 1…Sc6 [d] 2.Qxc6; post-key 1…Be5 [a] 2.Rxe5, 1…Bd6 [b] 2.Qxd6, 1…b4 [c] 2.Be4 [A], 1…Sc6 [d] 2.Sab6 [B]. Remarkably, a third transferred mate occurs between the set 1…b4 [c] 2.Bc4 [C] and the actual 1…bxc4 2.Bxc4 [C].

Andrew Buchanan: After 1…Bd6/Be5, 2.Qxd6/Rxe5 look plausible as new mates, but unfortunately can just be captured. So is 1.Sc4 too obvious as a key then? It offers itself for sacrifice, after which 2.Bxc4. Turns out to be a lucky first guess! All the lines are totally unique: I like this one.
Brian Stephenson: A tough mutate. Tough because the mates after 1…Bd6 and 1…Be5 are not as interesting as those before the key and because the a3-bishop is unused after the key.
George Meldrum: Nice key move. Heaps of changed mates. A very high-class problem overall.
Nigel Nettheim: A good key in a complete block, and most mates (all the interesting ones) are changed. Brilliant! The a3-bishop just sets a mate after 1…c4, completing the block and thus hiding the key.
Jacob Hoover: A very interesting mutate in that: (a) the set mates from the bishop's correction moves are transferred to other defences in the actual play; and (b) the set mate for 1…b4 is transferred to the pawn move created by the key.
Paz Einat: A great problem, way ahead of its time. Not only does it show an Ideal Rukhlis, but it also involves an additional mate transference, making it a triple Rukhlis.

A first-class key 1.Se5! yields three flights to the black king. The threat is 2.Sg4+ Kxf4 3.Bh6. Black’s only defences are to take the flights, and each move leads to a different continuation. 1…Kxd4 2.Sd3+ Kc4 3.Rc6 or 2…Ke3 3.Rxg3. 1…Kxe4 2.Sc4+ Kd5 3.Se3 or 2…Kxf4 3.Bh6. 1…Kxf4 2.Sf3 and 3.Bh6 (not 2.Sf7? Ke3!). Good variety of battery play.

Jacob Hoover: The key grants three flights to the black king and sets up two batteries. There wasn't really anything in this problem that stood out to me except for the battery plays (yay!).
George Meldrum: Sometimes you look a problem and say, wouldn’t it be nice if that was the first move. Invariably it is a way out move that would never work. Such is the case here where I almost gave in to the tricky continuations. This problem is insane.
Nigel Nettheim: The best possible key attracts attention, making the solving a little easier. The outlying c8-knight, stopping 1.Sh4 and 1.Se7, seems a good deal better than white pawns on those squares. Excellent.
Brian Stephenson: The key gives three flights so the “wouldn't it be nice if…” approach to solving was again successful. The quiet continuation after 1…Kxf4 came as a surprise though. Good to see that the g2-rook isn't just there to guard f2. An enjoyable time for the solver courtesy of one of today's most prolific composers.

The key 1.Qxb4! (threat: 2.Qxf4) unpins the e6-bishop and self-pins the queen. The freed bishop produces two variations, unpinning the queen in one and checking in the other: 1…Bc4 2.Qe1 (pin-mate) and 1…Bxd7+ 2.Sxd7. The queen gives two more pin-mates by moving along the pin-line in 1…Rf6 2.Qe4 and 1…Bc1/Bd4 2.Qd4. The threat still works if Black accepts the granted flight, 1…Kf6 2.Qxf4, though it could be viewed as a distinct variation since the king is mated on a new square.

Ian Shanahan: The unpinned bishop then unpins its unpinner, the queen – the Schor theme. Sweet!
George Meldrum: First impressions of this problem setting were that it was awkward and clumsy. Once the key is found this feeling is overturned with an array of positives: (1) flight square given to the black king; (2) self-pinning of the white queen while unpinning the black bishop; (3) allowing a check on the white king; (4) all new mates, not being from set play.
Nigel Nettheim: The key is a highlight, allowing a capture with check as well as a flight, and it is a (minor) capture; it took me some time to find. The re-pinning of the e6-bishop after 1…Kf6 is another highlight.
Brian Stephenson: With 1…c6 and 1…Sc6, giving a flight at e4 and unprovided, it does not take long to find the excellent key. The star variation is 1…Bc4 2.Qe1. Old-fashioned quality and very enjoyable.

Two thematic tries and the key are all Novotny moves that place a white piece on a square where two black defensive lines intersect. By cutting off two black pieces simultaneously, White creates two threats, which are separated when each line-piece captures the white unit. 1.Re4? (2.Bd5/Qa1), 1…Rxe4 2.Bd5, 1…Bxe4 2.Qa1, but 1…Sc3! refutes. 1.Rf4? (2.Rb8/Qa1), 1…Rxf4 2.Rb8, 1…Bxf4 2.Qa1, but 1…Bb7! refutes. The key 1.Qf4! threatens 2.Rb8/Ra4, separated by 1…Rxf4 2.Rb8 and 1…Bxf4 2.Ra4. Black has two defences that handle both threats: 1…Bb7 2.Sb6 and 1…Bd5+ 2.Bxd5. A striking Meredith (12-unit) setting with no pawns.

Jacob Hoover: White has mates prepared for quite a few black moves in the diagram, e.g. 1…R~file 2.Ra4, 1…Be1/Bf2 2.Rb8. These variations provide a clue to the key: they say that Ra4 is mate if a4 isn't guarded, and that Rb8 is mate if b8 isn't guarded. Therefore, it is not difficult to find the key: 1.Qf4! invokes the Novotny theme to threaten both Ra4 and Rb8.
Ian Shanahan: This elegant Meredith parades three Novotnys.
George Meldrum: Worthy of note are the number of tries, especially 1.Re4? and 1.Rf4? as these provide dual threats of mate to avoid. I class this as a pop-corn problem.

The white queen aims for a1 while retaining its control of g2 with 1.Qg7! The threat is 2.Rxh3 followed by 3.Qa1 or Qxg2 (2…Kg1 3.Qxg2, 2…g1=Q, etc. 3.Qa1). Black defends by promoting the g-pawn – which self-blocks g1 – and this gives rise to three distinct variations. After 1…g1=Q, 2.Rg3 prevents 2…Qxg7/Qg5+, forcing 2…Qxg3/Qg2 3.Qa1. If 1…g1=B seeking stalemate, then 2.Rc4 bxc4 3.Qa1. And after 1…g1=S, only the waiting move 2.Bxb5 could deal with the knight check, 2…Sf3+ 3.exf3, and also 2…Sxe2 3.Bxe2. Unfortunately, multiple duals follow 1…g1=R when 2.Rg3/Rb3/Ra3/Qa7 are all effective, so the problem doesn’t quite achieve an Allumwandlung. Nevertheless, this is a splendid problem with a difficult key and surprising play, including the extra variation, 1…Kg1 2.Qa7 Kf1 3.Qa1.

George Meldrum: A pleasing array of play. The pawn promoting to a bishop almost got me.
Thomas Thannheiser: Very nice!
Jacob Hoover: I wonder if there's any way to remove the duals without completely wrecking the problem…

The thematic key 1.Qe8! (threat: 2.Qg6) unpins the black queen and also sets up a Q + K battery on the e-file. The released queen is allowed to check six times, each provoking a different mate: 1…Qd6+ 2.Kxd6, 1…Qd7+ 2.Kxd7, 1…Qd8+ 2.Kxd8, 1…Qxf6+ 2.Kxf6, 1…Qe5+ 2.Rxe5, and 1…Qxc5+ 2.Sxc5. Two additional defences by the queen give 1…Qd5 2.Rh4 and 1…Qxg1 2.Qxa8, so the piece produces an impressive eight variations, all dual-free. There’s good by-play with 1…Se3 2.Rf4 and 1…Rxg1/Rxg3 2.Sd2.

Andy Sag: The key unpins the black queen inviting six checks. Two other defences are self-blocks, and two are unguards making ten variations in all.
Ian Shanahan: The key is so strikingly thematic it's spotted almost immediately. Then the hard work comes in working out all those variations, capped by the royal battery mates.
Jacob Hoover: I took one look at the diagram and instantly said, “Oh, it's 1.Qe8.” Way too easy. However, the profusion of counter-checks made me one very happy solver.
Nigel Nettheim: The black queen clearly cannot be unpinned. But it is unpinned! Then all hell breaks loose, but the goodies win in the end.
George Meldrum: This feel good problem is bound to put a smile on every solver’s face.
Bob Meadley: A nice two-mover by the old firm of FR and FTH.

The key 1.Sd1! (waiting) sacrifices the knight to Black’s e-pawn and king but pins the c-pawn. The main variations consist of two pairs of promotion-captures on d1 and b1, all self-blocking moves which are exploited in different ways: 1…exd1=Q 2.Qb2, 1…exd1=S 2.Rxc2, 1…axb1=Q 2.Qd2, and 1…axb1=S 2.Bb2. The latter mate is the most interesting – the bishop move interferes with the queen while opening an indirect battery on the d-file. If 1…Rxb1 then 2.Qd2 again, while other captures on d1 lead to dual mates, unfortunately: 1…Rxd1 2.Rxc2/Qb2 and 1…Kxd1 2.Qd2/Bb2/Be3. Lastly, 1…S~ permits 2.Be3.

Andy Sag: The key adds two promotions to those that are set (albeit unprovided) and allows a flight capture. The duals make it very untidy.
George Meldrum: A nice diversity of five different mates for a king on the edge of the board problem.
Jacob Hoover: A lot going on in one problem.
Ian Shanahan: Promotion-captures by the black c-pawn give the black king a flight at c2, with no mate in sight. This leads to the astonishing key and a plethora of lovely, complex variations. A beautiful problem indeed!

The shortest game to reach the diagram is 1.h3 g5 2.Rh2! g4 3.hxg4 a6! 4.Rh6 a5 5.Ra6 e6 6.Ra7 Ba3 7.bxa3 b6 8.Bb2 Ba6 9.Bg7 Bd3 10.exd3 Sf6 11.Be2 Rf8! 12.Bf3 Rg8 13.Bc6 Sxc6 14.Qf3! Se5 15.Qe2 c6. Both players have to make two precise tempo moves (marked by ‘!’) to use up the extra time available. Neither side could waste the two moves by making a switchback with any piece – for instance, 1.h3 g5 2.Sf3? g4 3.hxg4 a5 4.Rh6 Ra7? 5.Ra6 e6 6.Sg1? Ba3 7.bxa3 b6 8.Bb2 Ra8? 9.Ra7 Ba6 10.Bg7 Bd3 11.exd3 Sf6 12.Be2 Rg8 13.Bf3, and with no more spare moves, Black must play 13…Sc6 and cannot capture the white bishop.

Andy Sag: After realising that the white bishop cannot be captured on f3, it is clear that the minimum number of moves to reach the diagram is 13 each. So each side has two tempo moves and must use them sparingly and time them accurately.
Jacob Hoover: At first I thought White’s extra moves consisted of moving the g1-knight out and back, but each time I tried it with those moves I kept ending up with the black c-pawn still on c7 and everything else matching up.
George Meldrum: At first sight, the position looks to be easily reached in less than 15 moves. Soon you realise that you need to dilly dally and dance pieces to their final destination. Nicely choreographed.