Weekly Problems 2016-B

The quickest way to reach the diagram is 1.f4 a5 2.f5 a4 3.f6 a3 4.fxg7 Sf6 5.gxf8=B Rg8 6.Bh6 Rg3 7.Bg7 Rb3 8.axb3 a2 9.Bf8 Ra3 10.bxa3 Kxf8 11.Bb2 Kg7 12.Qc1 Kg8 13.Kd1 Sh5 14.Bf6 Kf8 15.Qb2 Ke8 16.Kc1 axb1=R+. The promoted white bishop executes a three-move manoeuvre to lose a tempo, after which it is captured by the black king. The latter then also makes a tempo trek to use up three moves in a precise way. Both White and Black’s treks begin and end on f8. This doubling of the tempo play is combined with the Ceriani-Frolkin theme (capture of a promoted piece).

Andy Sag: Waiting move by White’s bishop and black king triangulation are necessary to get the tempo right.

The unexpected key 1.Rb6! (waiting) leads to two thematic variations: 1…cxb6 2.Rc4 Ke2 3.Rc1 and 1…c6 2.Bc4 Kc2/Kc1 3.Be2. Black’s c-pawn is kept immobilised as the c5-rook and b5-bishop interfere with each other on c4 – producing a white Grimshaw – to release the black king. The latter is forced by zugzwang to shift to a more exposed position and White mates by opening the battery formed by each Grimshaw move. The by-play makes further use of the key-piece: 1…cxd6 2.Bd3 and 3.Rb1.

Nigel Nettheim: A Grimshaw-like theme with reversed colours: not Black but White takes advantage of the mutual interferences on c4, to avoid stalemate. There are good tries and a wonderful key. I found this very hard to solve but well worth-while.
Jacob Hoover: Very difficult; kept me stumped for days.
Andy Sag: A precise lightweight setting by the Israeli master.

Michael McDowell informs us that this problem is anticipated: “The Makaronez three-mover rang a bell. It adds a variation to the attached Shinkman. I remember solving this one in a newspaper column when I was about 12 or 13!” The precursor seen below gives the same thematic play, and its sacrificial key by an unrestricted rook (1.Ra6!) is even better.

White begins with 1.e4!, which cuts off the f3-bishop and threatens various battery mates, 2.K~. The key is also thematic in that it opens the third rank and enables the black queen and bishop pair to check. Each possible bishop move is answered by a different opening of the K + R battery: 1...Bxe4+ 2.Kxe4, 1…Be2+ 2.Kxe2, 1…Bd1+ 2.Kc4, and 1…Bxg4+ 2.Kc2. So along with a duel between the black bishop and the white king, the problem shows a king-star. Minor variations include 1…Rxf2 2.Bxg3, 1…c5 2.Qd5, and 1…Sxg6/Se6 2.Qe6.

Andy Sag: The key interferes with the long white-square diagonal and creates a quadruple threat.
Jacob Hoover: No mates are prepared for 1…Bd5 or 1…axb4; White remedies this by playing 1.e4! and it activates the black Q + B battery.
Nigel Nettheim: The key counters the strong defence 1…c5. The multiple threats do not matter, because they are nicely separated into a star pattern.

After 1.Bf2!, White threatens 2.exd4 and Black defends by moving the e5-knight, which opens a line for the bishop on h8. 1…Sf7 interferes with the other black bishop and permits 2.Rc1. 1…Sc4 again cuts off the bishop and also self-blocks, enabling 2.Sb3. A similar pair of variations occurs when the knight obstructs the h6-rook twice: 1…Sg6 2.Qb6 and 1…Sc6 2.Sa6 – the latter is a self-block as well. The fifth defence by the knight is yet another interference: 1…Sg4 2.Sxe4. The by-play consists of 1…dxe3 2.Bxe3, 1…Rd6 2.Qb5, and 1…Rb6 2.Qxb6.

Andy Sag: The five knight defences produce five black line interferences and two self-blocks, and 1…Rd6 adds another self-block.
Nigel Nettheim: The e1-bishop and g1-rook had to take part, so the key was easy to find. The theme is a partial black knight-wheel. The g8-bishop prevents 1.Bd5 (2.Sb3).
George Meldrum: The knight on e5 does cartwheels providing a pleasing variety of mates. Variations great; key move rather ordinary.
Jacob Hoover: All of the main variations except for 1…Sf7 2.Rc1 are set. A nice illustration of line play.

The solution to part (a) is 1.Bd2 Bd4 2.Rg6 Bf5. Black starts with a self-blocking bishop move that also clears the long diagonal for the white bishop, which goes to d4 to control the e3-flight and unpin the black rook. The latter then opens the d-file for the white rook (to guard the d4-bishop) and interferes with the h7-bishop, allowing the second white bishop to mate. Part (b), with the black king starting on e5, is solved by 1.Rf6 Rd4 2.Bb4 Sc4. Now the black rook self-blocks and permits its white counterpart to get to d4, where it covers two more flights and unpins the c3-bishop. This bishop then opens a line for the white one on a1 (to guard the d4-rook) and cuts off the black queen, enabling the white knight to mate. A well-constructed orthogonal-diagonal transformation, showing perfect analogy between the two parts.

Andy Sag: Good twin with self-block, unpin, black line self-interference, mate sequence in each case.
Jacob Hoover: This was quite difficult, but once I understood what was going on in the first part, the second part was very easy.

The key 1.Bf1! (waiting) creates a B + P battery and completes the block. The c3-rook produces four variations: 1…Rd3 2.exd3, 1…Re3 2.Sxe3, 1…Rf3 2.exf3 and 1…Rg3/Rh3 2.e3. The latter mate also follows 1…cxd1=S, exploiting the half-pin, while 1…cxd1=Q admits 2.Rxc3. Basic correction play is seen in 1…Q~ 2.Qb5, 1…Qxb6+ 2.Sxb6 and 1…Bf~ 2.Qxc3, 1…Bxe5+ 2.Sxe5. The remaining defences are unguards: 1…Rb~ 2.Sb2, 1…Be~ 2.Qd5, 1…Sb~ 2.Qc5, 1…fxg6 2.Qxe6, and 1…a4 2.Rb4. Straightforward play and the position is super-heavy (using almost the full chess set!), but justified by the great number of variations, all dual-free.

Andy Sag: Waiter with fourteen variations!! Eleven are set and the key sets up a battery to deal with the rest.
Jacob Hoover: Quite easy to solve due to the fact that the g2-bishop is the only white unit not participating in the action. But it was also a rewarding solve at the same time.
Nigel Nettheim: Very nice and elaborate. The black f6-bishop had to be promoted, because it could not have escaped from f8; thus it is an intrusive piece. The position is legal, although it is not quite trivial to establish that. The only missing units are four white pawns and two black pawns. The f6-bishop must have been promoted on a black square, which could have been c1, with either of the black pawns starting on c7 or d7 (in either case, White’s c-pawn was captured). The e4-pawn must have captured a piece promoted on h1. Thus the position is legal.

The black king has two flights, both provided: 1…Kxe4 2.Qe2 and 1…Kd3 2.Qf3. If White aims to preserve these variations with a waiting move – 1.Ke6?, for instance – then 1…b4! refutes. The key 1.Bd1! involves two threats, 2.Qf3 and 2.Qe2, which are separated by 1…Kxe4 2.Qf3 and 1…Kd3 2.Qe2. These variations demonstrate a reciprocal change with respect to the set play, by reversing the two queen mates. Note also the paradoxical elements: in the set play, 1…Kxe4 enables 2.Qe2 and 1…Kd3 enables 2.Qf3, but after the key, 1…Kxe4 disables the threat of 2.Qe2 and 1…Kd3 disables the threat of 2.Qf3.

Nigel Nettheim: Two threats, but the point is the changed mates.
Jacob Hoover: Too easy! The king's moves separate the threats; and a miniature to boot.
Andy Sag: An interesting miniature. The b5-pawn appears not to contribute but without it there would be eight solutions!

The key 1.fxg6 e.p.! is legal if we could prove by retro-analysis that Black’s only possible last move was …g7-g5+. In the initial position, White is missing only the b-pawn, which was captured by Black’s pawn on b6. With no other white units to capture, Black’s f-pawn must have moved straight down the file to f2. This means White’s f5-pawn needed to have captured to get around the black one, and the four white pawns on the king side have made a total of three captures (e.g. fxg, gxf, gxh). These three captures account for all of Black’s missing pieces (queen, rook, and bishop).

Since Black is checking with the g5-pawn, it has just moved from f6, g6, or g7. This last move couldn’t have been …f6xg5+, however, because of the lack of spare white units to capture. If Black has just played …g6-g5+, what was White’s move before that? It couldn’t have been:

• Qg5-g4, Se7-g8, or Sf6-g8 because Black would have been in check with White to play;

• Sxg8 since Black’s missing pieces were all captured by the white pawns;

• Kg5-h4 as that must be preceded by …g7xh6+, again an impossible black capture;

• d3xe4 because that would imply too many white pawn captures had taken place (five in total);

• g2xh3 because an uncaptured queen or rook on h3 would have been checking White with no way of delivering that check, while the third missing black piece is a black-squared bishop which couldn’t have reached h3 to be captured.

Hence we have shown that …g6-g5+ would mean an illegal position with no further white retraction possible. That leaves …g7-g5+ as the only possible last move, prior to which White had played Bg6-h7 or Qg6-g4. So White can play 1.fxg6 e.p.!, with the short threat of 2.Rf8. 1…Sxf4 2.Qc8+ Kxc8 3.Sf6, and 1…Bxg4 2.Sf6+ Ke7 3.Re8. Some duals follow other black defences, e.g. 1…exf4 2.Qc8+/Sf6+.

Andy Sag: The main issue is the need to establish that black's previous move was …g7-g5+ thus enabling the en passant key.
Jacob Hoover: This is the first chess problem I have seen on this blog where White is in check in the diagrammed position. And it was also a moderately difficult solve.
George Meldrum: Very nice.

In this complete block position, every black move has been prepared with a white mating response. Only the key 1.Re2! (waiting) manages to keep all of these set variations in place. The d7-bishop illustrates focal play as it cannot maintain its guard of both b5 and f5: 1…Be6/Bc8 2.Sxb5 and 1…Bc6/Be8 2.Sxf5. A random move by the g4-knight, 1…S4~, permits 2.Bf6, while the correction 1…Se5 is a self-block that enables 2.Be3. White exploits a line-opening for the g6-bishop in 1…f4 2.c3. And the d2-knight mates twice with 1…S1~ 2.Sf3 and 1…a3 2.Sb3. Good tries include 1.Bf7? (waiting) f4!, 1.Bh7? (waiting) Be8+!, 1.Bxf5? (threat: 2.c3) Be8+!, and 1.Bd8? (threat: 2.Bb6) Se2!

Jacob Hoover: White preserves all of the set mates with 1.Re2!
George Meldrum: Could be quite baffling to someone who did not notice the set play.

White utilises the half-battery on the f-file in the try 1.Be7? (threats: 2.Be4/Bg4/Be6), refuted by 1…Rf6! The key is made by the other white bishop, 1.Bg6!, which threatens 2.Bxh5. In two highly thematic variations, the black rooks leave each other pinned by the white queen and interfere with a3-bishop, enabling White to fire the R + B battery while shutting off each defending rook: 1…Rb4 2.Bd4 and 1…Rc5 2.Be5. Two more rook defences disable the a6-bishop and permit White to open the R + P battery: 1…Rb5 2.d4 and 1…Rc4 2.dxc4. There’s by-play with 1…Bxd3 2.Rxd3.

Andy Sag: Rook defences self-pin the remaining rook and block a black bishop line allowing either a vertical or horizontal rook battery mate, depending on which bishop line is closed.
Jacob Hoover: Another chess problem featuring battery play, with interferences and a half-pin as well! Yay!

This miniature is solved by 1…Kd5 2.Sf4+ Kc5 3.Re6 Sd6+ 4.Ke5 Sd7 and 1…Se6 2.Se5 Kc5 3.Rf6 Kd5 4.Sg6 Se3. In both solutions White must lose a tempo, and the king does so by visiting c5 and d5 in reverse order. Two ideal-mates complete a lovely problem.

Andy Sag: In each case the white king moves twice to lose a tempo.

If White unpins the d5-bishop then 2.Bf7 is threatened, but 1.Kc2/Ke2? fails to 1…Rxa8! while 1.Qd4? is defeated by 1…Kd7! The key 1.Qe2! threatens 2.Qxe7, which is still effective if Black takes the granted flight, 1…Kd7. The black knight defends by opening a line for the a3-bishop, and a random move 1…S~ allows 2.Qb5 (a change from the set mate, 2.Qa4). Two correction moves prevent the secondary threat 2.Qb5, but unpin the white bishop: 1…Sd3 2.Bc6 and 1…Sd7 2.Bf7. One more variation is 1…e6/e5 2.Rxd8.

Andy Sag: Meredith with queen withdrawal key giving a flight albeit non-defensive.
Jacob Hoover: The correction moves unpin the d5-bishop and allow it to mate.
George Meldrum: Effective and a flight square too.
Nigel Nettheim: The threat is not subtle, but everything else is really elegant, including some changed mates.

Several queen moves off the third rank, such as 1.Qf4?, threaten 2.Rxb3+ axb3 3.Qd6 (etc.) and 4.Qa6, or 2…Kxb3 3.Qe3+ (etc.) Kxc4 4.Qd3. But 1…Sg5! refutes because of the impending check on f3 or h3. The fine key 1.Qh6! doesn’t entail a threat, and the rook sacrifice is playable only after the black knight has weakened its position: 1…Sxf6 2.Rxb3+ axb3 3.Qxf6 Ka4 4.Qa6, or 2…Kxb3 3.Qe3+/Qh3+ Kc4 4.Qd3; 1…Sf8 2.Rxb3+ axb3 3.Qxf8 Ka4 4.Qa8, or 2...Kxb3 3.Qe3+/Qh3+ Kc4 4.Qd3. The star variation, however, is 1…Sg5 2.Bxg5 f6 3.Bc1 bxc1=Q+ 4.Qxc1 (pin-model mate). Now we see that the key is a clearance move that allows the bishop to travel along the line traversed by the queen but in the opposite direction (a Turton manoeuvre), and this is capped off by a mating move in which the queen reverses its direction and follows the bishop on the same line.

Jacob Hoover: 1.Be7? threatening 2.Qc3 is a good try, refuted by 1…Sg5! This one was difficult to solve.
Andy Sag: The key is a line clearance allowing the bishop to work on the c1-h6 diagonal as well as keeping open the possibility of an a-file mate. The theme is stalemate avoidance. 3.Bc1 is a classic masterstroke.

The thematic try 1.Qf2? (waiting) sets up a Q + S battery that fires directly after the king moves: 1…Kb6 2.Sec4 and 1…Kd4 2.Sexf5; but there’s no mate after 1…dxe6! The key 1.Qe7! (waiting) creates another Q + S battery, and it works indirectly after the flights: 1…Kb6 2.Sdc4 and 1…Kd4 Sdxf5. Two unusual changed mates in which different knights play to the same squares. If 1…dxe6 then 2.Qxa7.

Andy Sag: Key preserves all three set legal moves including the two flights and sets up an indirect battery to guard c5. Easy to solve.
Nigel Nettheim: The try uses the e3-knight; the key uses the d6-knight moving to the same squares.
Jacob Hoover: 1…dxe6 2.Qxa7 is a pin-mate. This one's easy once you realize that the only white unit that isn't participating is the queen.
Paz Einat: Pales in comparison to earlier works. The price of two unprovided flights and a white queen out of play is just too high.

The solutions are 1.Bxc6 dxc8=Q 2.Kd5 Qf5 and 1.Qxd7 Qxb7 2.Ke6 Qe4. The two parts show reciprocal captures between the white queen and the b7-bishop, and between the white pawn and the black queen. The Zilahi theme is also seen in that the two white units swap their roles in giving mate and getting captured. The echo mates are brought about by rather symmetrical play, though the pawn promotion in one solution helps to break the symmetry.

Andy Sag: In each case the black capture prepares a self-block so the (original or promoted) queen can mate after the king moves to its final position.
Jacob Hoover: In each solution Black's first move is a necessary self-block (in the 1.Qxd7 solution this move is also an unpin), and Black's second move puts the king in a position where it is the least mobile.
Nigel Nettheim: A white queen functions similarly in both mating positions. Without the g7-bishop there would also be 1.Ke6 dxc8=S 2.f5 Qxd6, but Black’s move order is not forced.

All black moves in the diagram are provided with set mates, and 1.Kh7! (waiting) is the only way to maintain the block. The two black knights illustrate correction play: 1…Sd~ 2.Sf6, 1…Sdxe3 2.Qa8, 1…Sf~ 2.Sg3, and 1…Sfxe3 2.Qg6. In each case, random moves by the knight permit its white counterpart to mate, while the correction capture on e3 – removing a guard of f4 – self-pins the piece and enables a queen mate. These four black knight variations are supplemented by four involving black pawn defences: 1…exf4 2.Qxe6, 1…f2 2.Qg2, 1…dxe3 2.c3, and 1…d3 2.cxd3.

Andy Sag: The key invites a royal fork (1…Sf6+) but leaves all eight set mates undisturbed and also eliminates a dual after 1…Sfxe3 (2.Qh7).
Nigel Nettheim: Black is stymied; the key is the only available waiting move and it eliminates the dual after 1...Sfxe3. Very neat.
George Meldrum: Not 1.Qxe6? f2!, or 1.Qg7?/Qg5?/Qg4? exf4! Tried every queen move on the board, then realized had picked the wrong royal. Frustratingly simple.
Jacob Hoover: Two knight corrections and two pawn moves allow mates from four diagonal directions.

The key 1.Qc2! contains a quiet threat, 2.Ke3 and 3.Qxg6, and if 2…exd4+ 3.Sxd4, 2…exf4+ 2.Sxf4, and 2…e4 3.Qxe4. Black has three defences on b5, of which two are more strategic because they involve self-obstructions on that square. After 1…Sxb5 (which thwarts the threat because of 2.Ke3? exd4+!), White can play 2.Kf3 since …cxb5+ is disabled, and the threat of 3.Qxg6 provokes 2…Sxd4+ 3.Sxd4 and 2…e4+ 3.Qxe4. And 1…Rxb5 (to answer 2.Ke3? with 2…Rb3+!) precludes …Sxb5 or …cxb5+, enabling White to continue with the square-vacating 2.dxe5 and 3.Sd4. The third defence on b5 is a discovered check that unguards d5: 1…cxb5+ 2.d5+ Bxd5+ 3.cxd5. If 1…Rbf8/Rgf8 then 2.exf8=S+ Rxf8 3.Re7. There are some short variations: 1…exd4 2.Sxd4, 1…exf4 2.Sxf4, and 1…g5 2.f5. Including the threat play, the white king invites multiple checks while standing on e4, e3, and f3.

Jacob Hoover: Note that in 1…Sxb5 2.Kf3 Sxd4+ 3.Sxd4, with the king off the e-file the e5-pawn is pinned! The all-checks variation 1…cxb5+ 2.d5+ Bxd5+ 3.cxd5 is a nice touch.
Andy Sag: Cross-check theme with heaps of variations from the Wizard of Oz. A few shorts as well but what the heck!

The sacrificial key 1.Se6! (threat: 2.Sxc5) vacates the diagonal controlled by the black B + S battery, setting off the cross-check 1…Sd~+ 2.d6. The white B + P battery fires again with 1…fxe6 2.dxe6. Various black queen defences unguard d3 or e3 and the white queen mates accordingly: 1…Qxc4/Qe3 2.Qe3 and 1…Qxg4/Qf2/Qd3 2.Qd3. And the c4-knight mates twice with 1…Qxd2 2.Sxd2 and 1…Bg1 2.Sxd6. Hence there are three pairs of variations, each employing the same mating piece.

Andy Sag: Sacrificial key allows a check. Threat plus six variations comprising pairs of pawn moves to discover mate, queen mates and knight mates. Tries: 1.Sa6? (2.Sxc5) Qxd2!, 1.Rxe2+? Bxe2 2.Qe3, but 1…Kd4!
Jacob Hoover: This one was made easy due to the fact that only one white unit (the c7-knight) wasn't participating.
Nigel Nettheim: The key was not hard to find, despite the f7-pawn, because the latent cross-check was bound to be used. Several variations, no duals. The c5-pawn prevents an extra threat, 2.Rd4.

The first solution 1.Sd4 Ra5 2.Rb5 cxd4 3.Rb6 d5 begins with a knight sacrificing itself to activate the white pawn. The white rook makes a clearance move to allow its black counterpart to follow along the same line – this illustrates an idea called the Loshinsky’s magnet. The black rook is thus able to self-block on b6, and the pawn mates with the support of the white rook. In the analogous second solution, 1.Sb4 Bb8 2.Bc7 cxb4 3.Bb6 b5, the black knight is sacrificed to the same pawn but on another square. The white and black bishop pair executes a diagonal version of the Loshinsky’s magnet, aimed at giving the black piece access to b6 for a self-block. Lastly the white pawn mates on a different square, supported by the rook from another direction. A fine example of an orthogonal-diagonal transformation. The only flaw is that while the white rook’s move shows a nice anti-critical effect by crossing over the eventual mating square d5 (so avoiding a self-interference in the mate), the white bishop’s move doesn’t have a similar effect.

Andy Sag: Perfect twin in typical Jones style. In (1) the black rook self-blocks on b6 and the white pawn mates on d5. In (2) the black bishop self-blocks on b6 and the white pawn mates on b5. The three black pawns are there to stop cooks; some are very subtle, e.g. if a black pawn is not on f2, then 1.e5 Rxe5 2.Kc7+ Kg1 3.Kc8 Re8.

A white king move off the diagonal would threaten 2.Bd2, but most attempts fail to black checks: 1.Ka3? a1=Q+!, 1.Kb3? a1=S+!, 1.Kc5? Rc8+!, and 1.Kc4? Rc8+/Bf7+! Only 1.Kb5! works, and this fine key still elicits three checks. 1…Be8+ interferes with the f8-rook and permits the cross-check 2.d7, while 1…Rf5+ cuts off the g6-bishop and leads to another cross-check, 2.d5. So Black’s rook and bishop close lines controlled by each other, but unlike an ordinary Grimshaw, the mutual interferences here take place on different squares. The third check is answered by a more straightforward recapture, 1…Bxd3+ 2.Sxd3, which in turn is similar to 1…Rxe2 2.Sxe2. The h4-knight has two defences; one cuts off the g6-bishop again but the weakness is exploited differently: 1…Sf5 2.Re4, and the other is a self-block: 1…Sf3 2.e3.

Nigel Nettheim: The key walks into three checks, but the a4-rook and a5-bishop had to be activated. Six interesting variations.
Andy Sag: The highlight of this problem is the first pair of checking defences where the resultant black interferences allow cross-check mates. A pair of pawn capture defences allow knight mates. A pair of knight defences make up a total of six variations.
Jacob Hoover: The mutual interferences and cross-checks in this problem make it a lovely one.

Every black move in the diagram has been provided with a set mate: 1…Sd~ 2.Rxe4, 1…Sa~ 2.Qxc5, 1…Sb6 2.Qa1, 1…b6/b5 2.Qg7, and 1…exd3/exf3 2.Bxe3. Tries that aim to maintain the block include 1.Kb1? Sc3+!, 1.Se1? Sc3!, and 1.Sb2? Sb6! The latter try-move disables 2.Qa1 mate and it goes well with 1.Re7? which prevents 2.Qg7 mate after 1…b6/b5!, though the pair of refutations means the rook move isn’t technically a try. The key 1.Se5! (waiting) generates plenty of changes. 1…Sd~ 2.Rc4, 1…Sa~ 2.Qxc5, 1…Sb6 2.Qa1, 1…Sc3 (a new correction) 2.Rd2, 1…b6/b5 2.Sc6, and 1…exf3 2.Sxf3. Splendid mutate. The white bishop, used as a mating piece in the set play, is required to pin the e3-pawn in a post-key variation.

Jacob Hoover: The key causes an almost complete change in the play.
Andy Sag: Near try 1.Re7? b6/b5! Complete block with four changed mates. The 1…Sc3 self-block allows a pin mate.
Nigel Nettheim: Most mates are changed (though not 1…Sb2 2.Qxc5 and 1…Sb6 2.Qa1). 1…Sb6 2.Qa1 nicely recalls 1…b7~ 2.Qg7. 1…Sc3 2.Rd2 is excellent.

In the set play, 1…Ra4 2.Kxa4 Sd4, the white rook sacrifices itself to allow the black king to reach a4, where it’s mated by White firing the B + S battery. When Black commences, there’s no waiting move that could preserve the set play, and the solution becomes 1.Kxc4 Bd5+ 2.Kxd5 Sd6. After an initial capture, it’s the white bishop that sacrifices itself to give the black king access to d5; then White mates with the R + S battery aimed at that square. The rook and bishop swap their roles in getting captured and giving mate, so the Zilahi theme is produced. The b5-knight nicely opens both batteries which operate on different lines.

Nigel Nettheim: The theme is white sacrifice. The b5-knight fires a different battery in each phase. The back piece of the battery and the sacrificed piece exchange roles in the two phases. The mate is model and the set mate nearly so.
Jacob Hoover: There is a definite battery-play theme here, but there is also a diagonal-to-orthogonal transformation effect where the bishop and rook interchange roles between the set play and actual play.

The black king has two unprovided flights on e4 and e5, and the key 1.Sg2! threatens a queen mate that covers these squares – 2.Qe3. Now both king defences, 1…Ke4 and 1…Kxe5, are answered by 2.Qf4, though because the king is mated on different squares, these variations may be regarded as distinct. Black has three more defences on e4, committing self-block errors that are exploited in a variety of ways: 1…Be4 2.f4, 1…Sce4 2.Rxd5, and 1…Sge4 2.Sf3. Likewise, there are three further defences on e5 that prevent the king from escaping to that square: 1…Bxe5 2.f3, 1…Qxe5 2.Rxb4, and 1…Rxe5 2.Qc4. Eight thematic variations!

Nigel Nettheim: Four defensive captures on e5 and four defensive moves to e4, with some wonderful mates. Virtuoso playing by two quartets. A nice open and materially balanced position.
Andy Sag: Try 1.S3g4? Ke4! The key leaves the e5-knight en prise and Black can defend by either capturing it or by blocking on e4.
Jacob Hoover: 1…Qxe5 2.Rxb4 sees a removal of a dual from the set 1…Qxe5 2.Rxb4/Qc4, and 1…Bxe5 2.f3 shows a change from the set 1…Bxe5 2.Qc4. Eight defences and eight distinct mates. Nice.

Any move by the white knight on d3 would guard that square and threaten 2.c3. A random try by the knight, 1.Sd~? (e.g. 1.Sc1?), fails to provide for 1…Bg6!, pinning the white pawn. Further tries by the knight correct this error by exploiting the interference of the h6-rook caused by the bishop move. Thus 1.Sxf4? Bg6 2.Se6, but now 1…Rg3! refutes because the knight has obstructed 2.Qxf4. Similarly, 1.Sdxc5? Bg6 2.Se6, but there’s no answer to 1…Ba5! as the knight has prevented 2.Qxc5. One more correction try is 1.Se5?, which leads to the changed mate 1…Bg6 2.Sc6, and it’s defeated by 1…Qh7! when 2.Be5 is ruled out. Finally, the key 1.Sb4! works by avoiding the self-obstructions. 1…Bg6 2.Sc6, 1…Rg3 2.Qxf4, and 1…Qh7 2.Be5. It’s a pity that 1…Ba5 no longer stops the threat, though the missing variation is compensated by 1…cxb4 2.Qxb4. A clear illustration of white correction play.

Nigel Nettheim: Good. Well-controlled tries.
Jacob Hoover: Sacrificial key.
Andy Sag: Two pin defences allow minor piece mates. Remaining two defences allow lateral queen mates.

This miniature is solved by 1.Sf3 Qf2 2.Se5 Bf5, 1.Kd3 Qc1 2.Be4 Bc4, and 1.Bc4 Qg5 2.Bd3 Bd5. The same mating configuration occurs in all three solutions but on different parts of the board, so a triple echo is shown. The first two mating positions display a reflection echo, while the first and the third exemplify the rotation type.

Jacob Hoover: In each solution the black knight and bishop take up self-blocking positions so that the queen and bishop can deliver a model mate in the centre of the board. Another thing the three solutions have in common is that the three mates are echoes of each other.
Andy Sag: The king on a7 stops the knight from going via c6 in the first solution.
Nigel Nettheim: Of the nine squares, the white queen will cover five: three black, the mating bishop and another white one. The white bishop will cover two, and the black pieces the remaining two. It seems surprising that there are three dual-free ways to do this.

The diagram is a complete block position in which white mates are prepared against all legal black moves. 1…Kd4 2.Qd2, 1…Sg~ 2.Se2, 1…Sd~ 2.Be5; most bishop moves permit a dual by opening the fourth rank – 1…B~ 2.Bb4/Rc4, though 1…Bc2/Bd3/Bd5 are answered uniquely by 2.Bb4. White is unable to maintain the block with a waiting move, e.g. 1.Kh6? Sf5+, 1.Rf4? h4! The surprising key 1.Bf4! not only closes the fourth rank but carries a threat, 2.Qd2. Three changed mates result: 1…Kd4 2.Qc4, 1…Bc2 2.Qa1, and 1…Bd3 2.Bd2 (the latter reactivating the white rook). One more variation in this deceptive block-threat problem is 1…Sf1 2.Se2.

Andy Sag: Pin-mate in the set variation, 1…Kd4 2.Qd2.
Nigel Nettheim: The set knight-play is reduced after the key, when only 1...Sf1 2.Se2 is needed.
Jacob Hoover: A very nice threat-mutate.

After the key 1.Qc1!, White threatens 2.Qxe3 followed by 3.Qh3, and if 2…fxe3 3.Sxe3, or 2…f3 3.Qg5. Black has three pawn defences, in each case partially opening a line that remains blocked by another black pawn. White responds by sacrificing a unit to the second pawn, in order to open the line fully. 1…d2 2.f3 (threat: 3.Rh5) exf3 3.Qb1. 1…cxd4 2.Rxd5+ cxd5 3.Qc8, or 2…Be5 3.Rxe5. And 1…e2 (to answer the threat 2.Qe3 with 2…exf1=Q) 2.Sg3+ fxg3 3.Qg5. The line-openings are all utilised by the white queen in the three harmonious variations.

Andy Sag: Threat and three variations sacrifice a piece on the second move. Three diagonal, long-range queen mates and one short mate. Position is legal involving eight captures of white pieces/pawns.
Jacob Hoover: A masterfully crafted three-mover featuring strategic play.