Weekly Problems 2019-B

To force Black to mate, White has to put the king somewhere on the long diagonal and block most of its flight-squares with the available units, and also control the black king such that it must fire the B + K battery. The flight-blocking units need to avoid hindering the mate, and this factor eliminates many possible squares for placing the king, e.g. mating it on d5 requires both d4 and e5 to be blocked by bishops but a d-pawn promotion to one would take too long. Only a mate on c6 would allow both pawns to self-block without promoting. This scheme necessitates six blocking units altogether, leaving one spare piece to help compel Black’s mating move. 1.Rb6 2.Kd6 3.Sd7 4.c5 5.c6 6.c7 7.Kc6 8.d6 9.Qb5 10.Bc5 11.Ra3 12.Rh3 and now with the black king restricted by White’s queen, bishop, and rook, …Kxh3 is forced by zugzwang. White takes care not to tangle up the pieces in this fine sequence, which finishes with a surprising waiting move.

Composer: That was 32 years ago and the truth is I couldn’t remember the solution and gave up after trying all day Saturday. Luckily, I still had a copy of Chess in Australia with the solution in a box in the garage. Would be interesting to find out if anyone realised it was a non-checking finale with the a1-rook ending up on h3!
Jacob Hoover: I expected the 12th move to be a check initially, and so my early efforts were stymied. Then I realized that the queen could reach b5 in one move if she had a clear path, and after that solving the problem became significantly less difficult.
Ian Shanahan: White builds his fortress around his king, with subtle timings. It is excellent that the last move in the series is not a check. Classy work!

The black king has a flight-move that’s provided for, though another strong defence, 1…Bxc2, has no set reply. The thematic try 1.Rb2? threatens 2.Rb8 but 1…Bb5! refutes, since 2.Rxb5 is stalemate. The key 1.Se4! threatens 2.Sc5 and 3.Sb6 (which 1…Bxc2 doesn’t handle). Black defends by capturing the offered knight, 1…Bxe4, and now that the bishop is decoyed to the long diagonal, White can proceed with the original plan, 2.Rb2 (3.Rb8), because Black’s substitute defence, 2…Bb7, carries the weakness of self-block, permitting 3.Sb6. This three-move miniature hence exemplifies the Roman decoy theme. The flight variation is unchanged from the set play: 1…Kb7 2.c8=Q+ Ka7 3.Rc7.

Andy Sag: A tricky miniature with a sacrificial key. Nice try is 1.Sb3? Be4!
Andrew Buchanan: The d2-knight is so far from the action it looks like it must move as the key.
George Meldrum: The far outpost knight on d2 begs to play. First attempt is stopped: 1.Sb3? Be4! Surprisingly then the knight finds its way to e4 in face of the bishop.

The diagram position is a complete block, where most black moves permit a knight mate on d5 or g2. The black queen is unable to maintain its focus on these squares: 1…Q~file 2.Sd5 and 1…Q~diagonal 2.Sg2; there are no duals when the queen lands on either mating square – 1…Qd5+ 2.Sxd5 and 1…Qg2+ 2.Sxg2 – though 1…Qh8 enables both mates. The f8-knight and h6-bishop cannot avoid interfering with the queen: 1…Se6 2.Sd5 and 1…Sg6/Bg7/Bg5 2.Sg2. Only the h1-knight elicits a different mate with 1…Sf2 2.Qxf2, while a dual follows 1…Sg3 2.Qf2/Sg2. White has numerous tries that aim to preserve the block but are subtly defeated by the black queen. 1.Bb~? Qxa2! and 1.f6? Qg5! allow the queen to keep its focus on the mating squares. Also, 1.Bh5? Qg4!, 1.Kb6? Qg1!, and 1.Ka6? Qxa2+! Only 1.a3! (waiting) solves. The unusual twinning calls for the position after 1.a3 to be solved anew with White to play. Again this is a complete block situation that White wants to retain, and now 1.Ka6! does the job, given that 1…Qa2 no longer checks.

When this problem was originally published, Frank Ravenscroft pointed out that it could be extended to three parts by transferring the b2-bishop to f6 in the diagram. The new (a) position would then be solved by 1.Bb2!, leading to the initial setting. Here 1.Bb2! completes the block (by providing for 1…Qxa2), unlike the other keys which maintain an existing zugzwang.

Andy Sag: The keys preserve set play but there are two duals.
George Meldrum: The fun in this complete block position comes from finding out what does not work and why.
Andrew Buchanan: The core geometry is a duel between the e3-knight and g8-queen, over control of g2 and d5. 1.Kb6? allows the beautiful 1…Qg1! 1.Bh5? suffers 1…Qg4! cutting off access to f3. If the other white bishop moves then 1…Qxa2! covers both of the key squares.
Ian Shanahan: The first key is irreversible; the second doesn't work in the first part because of check. Focal theme, with play unchanged. Cute!

The key 1.Sd7! attacks f6 and threatens a battery mate, 2.Bh6. By opening the long diagonal, the thematic key also permits the d4-knight to give various discovered checks. A random placement of this piece, 1…S~+, allows the a4-rook to guard f4 and so admits the cross-check, 2.Bf6. The black knight has two correction moves that disable 2.Bf6 by controlling the white R + B battery, but these defences interfere with a black line-piece and lead to other cross-checks: 1…Se6+ 2.g7 and 1…Sf3+ 2.d4. Only three variations and the two white diagonal batteries (both unusually employing a pawn as the front unit) fire just once each, but the strategic intensity of the play makes this a case of quality over quantity.

Andy Sag: The key allows battery checks, all defeated by cross-checks. Adding a white pawn on h4 would be a slight improvement as it would give a true changed mate (set 2.Be7) for random moves of the knight.
Jacob Hoover: The key activates the black B + S battery on the long diagonal… There is no distracting by-play.
George Meldrum: A high-quality problem that sticks to its theme. A very minor flaw with the dual after 1…Be4.
Ian Shanahan: The key clears the line of a black battery directed at the white king, Good-Companions style. Old-fashioned for the date of publication, but timelessly beautiful nevertheless.

The black king, though trapped in the corner, is also well protected, ironically because White’s bishops and pawns create a barrier that prevents any direct assault by the queen. A delicate approach is required to get the queen through this barrier, as White steers the black pawn on c6 into clearing a path for the piece. 1.Qa6! cxb5 2.Kb4 bxc4 3.Kc3 cxd3 4.Kd2 dxe2 5.Ke1 exf1=Q+ 6.Qxf1.

Andy Sag: The long pawn chain is an obvious clue. What the pawn promotes to is immaterial. A very amusing one-liner.
Jacob Hoover: The queen flies down the now-open a6-f1 line for the mate.
George Meldrum: Too easy reduces the smile factor, nevertheless cute.
Nigel Nettheim: Amusing! The f6-pawn can be removed, if the e3-bishop is shifted to d4 [stopping the cook, 1.Qh8 cxb5 2.Kb4 bxc4 3.Qc3, etc.].
Ian Shanahan: The solution is spotted immediately, but the ladder mechanism is cute.

If White shifts the queen from the f-file to another square where it doesn’t control Black’s R + B battery, 2.Be3+ will be threatened, forcing 2…Bxe3. The choice of 1.Qd7! is natural, half-pinning the two black pieces, but it’s not obvious how White should proceed when Black captures the c4-knight with either piece (to answer 2.Be3+ with 2…Ke5/Sxe3!). Each capture by the bishop or the knight leaves the remaining piece on the d-file pinned, after which White wants to incapacitate the capturer on c4 in order to force Black to open the battery through zugzwang. Now pinning the c4-piece with one of the white rooks seems to create an unwanted flight on the second rank and spoil the battery mate. But it turns out that White can make such a pinning move by cleverly exploiting the position of the c4-piece, which has inadvertently placed a guard on one of the rook-squares, allowing it to be unblocked. 1…Bxc4 2.Ra4 Bg~ and 1…Sxc4 2.Rb4 Bg~. One other defence, 1…Sf5, is met by a grab, 2.exf5 Bg~.

Andy Sag: Tries: 1.Be3+? Bxe3+ 2.Qf1, and 1.c3+? Kxd3 2.Qxd5+ Ke2!
Jacob Hoover: In each of the main lines the capturing unit guards the square that the pinning rook vacates.
George Meldrum: The composer has clearly hung signs over the two rooks and pawn in front of the white king saying, “Do Not Disturb”. Little wonder a solver may go into panic mode before finding that both rooks are needed in variations. Deceptively good.
Nigel Nettheim: It took me two attempts to find the play, with the attractive use of the white rooks.
Ian Shanahan: The key establishes a half-pin, after which the piece that moves is pinned in the thematic play, forcing the bottom-rank battery to open due to zugzwang. Pretty strategy.

Initially Black has three legal moves, all of which are prepared with white mating replies: 1…d5 2.Se6, 1…c5 2.Qd3, and 1…f3 2.e3. White has no way of maintaining the block, however, and the key 1.Qb3! actually entails a threat, 2.Qb4. Two flights are granted by the queen, and when the king takes these flights, White answers with two of the mating moves seen in the set play: 1…Kc5 2.Se6 and 1…Ke4 2.Qd3. Hence the problem demonstrates mate transference. It’s a flaw that the set variation 1…c5 2.Qd3 is still effective, duplicating the thematic queen mate linked to the new 1…Ke4 defence. The transfer of the knight mate 2.Se6 is clearer because its original defence 1…d5, unlike 1…c5, doesn’t deal with the threat and so can be ignored. In any case, this is a splendid example of the block-threat form.

Andy Sag: Complete block with key giving two flights and threat replacing set play.
George Meldrum: A quiet, multiple flight giving key.
Nigel Nettheim: Two flights add to the difficulty of solving. The mate after 1…Kc5 is pure.
Ian Shanahan: A block-threat, whereby the key gives two flights – with mate transference. (It's a pity that the post-key mate 2.Qd3 is repeated.) What a superb and utterly memorable little Meredith problem! Bravo!

The key 1.Gxc5! creates a R + G battery that can open in four different ways, and these moves function as multiple threats: 2.Ga5/Gc7/Gg5/Gg1. Four black defences induce each of the mating threats in turn: 1…Ga2+ 2.Ga5 (switchback and shut-off), 1…Gc8 2.Gc7 (shut-off), 1…Gg5 2.Gxg5, and 1…g5 2.Gg1 (recovering the g6-flight) – hence the Fleck theme is rendered. One more defence parries all of the threats by capturing the grasshopper, but provokes a new mate: 1…bxc5 2.Rxc5. Since Black employs the grasshopper in three of the main battery variations, this harmonious problem also features a G vs G duel.

George Meldrum: Grasshoppers take some getting used to. Opening the rook line while closing Black’s lines of defence is the theme, plus a nice response after Black plays 1…g5.
Jacob Hoover: Although the Fleck is a very nice touch, I think it would have been better if the four thematic defenses had all been grasshopper moves; that way the problem would display a nice bit of unity.
Ian Shanahan: A grasshopper duel, also showing a 4-fold Ideal Fleck theme – all threats separated by each black defence – with an elimination mate (transferred from the set defence 1…bxa5) thrown in for good measure. Fine construction!

The thematic key 1.Re5! (threat: 2.Rd5) not only unpins the black queen, enabling it to check twice, but also shows a double-sacrifice of the rook. The first checking defence 1…Qxf5+ prompts a recapture, 2.Rxf5, that fires the B + R battery. The second check 1…Qc6+ is answered by the threat move, 2.Rd5, though this may be viewed as a distinct mate that requires the battery to operate again. If Black takes the offered rook, then 1…Qxe5 2.Se6 sees the queen re-pinning itself, while 1…Kxe5 permits 2.Qf4. The self-block 1…Rxc5 results in another pin-mate, 2.Re4. Lastly, the black knight admits a pair of queen mates that are nicely non-symmetrical: 1…Sc3 2.Qe3 and 1…Se3 2.Qb2.

Composer: Sacrificial give-and-take key unpinning the black queen. This allows it to give check answered by the threat but this time with a required double-check, and a second check answered by a battery mate.
Jacob Hoover: The key allows two checks from the queen, but each time White has a cross-checking answer.
Atagün Karayel: The c5-pawn was so much of an obstacle in all tries: Let's just protect it!
George Meldrum: The key provides a give-and-take flight and releases the black queen to attempt counter play.
Nigel Nettheim: A marvellous key. The white rook seemed likely to move to threaten Se6; that didn’t work, but the rook surprisingly moved anyway, to its least likely square and for a different purpose. Congratulations!
Bob Meadley: Nice two-mover by Andy.
Ian Shanahan: The unpinning key takes the unprovided flight but offers a flight-capture. Solid traditional work.

White has no reply set against either of the black pawn’s moves, and the particularly strong 1…hxg2 would defeat 1.Bxb2? (threat: 2.Ra1). If White moves the a2-rook somewhere along the file (except a8), that deals with 1…hxg2 by preparing a rook mate on the h-file, and 2.Bxb2 becomes a threat. The black bishop’s defences on the long diagonal are mostly answered by its capture, e.g. 1.Ra7? Bd4+ 2.Bxd4 (3.Ra1) hxg2 3.Rh7, while 1…h2 permits 2.Rxh2+ Kxh2 3.Rh7; but Black cleverly refutes with 1…Bg7! since after 2.Bxg7 hxg2, the white bishop finds itself interfering with the rook’s mating move (or 2.Rxg7 fails to 2…h2). Likewise, 1.Ra6? Bf6! 2.Bxf6 hxg2 and 1.Ra4? Bd4+! 2.Bxd4 hxg2 are spoiling. Another tempting try is 1.Ra3? which handles 1…Bc3 with a new idea, 2.Rxc3 hxg2 3.Rh3 and 2…h2 3.Rc1, but now 1…h2! defeats as there’s no mate after 2.Rxh2+ Kxh2. The ingenious key 1.Ra5! (2.Bxb2) generates similar play to that of the tries after random bishop moves: 1…Bc3/Bd4+/Bf6/Bg7/Bh8 2.Bxc3/Bxd4/Bxf6/Bxg7/Bxh8 (3.Ra1) hxg2 3.Rh5, but here the interception move 1…Be5 can be exploited as an unguard that allows 2.Rg1+ Kh2 3.Bxe5. The remaining bishop defences, 1…Ba3/Bc1, also unguard e5 and prompt the same 2.Rg1+ (though a dual follows 1…Bc1 with 2.Rh5 also working). Lastly, 1…h2 gives 2.Rxh2+ Kxh2 3.Rh5.

Andy Sag: The short mates 1…hxg2 2.Rh5 and 1…Bxa1 2.Rxa1 detract slightly. Too many tries to mention but I like 1.Ra3? h2!
Jacob Hoover: Black has clever refutations for most of the a2-rook’s moves. The black bishop forces the white bishop to capture it on a square where it will be blocking the rook’s access to the h-file.
George Meldrum: A problem with many a choice of first moves, and a non-too obvious key.
Nigel Nettheim: Excellent. The a2-rook was bound to move, but where? A hard-to-find factor was needed: the weakening of e5 by 1…Be5 for an unexpected mating scheme.

The key 1.Bd7! controls c6 and threatens 2.Qxa5, which remains effective after the flight-move, 1…Kxa4. Random moves by the a5-knight allow a potential dual, 2.Sxb4/Rb8, but these secondary threats are separated by 1…Sb7 2.Sxb4 and 1…Saxc6 (self-pin) 2.Rb8. The correction 1…Sc4 prevents both mates (besides the main threat) but self-blocks, enabling a battery mate that interferes with the g4-rook, 2.Sd4. All moves by the b4-knight also defend, by opening a line for the black bishop, and they lead to similar correction play. The potential dual after the knight’s random moves is separated by 1…Sd5 2.Sxa5 and 1…Sbxc6 (self-pin) 2.Rf5. Now 1…Sa6 disables both secondary threats, and the self-block error is exploited by another battery mate, 2.Sa7, which cuts off the white queen. Judges F. Hawes and J. J. O’Keefe called this problem, “A very charming echo-study, with a key-move weakness peculiar to symmetrical positions in general.”

Andy Sag: The key sets up a threat and a battery and if the trigger knight is captured, a pair of pin-mates result. The three pawns on second rank avoid all duals.
Nigel Nettheim: The key is too strong and therefore easy for a player to find but, paradoxically, harder for a problem-solver to find (“it wouldn’t be that!”).
Jacob Hoover: This problem has a lot of thematic elements to it that held my interest, and the symmetry between the black knights is a nice touch too.
George Meldrum: A less than ordinary key move. It does, however, create crisscross play by the black knights with amazing mirrored responses by White on different planes. Black pawns on the second rank appear to be placed to prevent duals. Modern practice, I am led to believe, is to exclude such pawns as duals are tolerated more than the extra material.
Ian Shanahan: The key-piece (initially out-of-play) sets up a direct battery. Both black knights make random moves and secondary corrections to defeat the threat in a matrix I’ve seen used several times since. A very elegant problem!

Black’s only mobile unit is the c6-rook and immediate mates are set against its moves: 1…R~rank 2.Sc7 and 1…R~file 2.Sb6. White has no way of preserving the block, however, and the flight-giving key 1.Kg4! extends the solution to three moves. After 1…Ke4, 2.Bxc4 puts Black in zugzwang again, and now the focal play of the rook gives new mates: 2…R~rank 2.Sxc5 and 2…R~file 2.Sd6. If the rook defends on the first move, some duals result (either on White’s second or third move), e.g. 1…Ra6 2.Sc7+ Ke4 3.Sxc5/Bb1, but there are two dual-free variations, 1…Rd6 2.Sc7+ Ke4 3.Sxc5 and 1…Rc8 2.Sb6+ Ke4 3.Bb1.

Andy Sag: The key abandons the set block and gives a flight. If the flight is taken, a new block forces the rook to unguard at least one of the two mating squares for the b7-knight. If instead the rook moves first, the a8-knight checks to force the king into an ambush.
Jacob Hoover: A pseudo-two-mover. The problem clearly displays the focal theme, but the duals on the third move are unfortunate.
George Meldrum: The flight given to the black king reveals the pretty pattern of four black squares surrounding the rook and the interplay between the rook and knights.
Nigel Nettheim: A nice echo effect after White regroups.
Ian Shanahan: Changed focal theme, unusually set in a three-mover. The focal theme was a favourite of Norman Macleod in his earlier compositions.

The diagonal half-battery arrangement – initially masked by the black rook – suggests that the first move will be made by one white rook, followed by battery mates delivered by the other. The thematic try 1.Re3? threatens 2.Rxa3, forcing the black rook to vacate the bishop line: 1…Ra7 2.Rd7 and 1…Rf3 2.Rf5; but 1…axb2! refutes. The key 1.Rd3! has a similar threat and draws the same defences, but creates new shut-off mates: 1…Ra7 2.Re7 and 1…Rf3 2.Rf6. Now 1…axb2 is answered by 2.Ra6. The e6-rook executes two more tries: 1.Ra6? Ra7 2.Rd7, but 1…Rf3!, and 1.Rxe2? (threats: 2.bP~) axb2 2.Qxb2 (an extra change), 1…Rf2 2.Rf5, but 1…Re7!

Andy Sag: A Meredith setting with potential battery indicating a rook key but which one and where to?
Jacob Hoover: A nice demonstration of the half-battery concept. That all the mating moves in the actual play are made by the same piece lends a degree of unity to the whole thing.
Nigel Nettheim: Very neat rather than very deep, perhaps.
Ian Shanahan: A very trying problem! Here we see, shown most elegantly, a masked half-battery in Meredith. This sort of set-up is rather hackneyed (there are numerous examples from the 1960s), but here is done in Letztform.

In part (a), a potential mate is to place the black king on f5 for Rf6. This scheme requires the e4-flight to be covered, but none of the spare white units can arrange to guard that square. Instead, Black blocks it with the d5-pawn, a move that necessitates two preparatory sacrifices. 1.Be3 dxe3 2.Kf5 e4+ 3.dxe4 Rf6. The twinning for part (b) shifts the thematic pawn to b5. With d5 vacant, the new plan is to mate the black king on that square with Sf6. Now the issue is how to deal with the c4-flight, and once again it has to be blocked by the black pawn, after sacrificial play by both sides. 1.Sc3+ dxc3 2.Kd5 c4+ 3.bxc4 Sf6. Like many other problems by its GM composer, this helpmate features pawn play that highlights a special property of the unit – its need to capture so as to access certain squares.

Andy Sag: The name Chris Jones strikes fear in the heart of the solver; his problems are always tough and this is no exception. In each case the d2-pawn was the only way to achieve the required self-block so the check from f6 could be a mate.

In this block position, all black moves are prepared with set mates: 1…Sg~ 2.Qe6, 1…dxc5 2.Sxc7, 1…R~ 2.Scxb4, 1…h1=Q 2.Qxh1, and 1…Sb~ 2.Rd4 (with a dual, 1…Sxc5 2.Rd4/Sxc7). But White has no way of preserving all of these variations, e.g. 1.Re1/Re3? Ra2!, 1.Ke1? Ra1+!, 1.Kg3? Sh5+!, and 1.Qh4? which produces a change with 1…Sg~ 2.Rxf5, but is handled by 1…dxc5! The key 1.Qh8! (waiting) leads to three changed mates: 1…S~ 2.Qg8, 1…Se6 2.Se3, and 1…dxc5 2.Qd8. The remaining play is as set: 1…R~ 2.Scxb4, 1…h1=Q 2.Qxh1, and 1…Sb~ 2.Rd4 (1…Sxc5 2.Rd4/Sxc7). A fine mutate with a particularly good ambush key that places the queen in the corner.

Andy Sag: A tricky waiter with a withdrawal key, changed mates and tries. The dual after 1…Sxc5 is unfortunate.
Jacob Hoover: The correction 1…Se6 is a self-block that allows the white self-interference 2.Se3.
Andrew Buchanan: Three changed mates; satisfying to solve. Dual after 1…Sxc5 2.Rd4/Sxc7, and no other variation provides the knight mate.
Michael McDowell: Whether it’s there by accident or design 1.Qh4? is a superb try, giving a neat change after 1…Sg~ while maintaining complete accuracy.
George Meldrum: Great key move with changed mates. Particularly nice response after Black’s knight to e6. Crafty methods used to avoid cooks, making it tricky to solve.
Ian Shanahan: A clever mutate with black correction by the g7-knight. Fine work by these regular collaborators.

After 1.Kb6!, which opens the c-file without exposing the white king to check, White threatens 2.Qc2. Black’s main defences carry the same weakness of blocking a flight-square, and the manner in which White exploits the error is also congruous across the four variations. 1…Bc4 2.Sc5, 1…Sd4 2.Sb2, 1…Sd2 2.Be2, and 1…S1e3/S5e3 2.Be4. In each case, the mating move closes a white line of guard to the blocked square; and the scheme involves a pair of mating units interfering with four different line-pieces. We find by-play in 1…b3 2.Qc3, plus two non-thematic tries with multiple threats: 1.Qf4? gxf3! and 1.Qe5? Sd2!

Andy Sag: The key brings the queen into play with a self-block defence theme.
Jacob Hoover: Amazingly, the key is a retreating king move. Six defenses exist, and five of them are self-blocks that enable white self-interferences.
George Meldrum: Five new mates emerging in the solution. Two tries by White’s queen to e5 and f4.
Ian Shanahan: The white queen is initially out-of-play, and needs to be brought into the action. A king-key does the job. In the variation-play, we see four Theme B2 mates (self-block + white interference) by the a4-knight and f3-bishop. Sweet!

If White moves the knight to unguard b2, …Kb2 becomes a potential battery mate, even though an opening of the c-file would also let the queen intercept on c1. A random knight move, such as 1.Sb2?, would actually leave Black almost in zugzwang and provide for all possible moves of the a7-rook, but 1…Kxb2+! refutes since after 2.Qc1+, Black can avoid 2…Rxc1 mate and play 2…Kxb3 instead. Hence the key 1.Sa5! (waiting), which attacks b3 for 1…Kb2+ 2.Qc1+ Rxc1. White deals with the a7-rook’s moves in a nice variety of ways. Four times White captures the piece to force the black battery to open through zugzwang: 1…Rxa6 2.Qxa6 Kb2, 1…Ra8 2.Qxa8 Kb2, 1…Rb7 2.Qxb7 Kb2, and 1…Rd7 2.Qxd7 Kb2. After 1…Rc7, not 2.Qxc7? since the queen still controls c1, but 2.Qc1+ Rxc1. And 1…Rxe7, by restricting the white king, enables another queen deflection: 2.Qc2+ dxc2.

Andy Sag: After the try 1.Sa3+ failed, it seemed that 1.Sa5 (guarding b3) might work as the a7-rook is forced to move either to a controlling square or get taken by the queen. Note the b3-pawn is needed to allow 2…Kb2 mate after 1…Rb7 2.Qxb7.
Andrew Buchanan: Very nice selfmate-in-2. It took me a few minutes to see why 1.Sd6? and 1.Sb2? don't work.
Jacob Hoover: Three defenses require White to sacrifice the queen.
Bob Meadley: Very good indeed.
Ian Shanahan: Here we see the Grab Theme – common in selfmates – shown most elegantly. This was not too difficult to solve.
George Meldrum: This problem just keeps on giving; who would have thought four different mates. An absolute ripper, Mr Marysko!

A first-rate key, 1.Se6! (threat: 2.S6f4), grants three diagonal flights to the black king – one by direct unguard and two by interfering with the e8-rook and g8-bishop. The flight-moves to the fourth rank self-pin the black bishop on g4: 1…Kc4 2.Sc5 – a battery mate (not 2.S6f4? unpinning the bishop) – and 1…Ke4 2.Bh7 (again not 2.S6f4?). The third flight-move is answered by the threat, 1…Kxe2 2.Sf4, though this may be viewed as a distinct mate. The g4-bishop initiates two more variations; in each case it commits the error of opening a line of guard for the white queen: 1…Bxe6 2.Sxc1 and 1…Bxe2 2.Bh7. Two tries are 1.Sb3? Qd2! and 1.Ra4? Sd2!

Andy Sag: The Novotny-style key gives three flights including a flight capture, the latter answered by the threat. The two remaining flights invite pin-mates.
Andrew Buchanan: An excellent key: into en prise, giving three flights.
George Meldrum: A multiple flight-giving key and has multiple tries. Nice.
Ian Shanahan: I found the spectacular triple-flight-giving key instinctually (after spotting the intersection-square e6 and asking “What if...?”). 1…Ke4 2.Bh7! (2.S6f4?) shows a variant of the Schiffmann theme – avoidance of interference unpinning in the mate. A fine problem!

The key 1.Bc8! (waiting) gives the black king access to d3 but takes the flight on f5, leaving the piece with four available moves. An attractive model mate follows 1…Kf3 2.Qe3+ Kg2 3.Qh3. This mating configuration recurs twice with 1…Ke5 2.Qg5+ Ke4 3.Qf5 and 2…Kd6 3.Qc5; the latter mate shows a chameleon echo (where the bishops swap roles), though this isn’t a model due to the f6-pawn guarding e7. A pure mate that doesn’t involve the key-bishop occurs in 1…Kd3 2.Qe3+ Kc4 3.Qb3. Lastly, 1…Kd5 2.Qe3 leads to three sub-variations, two of which repeat mates already seen: 2…Kc6 3.Qc5, 2…Kd6 3.Qc5, and 2…Kc4 3.Qb3. A very fine echo-mate problem.

Thanks to Bob Meadley who brought to my attention that this three-mover wasn’t composed by the Australian problemist, William J. McArthur. Rather, the author was an Englishman, Sergeant Major William McArthur.

This problem originally had a white pawn on e5 and no black pawn on b2, and it contained a serious dual, 1…Kd5 2.Qf4 (intention)/Qe3/Qh4. Removing that white pawn gets rid of the dual but results in a cook, 1.Qg5 Kf3 2.Kc2, which I fixed by adding the b2-pawn. Andy Sag mentions that in the current version, the f7-pawn seems to be unnecessary. Computer-testing confirms that the problem would be sound without it, but here the key produces a threat, 2.Qe3+, instead of zugzwang. I think that a weakness of the problem – the repetition of 2.Qe3 in three variations – is exacerbated by the use of the same queen move as the threat. On the other hand, the threat of 2.Qe3+ Kd5 3.Qe6 is perfect as this is yet another echo of the thematic model mate!

Andy Sag: The bishop diagonals must be correctly separated to enable queen mates where one bishop guards the mating queen and the other guards escape squares. This makes 1.Bc8 a fairly obvious key.
Jacob Hoover: The give-and-take key 1.Bc8! exchanges the flight at f5 for a flight at d3. No matter which flight Black takes, the queen, supported by both bishops, can trap the black king.
George Meldrum: There is little clue to White’s first move other than the pawn on a2 begging the black king to come towards it. Last week’s problem had a pawn on g2 which gave the game away immediately by saying the black king is to be given a flight on the e-file. Here we have a selection of first moves and hard yakka following a king to five eventual mating squares. Not the sort of problem you want to face in a rapid solving competition.
Bob Meadley: Some lovely variations which mesmerised me.

The identities of three pairs of like pieces in the diagram – the white rooks, black rooks, and black knights – are exchanged across the two solutions: 1.a4 Sc6 2.Ra3 Sd4 3.Rc3 Sxe2 4.Rc4 Sc3 5.Qg4 Sf6 6.Qxg7 Rg8 7.Qh8 Rg3 8.Se2 Rd3 9.g4 b6 10.g5 Bb7 11.g6 Be4 12.g7 Sfd5 13.g8-Q f6 14.Qg1 Kf7 15.h4 Bh6 16.Qxd8 Bf5 17.Qh8 Rg8 18.h5 Rgg3 19.Rhh4 Rh3 20.Rhe4 Sf4 and 1.h4 Sc6 2.h5 Sd4 3.Rh4 Sxe2 4.Rc4 Sf4 5.Qg4 Sf6 6.Qxg7 Rg8 7.Qh8 Rg3 8.Se2 Rh3 9.g4 b6 10.g5 Bb7 11.g6 Be4 12.g7 S6d5 13.g8=Q f6 14.Qg1 Kf7 15.a4 Bh6 16.Qxd8 Bf5 17.Qh8 Rg8 18.Ra3 Rgg3 19.Re3 Sc3 20.Ree4 Rd3. In each part, the white rook selected to start the play must go to c4 and not e4 since the latter would prevent Black’s light-squared bishop from reaching f5 in time. Black’s thematic pieces that are developed first, namely the b8-knight and h8-rook, have to choose their final squares with care to avoid obstructing the other white rook’s trek to e4.

Andy Sag: To reach the final position in 20 moves it is necessary for the black queen, the black g-pawn and the white e-pawn to be captured on their home squares and for the white g-pawn to promote to a queen and then move to g1 no later than move 14.
George Meldrum: BIF, BOF, BAM, I feel like Batman has just belt me up! Only one solution found; it is mental.
Jacob Hoover: Between the two solutions we find three instances of role-swapping – between the white rooks (c4 and e4), between the black knights (c3 and f4), and between the black rooks (h3 and d3). Another gem of a problem from OzProblems.com’s own Peter Wong.
Andrew Buchanan: Proof games with multiple solutions are hard to get sound and so congratulations on this one, where the movement of rooks and black knights is cunningly orchestrated.

The thematic key 1.d6!, with the threat of 2.Qc4 (covering the e4-flight), allows Black’s rook and bishop pair on the fifth rank to check by discovery. The bishop has four possible moves and all result in different mates. 1…Bxd6+ abandons the long diagonal and permits 2.Qd5. The correction 1…Bf6+ interferes with the f8-rook, enabling 2.Qf5. Two more correction moves commit the error of self-block and lead to knight mates on the same square that are subtly differentiated: 1…Bc3+ 2.Sdc5 and 1…Bd4+ 2.Sbc5. The R + S battery utilised in the latter variation fires again indirectly in 1…Ke4 2.Sxd2. Lastly, 1…Rf5+ also admits 2.Qxf5.

Andy Sag: The key preserves a set flight and adds four battery checks by the pinned b5-rook, each answered by a different mate (with changes from the set play 1…Bd4/Bd6 2.Sxc1).
Jacob Hoover: Three of the black bishop’s moves allow pin-mates. Every line except one involves a battery play in some way – one line even has a black battery play answered by a white one.
Ian Shanahan: The key introduces four cross-check variations that include a correction by the black bishop. Classic strategic play, dating back to the “Good Companions” (around WW1 and after) by one of the masters of that era, here seen near the end of his career.

Most of Black’s moves in the diagram are given set mates, including 1…Bd4 2.Qc4 and 1…Rxb4 2.Qxe3, but no mates are prepared for 1…Bc3 and 1…Rb2. The key 1.Sd5! (waiting) completes the block and brings about some changes. A Grimshaw interference between Black’s bishop and a2-rook occurs on b2: 1…Bb2 2.Bc2 and 1…Rb2 2.Qc3; the same mates are permitted after 1…Rc2/R~file 2.Bc2 and 1…Bc3 2.Qxc3. Another Grimshaw takes place on d4 between the bishop and the other black rook: 1…Bd4 2.Qb5 (a change from the set play) and 1…Rd4 2.Sxe5. The e4-rook produces two more variations: 1…Rc4 2.Qxe3 and 1…Rxb4 2.Sxb4 (another new mate). Lastly, 1…S~ 2.Be2 and 1…e2 Sf2 show basic unguards.

Andy Sag: A very busy waiter with eight variations including two changed mates.
Andrew Buchanan: Eight mates without the smallest dual. The a1-bishop participates in two Grimshaws. There's a bunch of set-play, but I couldn't find an answer to 1…Bc3. Suggests 1.Sa4/Sd5, but one is a try and the other is a solution, so have to check all the defences. 1…Rxb4!
Ian Shanahan: The key did not easily reveal itself to me. A lovely double Grimshaw including some changed and transferred mates. Beautiful work from the Dutch Grandmaster!

In this block position, white continuations are arranged for all of the black knight’s moves, e.g. 1…S~random 2.Rh1+ Kg2 3.Rfg1, and a correction 1…Sxg1 enables 2.f3 (threat: 3.Qxg1) Sxf3/Sxe2/Kg3 3.Qf2. Tries by the f1-rook, such as 1.Rd1?, leave f2 unguarded and fail to 1…Sxg1! 2.f3 Kg3. The key 1.Ra1! (waiting) compensates by clearing the first rank for the queen, as preparation for 1…Sxg1 2.Qb1 (3.Qxg1) Sf3/Sxe2 3.Qh1 – this new variation demonstrates the Turton doubling manoeuvre. Random moves by the knight and another correction give the same play as set: 1…S~ 2.Rh1+ Kg2 3.Rag1 and 1…Sd4 2.f3 (waiting) S~ 3.Qf2. One last correction move, 1…Se1, forces 2.Raxe1 f3 3.Qxd6 (removing a set dual, 1…Se1 2.Rh1+/Rxe1). The well-placed white king yields more tries that aim to maintain the initial zugzwang but leave the piece vulnerable to checks, e.g. 1.Kg7?/Ke7? Sd4!, 1.Kf7? Se5+! A three-move mutate – one of Whyatt’s specialties.

Andy Sag: The complete block cannot be preserved as set so changed play must be found. Clearance key allows the queen to operate on first rank.
Jacob Hoover: A masterpiece by none other than the late, great William Whyatt.
George Meldrum: Another Bill Whyatt gem.

Black needs to shift the c8-bishop in order to help activate the white rook, and it has three non-checking moves, each of which leads to a different solution. 1.Be6 Rf8 2.Ke4 Qxf3, 1.Bf5 Re8 2.f2 Qe2, and 1.Bg4 Rd8+ 2.Kc4 Qd5. The black bishop’s moves don’t have any positive arrival effects, i.e. the piece’s placements don’t contribute to the three eventual mates, but rather, each move prevents two of these potential mates and thus forces White to set up the third one. Therefore a sort of cyclic dual avoidance is shown.

Andy Sag: In each solution Black’s white-squared bishop and the white rook take up different squares to prepare three different queen mates.
Jacob Hoover: We have line-opening in all three solutions; the bishop must choose its destination carefully so that it does not interfere with the mate.
George Meldrum: In each solution White’s rook aids the queen to mate on the d/e/f files.
Ian Shanahan: Two clever echoed mates and a near-echo. Ingenious work, as one would expect of a master like Feather.

The key 1.Rg7! contains three threats: 2.Rxc7, 2.Qxc7, and 2.Qe5. These threats are individually forced in 1…f4 Rxc7, 1…Bxg7 2.Qxc7, and 1…c6/c5 2.Qe5 – generating the Fleck theme. Random moves by the black knight prevent all of the primary threats, but allow three potential queen mates, 2.Qd2, 2.Qc2, and 2.Qb2, which are called secondary threats. Specific knight moves separate these queen mates – 1…Sxe1 2.Qd2, 1…Sxh4/Sf4 2.Qc2, and 1…Sxe3 2.Qb2 – and so a secondary Fleck is accomplished as well. Notwithstanding the “black dual” of 1…c6/c5 giving the same mate, and likewise for 1…Sxh4/Sf4, this is an elegant combination of two mate-separation ideas.

Andy Sag: A neat triple-threat separation study. Any move by the g2-knight stops all three threats but allows one of the three set queen mates from 2nd rank. Any other black move leaves only one of the three threats open.
George Meldrum: Replies to black knight moves are from set play. All other black moves eliminate two of White’s threats leaving one way to mate.
Jacob Hoover: We have a secondary Fleck, sort of, and also a primary Fleck.
Ian Shanahan: Here we see, in a very famous problem, the Fleck-Karlstrom theme in a specific form: a total primary Fleck, and a total secondary Fleck. This combination was much loved by the great Italian problemist Stocchi. A great and memorable problem!

If White moves the f4-bishop to open the f-file for the rook, 2.Qf3 becomes a threat. Black can defend by unpinning the knight on d4, and four such defences on b4 are given set mates: 1…Qb4 2.Sxg5, 1…Bb4 2.Sg3, 1…Rb4 2.Qxe3, and 1…Sb4 2.Rxe5. However, these set mates are obstructed by the white bishop when it’s placed on the wrong square: 1.Bxg5? Qb4!, 1.Bg3? Bb4!, 1.Bxe3? Rb4!, and 1.Bxe5? Sb4! Hence only 1.Bh2! solves, preserving the set play: 1…Qb4 2.Sxg5, 1…Bb4 2.Sg3, 1…Rb4 2.Qxe3, and 1…Sb4 2.Rxe5. The by-play consists of 1…Bg2 2.Qxg2 and 1…Bxg4 2.Qxg4. The attractive bishop-star formed by the four tries is unfortunately ruined by a double-refutation of 1.Bxe5?, which is defeated not only by 1…Sb4! but also 1…Sxe5!

Andy Sag: The key threatens a pin-mate. All six defences including four pin breakers on b4 unguard different mating squares.
Jacob Hoover: The thematic defenses involve moving a piece to b4 to unpin the d4-knight, but each such defense unguards another potential mating square.
George Meldrum: Four pieces are used on the b4-square to defend against the four tries by White’s f4-bishop.
Ian Shanahan: The bishop’s tries cause obstructions to White that are exploited by Black – a standard method of try-refutation. The black unpins of the knight on d4 are cute, and enrich the problem.