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401. Ottavio Stocchi
The Brisbane Courier 1933
11th Hon. Mention
Mate in 2

Four set variations account for all possible black moves in the diagram: 1…Kc6 2.Qb7, 1…Se~ 2.Qe4, 1…c6 2.Qd4, and 1…Sg~ 2.Bf3, so this is a complete block. White has no way of preserving all of these lines though, e.g. 1.Bd1? Se2!, 1.Be3? c5! The key 1.Qb5! (waiting) removes the flight on c6 but creates a new one on e4: 1…Ke4 2.Qc4. The e7-knight now exhibits correction play, 1…Se~ 2.Re5 and 1…Sc6 2.Bb4, bringing about two changed mates. A third change occurs with 1…c6 2.Qd3, while 1…Sg~ 2.Bf3 is as set. An especially difficult mutate with some surprising changes.

Andy Sag: The give-and-take key changes three mates as well as the flight. Noted the white pawn on a5 prevents the 1.Sa5 (2.Qc4) cook.
Jacob Hoover: The c5-bishop has numerous tries (1.Bf2/Be3/Bxa7?), all of which produce the changed mates 1…Se~ 2.Qc5 and 1…Kc6 2 Qc5, but they're all defeated by 1…c5!
Nigel Nettheim: The refutation of the try 1.Bd1? is neat. After 1.Qb5! Ke4 the pin of the e7-knight is irrelevant, perhaps a slight weakness.
Ian Shanahan: A beautiful mutate with a key that gives and takes a flight. Lovely (though the position is rather crowded, as is so often the case with Stocchi).

402. Brian Tomson
feenschach 1983
Series-helpmate in 29

If the two f-pawns were removed in the diagram position, the f8-rook could mate, and indeed it’s not possible to arrange any other mating configurations, given the fixed positions of the white units. Black must capture the f6-pawn with the king, since to do so with the rook would give check (forbidden during the sequence). This plan requires the black king to be shielded from all three white line-pieces: 1.Rg2 2.Kg1 3.Kf1 4.Re2 5.Re3 6.Ke2 7.Kd3 8.Kd4 9.Re7 10.Rf7 11.Kd5 12.Ke6 13.Kxf6. Now if Black captures the f4-pawn too soon, the opened f-file would mean the king cannot return to h1, as the black rook is unable to shield the king from both white rooks simultaneously. So the king goes back first: 14.Ke6 15.Kd5 16.Kd4 17.Re7 18.Re3 19.Kd3 20.Ke2 21.Kf1 22.Re2 23.Rg2 24.Kg1 25.Kh1. Finally the f4-pawn can be captured, followed by the rook’s return to h2: 26.Rf2 27.Rxf4 28.Rf2 29.Rh2 for 29…Rf1. An impressive black minimal problem that features numerous shields and rundlaufs by both black pieces.

Andy Sag: The mate is not hard to see, but how to get rid of the f-pawns in as few moves as possible avoiding checks leads to a unique series.
George Meldrum: A tortuous path but one without compromise on move order or move direction.
Ian Shanahan: A beautiful and perfectly constructed example of well-known ideas: king-shields, encirclement, a long trek with subtle manoeuvring and precise switchbacks.

403. David Shire
Australian Chess 2003
Mate in 2

After the key 1.d6!, Black can stop the threat of 2.Qxe5 by capturing the knight on d3. Such a capture would self-block and apparently enable the white rook to give various battery mates by moving along the f-file. But each capture by a black piece involves an additional effect that obliges the rook to play to one specific square: 1…Bxd3 2.Rf1, 1…Sxd3 2.Rf2, 1…cxd3+ 2.Rf7, and 1…Rxd3 2.Rf4. The multiple self-blocks on the same square lead to differentiated white mates or dual avoidance – a combination known as the Stocchi theme. There is by-play with 1…Rd5 2.Qe3.

Andy Sag: The key allows a check. This and three other set self-blocks after capture of the d3-knight require four different positions of the white rook when firing the battery. Note the rook capture requires a double check. Finally, the rook blocks the threat but again opens the line to e3 as well as creating a self-block on d5.
Jacob Hoover: If we were to replace the d3-knight with a dummy black piece, White would have five different mates: 2.Rf8, Rf7[A], Rf6, Rf2[B], Rf1[C]. Three of the four captures of the knight force a particular one of these rook discoveries: [A], [B] and [C]; thus, we have an incomplete Stocchi block since there is no capture that forces 2.Rf8 or 2.Rf6. The fourth capture, however, forces a new rook discovery: 1…Rxd3 2.Rf4.
Nigel Nettheim: Not hard to solve, because the a2-g8 diagonal was likely to come into play. But the four captures on d3 are very nicely handled.
George Meldrum: A quiet unassuming key move. Four defensive captures on d3, all with unique mating responses. Very nice.
Ian Shanahan: Four-fold Stocchi blocks – self-block plus dual avoidance – on d3. From memory, the record is five. An excellent problem!

404. Bernd Gräfrath
Australian Chess 2005
Helpmate in 3
2 solutions

This miniature is solved by 1.Ra5 Bc1 2.Ka4 Kc4 3.Rb3 axb3 (ideal-mate) and 1.Rab3 axb3 2.Ka3 Kc3 3.Ra2 Bc5. The two phases show exchange of functions performed by both white and black pieces. The white bishop and pawn take turns to guard a flight and to give mate, while the two black rooks swap the tasks of sacrificing on b3 and blocking a flight.

Andy Sag: A role reversal study.
Jacob Hoover: In each solution each unit moves exactly once and the kings move in the same direction.
George Meldrum: Mate with the bishop seemed most likely. Stumbled over the pawn mate solution but found the bishop mate solution most elusive. Both mates are very neat indeed.
Ian Shanahan: White’s non-royal units exchange functions between the solutions (known as a funktionwechsel). A fine and pretty miniature!

405. R. Sutherland
The Problemist 1981
Mate in 4

The astonishing key 1.Ke2! not only permits the black pawn to promote with check, but surprisingly also entails no threats! Neither 2.Kf2? nor 2.Kf1? is threatened because of 2…d1(S)+! and 2…d1(Q)+! respectively. Rather, White waits for the pawn to commit to a particular promotee, which then rules out the alternative. After 1…d1(Q)+ 2.Kf2 (threat: 3.Rh6), the queen has eight different checks, all answered with precise captures – 2…Qe2+ 3.Sxe2, 2…Qxf3+ 3.Sxf3, 2…Qd2+ 3.Sxd2, 2…Qc2+ 3.Sxc2, 2…Qxd4+ 3.Sxd4, 2…Qe1+ 2.Sxe1, 2…Qf1+ 3.Kxf1, and 2…Qg1+ 3.Sxg1 – followed by 3…g4 4.Rh6. Against 1…d1(S), White doesn’t continue with 2.Kf1? Se3+!, but 2.Rxg5 (3.Rg1) Sc3+ 3.Kf1 Se2 4.Rh6. The weakness of 1…g4 is distant self-block: 2.Rh6+ Kg2 3.Rh2+ Kg3 4.Sf5. Lastly 1…Kg2 leads to 2.Rxg5+ Kh3 3.Be6 or 2…Kh1 3.Rg1. The underutilised white bishop is the only flaw in this very tough four-mover, reminiscent of Sam Loyd’s three-move classic, “Steinitz’s Gambit.”

Andy Sag: I tried all other moves first and no joy. The key 1.Ke2!!! allows promotion and if to a queen, the next move leaves no safe checks and the queen is powerless to stop the mate.

406. Joseph Wilhelm
Australasian Chess Magazine 1920
Mate in 2

After the key 1.Rf4!, the threat of 2.Qe4 induces Black to defend with the two half-pinned pieces on the long diagonal: 1…Sc5 2.Sc7, 1…Sd6 2.Sxb6, 1…Re6 2.Qb5, and 1…Rc4/Rxc8 2.Qd7. White exploits not only Black’s self-pins in these thematic variations but also the self-blocks (by the knight) and self-block/unguards (by the rook). The black bishop triggers the by-play, 1…Be5 2.Qxe5 and 1…Bd4 2.Rxd4.

Andy Sag: The half-pin sets up two symmetrical pairs of pin-mates.
Jacob Hoover: The rook variations are changed from the set 1…R~file/Re6 2.Qe6. The set dual 1…Sd6 2.Sxb6/Qe6 is also removed by the key.
Nigel Nettheim: Easy to solve, because the rook had to remain on its rank. The half-pin on the long diagonal is well exploited.
Ian Shanahan: An economical rendering of a typical Good Companions idea: complete half-pin with three thematic self-blocks. And a fine, retreating key thrown in for good measure.

407. F. W. Walton
The Australian Problemist 1963
Mate in 2

In this complete block position, set mates are prepared for all black moves: 1…Sb~ 2.S1c2, 1…Sxd3 2.Qxd3, 1…Sh~ 2.Sf3, and 1…fxe1(Q) 2.Qf4. But White cannot maintain all of the set play with any waiting move, and the key 1.Qh1! involves a threat, 2.Qe4. Two defences by the b-knight bring about changed play, due to the different squares controlled by the queen: 1…Sc2+ 2.S3xc2 and 1…Sxd3 2.S1c2. One further line is as set: 1…Sg2/Sf3 2.Sf3. A good example of the block-threat type.

Andy Sag: A complete block with (arguably) three changed mates, the third one being the threat after 1…fxe1(Q) (set 2.Qf4).
Jacob Hoover: 1…Sxd3 2.S1c2 is also a transferred mate (relative to the set 1…Sb~ 2.S1c2).
Nigel Nettheim: Neat changed-mates for the b-knight. Not hard to solve, because the h1-a8 diagonal was inviting.
George Meldrum: The white queen abandons its defence of d3 which initially looked essential to respond to the black knight moving to c2 and d3. New enjoyable variations now cover those moves with all other lines being supplemental.
Ian Shanahan: A fine block-threat (all mates set, but the key threatens) with two changed mates. The key took longer to find than I expected.

408. Gennady Kukin
Australian Chess Problem Magazine 1997
Helpmate in 2
Twin (b) WSh5

The diagram position is solved by 1.Rb4 Kd2 2.Kc4 Bf7. When the h5-bishop is replaced by a knight, the solution becomes 1.Ke4 Sc6 2.Rd5 Sg3. Both parts finish with an ideal-mate, delivered by the starting piece on h5. Only the e3-bishop is a static piece in this miniature with an open setting.

Andy Sag: Not hard when you realise that at least two of the white pieces don’t move thus limiting the number of final scenarios to look at.
Jacob Hoover: In part (a) the black rook has to move across the critical square c4 before the king moves there, and in part (b) the king must vacate d5 so that the rook can move there.
George Meldrum: Neat.
Ian Shanahan: An attractive miniature showing two different ideal mates. Sweet!

409. Johannes Rietveld
The Brisbane Courier 1916
Mate in 2

The diagram is a complete block, and the only move that doesn’t disrupt any of the set play is 1.Rd2! (waiting). A random move by the black bishop unguards d4: 1…B~ 2.Rd4. The first correction 1…Be3 self-blocks, permitting 2.Sg3. The second correction 1…Bc5 is an anticipatory interference with the c6-rook, enabling the white queen to unpin the piece directly with 2.Qb1. This effect is known as a Gamage unpin, and it’s seen again in 1…Sd6 2.Qxe7, and a third time in 1…e6 2.Qh7. Another self-block occurs with 1…e5 2.Sg5, while 1…Sb5 2.Qxc6 makes further use of the white queen. A well-constructed waiter with no extra materials needed to control the white king or the f8-rook, both of which execute tries defeated by one of the thematic defences: 1.Kb3? Bc5! and 1.Rf7? e6!

George Meldrum: Good array of mates in the set play. Simple to solve.
Jacob Hoover: 1…Bc5 and 1…e6 open white lines and close black ones.
Ian Shanahan: The key piece has to tread carefully, after which the main thematic content is the three direct unpins by the white queen after Black's anticipatory interferences. I also enjoyed the two “secondary corrections” by the black bishop. An excellent problem in the Good Companions style.
Andy Sag: If you shift the f2-pawn to g5 and add a white pawn on e3, we have an eighth variation, 1…g4 2.Rf4. Now you get a pair of short-range lateral rook mates (following unguards) to complement the pair of knight mates (following self-blocks) and four queen mates from different directions.

410. Frederick Hawes
The Australasian 1934
Mate in 4

The farsighted key 1.Kg2! (waiting) opens the first rank for eventual access by the queen while avoiding a prospective interference with the same piece (1.Kf2?). After 1…Ka1, 2.Qd4 (waiting) pins the pawn and 2…Kb1 results in a short mate, 3.Qd1 (hence not 2.Qc3? Kb1!). The main variation continues with 2…Bb1 and now 3.Qg1! pins the bishop and puts Black in zugzwang yet again, forcing 3…Ka2 4.Qa7. Attractive sweeping play by the white queen, making the most of the piece’s power. Note also how the two black pieces exchange their positions.

Andy Sag: The key allows the queen to operate unobstructed. Almost a one-liner. A neat miniature four-mover.
George Meldrum: A super first move by White with the king making way for the queen to eventually use the first rank.
Jacob Hoover: The final position is a model mate [and so is the short variation mate].
Bob Meadley: A beauty and definitely a classic. Not a check to be seen until the end.

411. John James O’Keefe
Good Companions 1919
1st Prize
Mate in 2

After the key 1.Se2!, White threatens 2.Sxf4. Random moves by the f4-bishop lead to dual mates, which are separated by 1…Be3 2.Rxe3 and 1…Bc1 2.Sxc1. Correction play by the bishop disables these mates but admits new ones, twice by unpinning the white queen: 1…Bg5 2.Qxc3 and 1…Be5 2.Qe3, and once by blocking a flight: 1…Bd2 2.Bc2. The black knights have three defences, and two of them also unpin the queen: 1…Se5 2.Qd4, 1…Sd5 2.Qc2, and 1…Sxe2 2.Bxe2. A fifth unpin, via direct withdrawal by the pinning piece, occurs with 1…Qc4/Qxe8 2.Qc4. The black queen produces some by-play as well: 1…Qxc5+ 2.Sxc5 and 1…Qb4 2.Sxb4. A pity about the dual, 1…Qb8 2.Qc4/Qxc3 (duplicating queen mates already seen), which can be removed by adding a black pawn on b7.

Andy Sag: The threat plus eleven variations make this a busy problem. The h6-pawn preventing 1…Bh6 gives a clue to the solver. Better to have a black pawn on c6 instead of the a4-bishop for stopping the 1…Sd5 2.Qc2/Qxb5 dual, and then the f7-pawn can be removed [as 1…Qxe8+ is ruled out].
Jacob Hoover: The dual after 1…Qb8 is unfortunate, but the very rich thematic content more than makes up for that. I wonder if that dual can be removed?
George Meldrum: Not a great deal of new mates after the key yet still satisfying in its complexity. Had hoped that 1.Sh1 had been the key.
Nigel Nettheim: Wonderful! So many satisfying ingredients!
Ian Shanahan: Various unpins of the white queen combined with black correction by the menaced bishop. A lovely strategic problem!

412. Laimons Mangalis
The Problemist 1964
3rd Prize
Mate in 3

The key 1.Qb3! entails a sacrificial threat, 2.Qe6+ fxe6 3.fxe6. The c6-rook and e2-bishop defend on c4, causing a mutual interference between the two pieces. After 1…Rc4, 2.Qxb5 threatens 3.Qe5/Qe8, both stopped by 2…Rc5, but the rook has opened a line for the white queen and also cut off the b6-bishop, allowing 3.Qxe2, a capture of the other thematic black unit (or 2…Bd4/Rd5 3.Qd5). We find a beautifully matching variation in 1…Bc4 2.Qxc2+ Bd3 – opening a line for the queen and cutting off the d1-rook – enabling 3.Qxc6, which captures the thematic rook (or 2…Rd3 3.Sd2). The by-play consists of some short variations, 1…Rc5 2.Qe3, 1…Bd4/Rd5 2.Qd5, and 1…Bxf3 2.Qxf3.

Andy Sag: Try 1.Qa8? (threat: 2.Qe8) Bxf3! A well disguised threat involving a queen sacrifice. Tricky play after defensive blocks on c4. Three short mates detract slightly.
Jacob Hoover: Black has only two defenses, and they constitute a Grimshaw pair.
George Meldrum: Solving this problem is like taking a mouthful of sherbet powder and having your cheeks explode. The setting has more rough edges than Mount Everest; however, the jewels in the crown are after Black plays either the rook or bishop to c4 where play is amazingly done. I like it.