Weekly Problems 2021-B

Problems 554-568


Toma Garai
feenschach 1984

Helpmate in 2, 2 solutions


The black king on its original square has three flights on the c-file, too many to cover here. Instead the king aims to be mated on two e-file squares, which are initially controlled by the white rooks. Thus Black begins by capturing one of these rooks, and the resulting discovered check forces the other rook to sacrifice itself on the king’s target square, as the sole legal way to unguard it. 1.Rxe7+ Re6 2.Kxe6 Sf4 and 1.Bxe3+ Re4 2.Kxe4 Sc3. Black’s first move in each solution also acts as a self-block. Splendid demonstration of capture of white force in a helpmate, incorporating both passive and active sacrifices.

Andy Sag: I got nowhere until my suspicions were aroused by noticing the two batteries. Perfectly matched pair of solutions each starting with a battery check, dispensing with both white rooks and finishing with a model mate delivered by the knight.
Andrew Buchanan: The clues here are the separation of the kings, which invites the black one to step forward to two squares, and some curious pieces (e.g. white pawn on c6 and black pawn on d3) which only make sense if the black king moves. Still it took some time to see Black’s first moves.
Ian Shanahan: What an astonishingly paradoxical blood-bath (i.e. capture of white force) exhibiting a perfect harmony of effects and reciprocity between the two solutions! Only the white pawns on the c-file remain unused in the second solution here – a lamentable flaw…


Miroslav Havel
Besedy lidu 1920

Mate in 3


Of the two flights available to the black king, one is provided: 1…Ke1 2.Se3 d1=Q 3.Sg2. The white king can attempt various waiting moves, but if it stays on the first rank, then equivalent play on the queen-side fails: 1.Kh1/Kf1? Kc1 2.Sc3 d1=Q+! White avoids the queen check with 1.Kf2?, but that runs into 1…Kc1 2.Sc3 d1=S+! The final try 1.Kg2? evades both types of promotion checks, but it’s refuted by 1…Ke1! 2.Se3 d1=Q when the king on g2 obstructs the knight’s mating square. Only the furthest withdrawal move 1.Kh2! works, after which 1…Ke1 2.Se3 d1=Q 3.Sg2 and 1…Kc1 2.Sc3 d1=Q 3.Sa2 produce a pair of reflected echo model mates.

Andy Sag: The clue is in the symmetry of the set position. After the black king moves, White can force the pawn to promote and self-block, but first White must move the king so it cannot be checked by the promoted piece and also keep g2 vacant.
Ian Shanahan: Although the two variations after the key are perfectly symmetrical (ending in reflected model mates), only that which follows 1…Ke1 precisely determines the white king's destination-square in the key – a subtle form of asymmetry. Very pretty, and typical of its famous Bohemian composer.


Andrew Buchanan
Die Schwalbe 2013, Commendation


All units in the diagram are on their original squares, hence not many clues remain as to what transpired in the game. The missing h-pawn, g-pawn and f8-bishop suggest that the white pawn could have promoted by capturing the black units on their initial squares, before getting eliminated itself. The black queen seems the best candidate for removing White’s queen-side pawns efficiently. 1.h4 e6 2.h5 Qf6 3.h6 Qxb2 4.hxg7 Qxc2 5.gxf8=S! White avoids promoting to a queen/rook as that would check and disrupt Black’s plan of freeing the a1-rook next move. A bishop promotion also fails but for a reason that’s not apparent until two moves later. 5…Qxa2 6.Rxa2 Sa6 7.Rxa6. Now only the black pawn on e6 and the white pieces on a6 and f8 remain to be captured. The a6-rook is poised to take that pawn followed by a sacrifice on e8 to the black king, a scheme consistent with the latter capturing the f8-knight. However, 7…Kxf8? 8.Rxe6 would leave Black stuck without a waiting move, so Black wastes a tempo with 7…Ke7! first – which would have been impossible had White promoted to a bishop earlier. 8.Rxe6+ Kxf8 9.Re8+ Kxe8 sees the black king completing a round-trip. This terrific homebase proof game incorporates the Schnoebelen theme, in which a promoted piece is captured without making any moves. Such an occurrence always raises the question of why a specific promotion choice is required; that the motivation here is to provide Black with a tempo move gives the problem an extra spark.

Composer: This one is one of my personal favourites, but to my mind overshadowed by P1274528, which was technically much harder to compose.
Andy Sag: I needed a computer hint to solve this one. Each side can only have four non-capture moves and it is clear that White’s a-, b-, and c-pawns must be captured by the black queen. But who in their wildest imagination would see the h-pawn promoting to a knight on f8 to allow the black king to have a tempo move!


Leonid Makaronez
OzProblems.com 24 Jul. 2021

Mate in 3


The key 1.e6! threatens 2.e5+ Kxd5 3.Bxc4. Since that mate requires the rook on c6 to block that square, any move by that piece would defend. 1…Rd6 2.Qe3+ Ke5 3.Bc3 shows White exploiting the distant self-block on d6. 1…Rxe6 is answered by the threat-move but followed by a different mate: 2.e5+ Kxd5 3.Bf3, where the rook blocks another flight. The a4-bishop makes a third distant self-block with 1…Bc2 2.Be3+ Kc3 3.Qe5. If the same bishop guards c4 with 1…Bb5/Bb3, that prospectively closes the b-file and after 2.Kb2, Black can no longer give a discovered check; now the d2-bishop has two threats that are separated by 2…c3+ 3.Bxc3 and 2…Ba5 3.Be3.

Andy Sag: Leonid’s three-movers are usually hard to solve but this one is straightforward. The dual threat after 1…Bb5/Bb3 2.Kb2 is a minor blemish. The f6-pawn is purely there to stop 3.Qf6 in the 1…Bc2 variation. The g3-pawn appears to have no purpose.
George Meldrum: The true task is cleverly buried with the placement of the white pawns and for a long time I was looking for mates along the black squares. The involvement of the white king in the solution is brilliant. A superb problem.


Hilding Fröberg
Vart Hem 1939, 1st Prize

Mate in 2


A fine sacrificial key 1.Qc3! guards e5 to threaten 2.Scxd8. Taking the offered key-piece with the bishop or the queen leads to different promotion-captures on d8: 1…Bxc3 2.cxd8=S and 1…Qxc3 (or 1…Qd4/Qf7/Qxg7) 2.exd8=S. Capturing with the black rook opens a line for the white bishop to d6 and activates the b7-knight: 1…Rxc3 (or 1…Rxc6) 2.Sbxd8. If 1…Sxc6, that self-pins the defending knight and allows another promotion mate on the same square, 2.d8=S. Thus five knight mates occur on d8 (including the threat), the maximum possible. This impressive task problem is capped off by 1…Sf7/Bf7 2.exf8=S, yet another knight-promotion mate.

Andy Sag: The sacrificial key unpins the f5-rook, threatens a double-check mate and unleashes a variety of knight mates from d8 and f8 including promotions.
Karel Hursky: Wonderful geometrical key on the intersection square of pathways of a5-bishop, c5-rook, f6-queen and h3-queen. However, I didn’t find it easily because of a scrummage of pawns and pieces around the kings.
Nigel Nettheim: A magnificent key and four different knight-promotion mates. Somehow there is a good mixture of simplicity and complexity. The self-pinning 1…Sxc6 2.d8=S is excellent.
Andrew Buchanan: Five knight mates on d8 – and a bonus one on f8! All carefully delineated. Good key, with a couple of tries 1.Qh2/Qg3? Rf4! Very entertaining!
George Meldrum: A gem, and funny too.
Ian Shanahan: After a spectacular sacrificial key, one savours an extravaganza of knight-mates – two by pre-existing knights (including the threat), and four via distinct pawn-promotions. An astonishing task, and an unforgettable problem!


Vladimír Kočí
Pat a Mat 2012, 1st Prize


If the black king remains on its original square, each of White’s minor pieces has a potential mating move that would cover the g5-flight. In two solutions, Black prepares for these final moves by self-blocking on the other flight-square g6, using a promoted piece that won’t disrupt the mate. 1.a5 2.axb4 3.bxc3 4.c2 5.c1=R 6.Rg1 7.Rg6 Sf7 and 1.exd6 2.d5 3.d4 4.dxc3 5.cxb2 6.b1=B 7.Bg6 Bd2. Since the white knight and bishop exchange their roles of giving mate and getting captured, the problem illustrates the Zilahi theme (an idea usually seen in helpmates). A contrasting third solution involves a trip by the black king and here both thematic white pieces take part in the mating net: 1.Kg5 2.Kf4 3.Kxe5 4.Kd5 5.Kc6 6.Kc7 7.Kd8 Ba5. All three phases end nicely with a model mate.

Andy Sag: In each case, one black unit makes all seven moves and check avoidance ensures all sequences are unique.
Jacob Hoover: We have a double Excelsior and the Zilahi theme.
Andrew Buchanan: Well the third solution was a lot harder to find than the first two! It's a nice problem to solve to test lateral thinking.
George Meldrum: The two solutions involving pawn moves provided a perfect pair. The king tour was so left field from the other solutions that it made it difficult to see. Whilst I like this deception, I wonder, was this the purposeful intent of the composer?
Nigel Nettheim: The promotion solutions make a fine pair. The other solution is non-thematic, and in my opinion detracts from the effect.
Karel Hursky: The black king’s march to d8 is a bit of a surprise. Why is there a knight on g7 and not a black pawn I couldn’t see. Entertaining problem; it was a pleasure solving it.
Ian Shanahan: It's astonishing that there are three accurate sequences of exactly the same length, the last of which – a king-trek – took me ages to discover, being so very different to the first two solutions that are related by the Excelsior motif (i.e., a pawn begins from its home-square and marches onwards to promote).


Slobodan Mladenović
The Problemist 1987, 3rd Prize


Black has only three legal moves, all with white replies provided. In 1…Qxh5 2.Qg6+ Qxg6 and 1…Qxg5 2.Qe7+ Qxe7 (not 2.Qg6+? Qf6+), the black queen is deflected to give a mate that covers the d6-flight. If 1…Qxf4, the discovered check 2.Kd6+ compels 2…Qxe5. White has no waiting move that could preserve the set play, however, e.g. 1.Qg7? Qxf4! and 2.Kd6+ doesn’t work because the white queen is guarding e5. The key 1.d6! (waiting) blocks the initial flight but creates another one on d5. Now White must induce the black queen to mate on a diagonal line that covers the new flight. 1…Qxh5 2.Qf7+ Qxf7 and 1…Qxg5 Qg8+ Qxg8. After 1…Qxf4, the altered discovered check 2.Kd5+ Qxe5 means the white king gets mated on a different square. Three neat changes are brought about in this selfmate mutate.

Andy Sag: White must find a key that replaces the set play with changed play.
Jacob Hoover: A clever mutate.
Nigel Nettheim: Marvellous change-play.
Andrew Buchanan: A beautiful problem and very satisfying to solve.
Michael McDowell: Not difficult to solve, as having seen the set play the key is the only way to involve the pawns on the b-file, but changes after all three moves is quite an achievement. Given the rich content the ugly knight at g1 can be tolerated.
Ian Shanahan: A complex selfmate mutate (after a quiet key, all continuations are changed) in a tight and rather heavy setting. Very satisfying.
Thomas Thannheiser: Very nice selfmate this week. Truly worthy of a prize!


James Malcom
OzProblems.com 21 Aug. 2021

Mate in 8


To pre-empt the strong defence 1…Bf2+, White starts with 1.0-0-0!, pinning the bishop. Now Black’s pawns have four successive moves before they all become immobilised, and White must use the available time to prepare against the impending stalemate. The plan is to execute an Indian manoeuvre by bringing the rook back across the critical square c1, which the bishop can then occupy to cause an interference that would release the pinned black piece. This scheme requires the white king to make a Bristol clearance along the rank to give the rook access to another critical square, b1. 1…a5 2.Kb1 f6 3.Ka1 g4 4.Rb1 g3 5.Bc1 Bf2 6.Bd2+ (6.Bxe3+? Bg1 7.Bc1 Bf2!) Bg1 (6…Be1 7.Rxe1) 7.Be1 Bf2 8.Bxf2. The thematic clearances are followed by a four-move zigzag of the white bishop.

Composer: A demented Indian + Bristol combo!
Andy Sag: Queen-side castling is clearly necessary but what next? I spent a long time messing with the idea of a battery on the long white diagonal but to no avail. A battery is required but on the first rank after a Bristol style manoeuvre by king and rook.
George Meldrum: Love the setting, love the position, love the layout! There are enough alternate ways to try and solve this that makes it tricky with a fine solution.
Bob Meadley: A classic I reckon. Who would believe the white king ends on a1?


Sergey Rumyantsev
Mat 1989, 3rd Prize

Helpmate in 5, Set play


The interlocked units on the queen-side have to be untangled to allow at least one to aid in the mate. Since a freed white king would still be too far away to be useful, the aim is to release the black rook which can quickly obstruct a flight-square. The set play is 1…Rh2 2.Sg7 Rxb2 3.Kh8 Rxb3 4.Rh2 Rf3 5.Rh7 Rf8. When Black begins, the set play cannot be retained, e.g. 1.Kg7? Rh2 and the king prevents 2.Sg7. Instead, the black rook is unblocked on the a-file and that entails a different mating arrangement. 1.Sg7 Ra5 2.Kh7! Rxa3 3.Kh8 Rxb3 4.Ra8 Rb6 5.Rg8 Rh6. The black king makes an unexpected tempo move, and the two parts yield a pair of reflected echo mates. The black bishop is needed in the diagram to stop an alternative line, 1.Sg7 Rb5 2.Kh8 Rxb3 3.Ra1+ Kc2 4.Rh1 Rf3 5.Rh7 Rf8.

Andy Sag: In the main play, the black king must do a tempo move to allow White to unobstruct the black rook. In the set play, the tempo move is unnecessary and the mate is on the eighth rank instead of the h-file but conceptually the same configuration.
Jacob Hoover: Both mates are models. The presence of the black bishop totally threw me off. When I realized that it doesn't actually participate in either mate, the problem got a great deal easier to solve.
George Meldrum: Nice symmetry between solution and set play.
Nigel Nettheim: A very nice matching pair. The focussing on opposite corners is attractive. Not hard to solve because the black rook had to be freed as early as possible.


Comins Mansfield
Schach-Echo 1970

Mate in 2


Two prominent black checks in the diagram initiate the set play, 1…Qxc6+ 2.Rxc6 and 1…Bxg6+ 2.Rxg6, in which White employs the B + R battery. The thematic try 1.Se7? threatens 2.Bd3 by controlling d5, but since f4 is now solely guarded by the f6-rook, the set mates don’t work against the checking defences and are replaced by 1…Qxc6+ 2.Sxc6 and 1…Bxg6+ 2.Sxg6. The try is foiled by 1…c3! After the key 1.Sc3!, threatening 2.Bd3/Bd5, the set mates fail for the same reason. However, because the key-piece has cut off the b3-rook, White can utilise the R + B battery to deal with the black checks: 1…Qxc6+ 2.Bxc6 and 1…Bxg6+ 2.Bxg6. The three pairs of changed mates bring about the Zagoruiko theme, with the bonus feature that in each triplet of mates, different white pieces play to the same square. There’s by-play with 1…Rxc3 2.b8=Q and 1…Sf2/Sg5 2.f4.

Andy Sag: The key generates a double threat. The set checks are provided for by the diagonal battery but post key the vertical battery must be played instead.
Andrew Buchanan: The basic idea of two change mates between the two batteries is excellent, and the implementation is clean.
George Meldrum: Changed mates for Black’s checks are the main thing with the transition smooth and without a lot of distractions.
Nigel Nettheim: It’s surprising that the set discovered checks from h8 never materialise; they are replaced by those from e3 (thus file instead of diagonal play). The dual threat can hardly be called a weakness.


Enguelberto Berlingozzo &
Felix Sonnenfeld
Boletim da UBP 1981
J. Figueiredo Memorial Tourney, 1st Prize

Helpmate in 2, 3 solutions


A mate with the B + R battery is hindered by Black’s knight on d3 and three line-pieces converging on the same square. The knight needs two moves to unguard the diagonal and it uses them to simultaneously interfere with one of the line-pieces. White can shut off a second line-piece with the queen, and that leaves the third one to be handled by the rook when it fires the battery. 1.Se1 Qf5 (Qd4?) 2.Sc2 Rd4. 1.Sdxc5 Qd4 (Qc2?) 2.Se4 Rc2. 1.Sf4 Qc2 (Qf5?) 2.Sd5 Re4. An elaborate but clear demonstration of cyclic play, in which the three main actors (one black piece and two white ones) rotate their functions in closing three black lines. A white queen dual on the first move is avoided for disparate reasons.

Jacob Hoover: A curious cyclic shift is seen among the three solutions.
George Meldrum: Difficult to solve.
Andy Sag: White’s guard on the b4-pawn is maintained. The white king on f8 prevents a cook, 1.Sdxc5 Qf3 2.Se6 Qxc6. The black rook on a2 prevents a similar one, 1.Sxb4 Qc2 2.Sa6 Qxa4.
Nigel Nettheim: A great three-some. The d3-knight is the hero. Refuting the many temptations, including double-checks, was time-consuming.
Andrew Buchanan: Enjoyable with three thematic solutions and natural dual elimination.


Leonid Makaronez
OzProblems.com 18 Sep. 2021

Mate in 3


The key 1.e3! entails a sacrificial threat, 2.Rf5+ exf5 3.Qe7. The black bishop has three defences that are answered by different white queen checks. The self-block 1…Bxe4 enables 2.Qc3+ Kd5/Kd6 3.Rd7, 2…Sd4 3.Qxd4. A second self-block, 1…Bd5, gives 2.Qb8+ Kxe4 3.Qf4. And 1…Bc8 unguards the fifth rank to allow 2.Qc5+ Kxe4 3.Rf4. A good duel between the black bishop and white queen gives rise to a variety of mates, in a Meredith setting.

Andy Sag: The threat involves a second-move rook sacrifice to force Black to open the e-file. The set self-block on d5 is a clever touch.
Jacob Hoover: White response to each of three bishop defenses is different.
Nigel Nettheim: The key further surrounds the enemy king, although it does forfeit the two pawn-captures. But the variations are the highlight, and they resisted finding for some time.
George Meldrum: Beautiful.
Bob Meadley: A lovely light problem worthy of LM. The white king is close enough to tease.


Joost de Heer & Michel Caillaud
Probleemblad 2001


White is missing five units and since only six moves are available, all black moves except the first must have been captures. Given the five visible black pawn moves in the diagram, including the initial non-capturing one, four of these captures were made by the pawns. The main questions are thus how to quickly place four of the missing units in the paths of the black pawns, and how to eliminate the fifth white unit with Black’s remaining move. Only the missing black queen could have executed this capture, and time is saved if it removed the d2-pawn on its original square, on which the black piece could also be sacrificed to the b1-knight. 1.e4 d5 2.Bc4 dxe4 3.Be6 Qxd2+ 4.Sxd2 fxe6 5.Sdf3 exf3 6.Qd6 exd6. The try 1.e4 f5? 2.Bc4 fxe4 3.Be6 dxe6 4.?? opens the d-file too slowly for the black queen. The deceptive diagram position conceals the fact that Black’s original d-, e-, and f-pawns have cyclically switched their files.

Andy Sag: A unique solution involving capture of five white units, a black queen check and three black pawns ending up on different files.
Karel Hursky: I enjoyed this sparkling gem. A key to a quick solution is to realize how the pawns from d7 and e7 moved.
Jacob Hoover: We see three line-opening moves: (1) Black capturing on e4 to open the d-file; (2) the same move opens the c4-e6 line; and (3) the knight opening the d-file yet again later on.
Andrew Buchanan: Very tricky for a dozy Saturday morning!
George Meldrum: With five black pawn moves already on the table the last thing to choose is where the black queen moves to. At first d6 looked good, then d4, and at last d2, where the position finally played itself. Really weird and wonderful.


Udo Degener
Springaren 1988, 5th Prize

Mate in 2


The white king has four possible moves, any of which would threaten 2.Sg6. Since the threat-move interferes with the h7-bishop’s control of f5, Black can defend by cutting off (or removing) the a5-rook, anticipating its required guard on the same square when the fifth rank is opened. This type of defence is employed to defeat three of the white king’s moves. 1.Kf7? Rb5! (2.Rf8?), 1.Kh5? Qb5! (2.Sxd3??), and 1.Kh6? c5! (2.Qh6??). The key 1.Kg7! avoids the self-obstructions and the black queen's pin seen in the tries. 1…Rb5 2.Rf8, 1…Qb5 2.Sxd3, and 1…c5 2.Qh6. Also, 1…Bxa5 2.Rxd4. The subtle line-play involved – (1) White’s threat closes a white line of guard and (2) each of Black’s defences closes another white line to the same flight-square – is termed Theme A, one of the eight (A to H) lettered line themes.

Andy Sag: The vacation of g6 allows a knight to threaten mate relying on the a5-rook to guard f5. Four defences remove this guard but allow different mates. Incorrect king moves are tries.
George Meldrum: A strange setting with many pieces out of play. The variation involving the white queen is a gem.
Nigel Nettheim: Good tries and play – clear, if not specially deep.
Jacob Hoover: I’m kind of disappointed that there wasn’t a try that was defeated by 1…Bxa5, but I guess you can’t have everything, can you?
Andrew Buchanan: The bishop on h7 is very suspicious, and the equally suggestive empty space round the white king gives the necessary pointer. It’s a pity there is no try defended by 1…Bxa5. A good one!


Zdravko Maslar
feenschach 1986, 2nd Hon. Mention

Helpmate in 3, 2 solutions


In the first solution, the two sides arrange for the black king to be mated on c6 by the bishop along the long diagonal. 1.Bh3 Bh1 2.Bg2 Ra5+ 3.Kc6 Bxg2. Black’s initial move opens the diagonal for the white bishop, which traverses the line to cross over the critical square, g2. The black bishop then returns to g2, interfering with the white piece so that the black king could access the diagonal. After a rook check to guard the fifth rank, the king goes to c6 and the white bishop mates by capturing the piece on the interference square. The second solution shows analogous strategy aimed at mating the king on a6 with the white rook along the a-file. 1.Sb4 Ra1 2.Sa2 Bc6+ 3.Ka6 Rxa2. Now the black knight opens an orthogonal line on which the rook travels over the critical square, a2. A switchback by the knight to that square closes the same line and allows the black king to reach a6, after a bishop check that controls b5 besides b7. And the white rook mates by capturing the piece that caused the interference on a2. Terrific interplay between the white and black forces in this fine example of the Maslar theme, named after this composer.

Andy Sag: Well matched twin! In each case a black piece opens a line to allow the mating piece to do a critical move and then switches back to allow the black king to go into the mating line. The white king is cleverly placed to ensure only one square is available for the initial black move.