Weekly Problems 2021-B
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…
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.
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!
OzProblems.com Jul. 24 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.