Weekly Problems 2013-B

The terrific key, 1.Sd5!, concedes two flights, enables Black to check, and also unpins the c4-bishop. A wealth of battery play follows, including the threat of 2.Sd8. 1…Q/Bxd4+ 2.Sxd4, 1…Kd6 2.Sxa5, 1…Kd7 2.Se5, 1…Bxb5 2.Sxc7, 1…Bxf4 2.Sxf4. The two white knights act as the front pieces of four different batteries, and participate in five double-checks (the threat included). The by-play sees the white queen regaining control of the two flights while giving mate: 1…Bxd5 2.Qxd5 and 1…Sxc6 2.Qxc6.

After the key 1.Bf6!, White threatens 2.Re5. Since the threat cuts off the white bishop’s control of d4, any move by the d4-knight would defend by creating a potential flight. Each knight move induces a distinct white mate, to produce the maximum possible eight variations. 1…Se2 2.Re3, 1…Sc2 2.d3, 1…Sb3 2.Qxb1, 1…Sb5 2.Qxa8, 1…Sc6 2.Qd5, 1…Sxe6 2.Qxe6, 1…Sf5 2.R5g4, 1…Sf3 2.R3g4. In this accomplished demonstration of the knight-wheel theme, the knight causes five self-interferences, two self-blocks, and one square-clearance.

Set play is provided for three captures on e5: 1…Kxe5 2.Qxc3, 1…Rxe5 2.Qa4, and 1…Sxe5 2.Qg1. The thematic try 1.Bc7? attacks e5 to threaten both 2.Qa4 and 2.Qg1, and while 1…Sxe5 compels 2.Qg1, 1…Rxe5! now refutes because the try has left c5 unprotected. Similarly, 1.Sf7? entails the double queen threats, and 1…Rxe5 forces 2.Qa4, but now 1…Sxe5! is spoiling as the try has unguarded e4. The key 1.Rf3! (threat: 2.Rd5) preserves the set play, 1…Kxe5 2.Qxc3, 1…Rxe5 2.Qa4, and 1…Sxe5 2.Qg1. There’s by-play with 1…Bxf3 2.Sxf3 and 1…Rd8/Se7 2.Re4. An elegant presentation of multiple defences on the same square infused with paradoxical elements.

An imminent stalemate occurring after 1…f6 has to be dealt with. By playing 1.Rh8! White takes the rook across the critical square g8, with the plan of placing another piece on that square to cause a self-interference. Thus after 1…f6, 2.Bg8 releases the stalemate. The bishop move has formed a battery, which the black king must walk into due to zugzwang: 2…Ke8/Kd8 3.Be6. The famous Indian theme is rendered in a neat miniature setting.

The black king has three flight-taking moves, of which the one to b6 has no set mate. The try 1.Rb8? provides for it with 1…Kb6 2.Ba8, but now there’s no answer to 1…Kc4! The key 1.Ba8! (waiting) enables 1…Kb6 2.Rb8 while retaining the set play, 1…Kc4 2.Sd4 and 1…Ka4 2.Sc7. This light problem illustrates the Y-flights theme, in which three king moves form a Y-pattern and yield different white mates.

Set mates are prepared against all black moves except for 1…Qxh7. The delightful key 1.Reg6! (waiting) dramatically increases the mobility of the black queen by unpinning it. A random queen-move, 1…Q~, permits 2.R6g3. Five correction moves by the queen foil 2.R6g3 but elicit new mates: 1…Qxg2+ 2.Rxg2, 1…Qg4+ 2.R6xg4, 1…Qe6+ 2.Rxe6, 1…Qf5+ 2.Qxf5 (changed from 2.Bxf5), and 1…Qxg6 2.Bxg6. The remaining play is as set: 1…Bc2 2.Qxc2, 1…Sa~ 2.Qc3, 1…Sf~ 2.Rd2, and 1…b4 2.Qxa6.

The key 1.Rg5! threatens 2.Qg7. The two black knights are half-pinned by the white bishop, so that each is liable to be fully pinned when the other moves to stop the threat. White exploits the resulting pin in three of the five knight variations: 1…Sbd7 2.Rg4, 1…Sc4 2.Sb3, 1…Sxd5 2.Rxd5, 1…Sc~ 2.Qb4, and 1…Sd3 2.Re4. Lastly, 1…Qxf3 allows 2.Sxf3.

The sweeping key 1.Qa3! with the threat of 2.Qa8 is difficult to find, not least because it involves a triple-sacrifice of the queen. Three black pieces are diverted from their defensive positions: 1…Bxa3 2.Sf6, 1…Sxa3 (or 1…Sb~) 2.Sc7, and 1…Qxa3 2.c4. Other black queen defences enable a different mate: 1…Qxe4/Qa4 2.Qxc5 (1…Qa5 produces a dual, 2.c4/Qxc5).

The aggressive key 1.Qe6! removes an unprovided flight on e7, and entails a short threat of 2.Sc6 mate. On the positive side, the white queen allows itself to be taken with check: 1…Qxe6+ 2.Sc6+ Kc8 3.Rd8. Two other defences by the black queen are answered with its capture by the white rook: 1…Qxd4+ 2.Rxd4+ Sd6 3.Rxd6 and 1…Qg1 2.Rxg1 S~ 3.Sc6. A pawnless miniature in which, oddly enough, the white queen never moves again after the key!

The thematic try 1.Qh1? threatens 2.Qd1, and 1…Rf1/Rf2 permits 2.Qxe4, but 1…e2! refutes. The key 1.Qg4! threatens 2.Qxe4 instead, and now 1…Rf4 is answered by 2.Qd1. The threat and mating move in the try play (2.Qd1 and 2.Qxe4) are reversed in the actual play (2.Qxe4 and 2.Qd1) following different defences – such a relationship between the two phases is known as the pseudo le Grand theme. The black knight sets off three variations: 1…Sf4 2.Qg7, 1…Sg5 2.Qd7, and 1…Sc5 2.Bc3. Two additional tries are 1.Qg1? (2.Qd1) Rf1 2.Qxe3, but 1…Rf2! and 1.Qe2? (2.Qd1) Rf1/Rf2 2.Qxe3, but 1…Sf4!

If the c2-knight could be eliminated, Black would be forced by zugzwang to unguard f7 and allow a knight mate. Accordingly White aims to trap and capture the black piece, starting with 1.Sa1!, which by attacking c2 takes care of the black knight’s return to that square in most variations. 1…Sb4 2.Bc4 Sa6 3.Bxa6 S~ 4.Sf7, 2…Sc6 3.dxc6, 2…Sxd5 3.Bxd5, 2…Sd3 3.Bxd3, 2…Sc2 3.Sxc2, 2…Sa2 3.Bxa2. 1…Sd4 2.Bd3 Sb3 3.Sxb3, 2…Sb5 3.Bxb5, 2…Sc6 3.dxc6, 2…Se6 3.dxe6, 2…Sf5 3.Bxf5, 2…Sxf3 3.gxf3, 2…Se2 3.Bxe2, 2…Sc2 3.S/Bxc2. 1…Sa3 2.Bd3 Sb5 3.Bxb5, 2…Sc4 3.Bxc4, 2…Sc2 3.S/Bxc2, 2…Sb1 3.Bxb1. 1…Se1 2.Bf1 Sxg2 3.Bxg2, 2…Sxf3 3.gxf3, 2…Sd3 3.Bxd3, 2…Sc2 3.Sxc2. 1…Sxa1 2.Ba4 Sb3 3.Bxb3, 2…Sc2 3.Bxc2. 1…Se3 2.dxe3 fxe3 3.Be2. The multiple captures of a black piece shown in such a variety of ways constitute the Grab theme.

Every possible black move in the diagram has been provided with a set mate. The key 1.Rf3! (waiting) preserves all of the set play but adds a variation by sacrificing the rook to the e4-pawn. 1…exf3 2.Kd3, 1…e2 2.Kd2, 1…Qxc2+ 2.Kxc2, 1…Qb3+ 2.Kxb3, 1…Qb4+ 2.Kxb4, 1…Qxc4+ 2.Kxc4 – six white king battery mates are individually forced. 1…Qb5/Qxe8 2.Qd4, 1…Qd7 2.Sxd7, 1…Qc6 2.Kb3/Kb4, 1…Rb5 2.Sd7, 1…Rc5 2.Qxc5, 1…Rd5 2.Qxd5, 1…Sa~ 2.Qc7, 1…Sg~ 2.Qe6 (1…Sxf5 2.Qe6/Rxf5), 1…h6/h5 2.Sg6.

The two solutions are 1.Bd1 Rc7 2.Sf6 Rg7 and 1.Be1 Rc6 2.Sg6 Bf6. In each case, Black’s initial bishop move not only unpins the c1-rook but also unblocks a flight-square. The white rook must choose its first move with care to prepare for a mate that will recover the flight. Then one of the two half-pinned black knights moves so as to self-pin the other and enable a pin-mate. Simultaneously, that knight self-blocks a square in anticipation of the mating move – a white self-interference that unguards a flight. Thus we also see a sort of white Grimshaw interference between the c1-rook and h8-bishop (though they intersect on different squares, g7 and f6).

After the key 1.Rd5!, the pinned white queen threatens to mate by moving along the pin-line: 2.Qc6. 1…Bc3 cuts off the d3-rook’s control of a3 and b3, but the defence has also unpinned the queen, enabling 2.Qxa2. 1…Bc5 is similar and by shutting off the d5-rook it forces 2.Qa6 instead. A third thematic variation, 1…Sc3 2.Qxb4, sees the white queen unpinned by interposition once more. There’s one line of by-play in this nicely constructed Meredith: 1…Re6 2.Bxc2.

The black king has access to two flights, providing for which turns out to be impossible for White. So the key must aggressively eliminate them, but 1.h8=Q? with the threat of 2.Qf6 and 3.Qxf4 fails to 1…c5!, when stalemate looms. Instead the key is 1.h8=B! (waiting), and if 1…c5 then White exploits Black’s lack of mobility with 2.Bf6 Kf5 3.Bd3. The other two pawn defences bring about a nice change of promotion by the e7-pawn: 1…c6 2.e8=Q c5 3.Qa8 and 1…cxd6 2.e8=S d5 3.Sd6.

The brilliant key 1.Se4! (threat: 2.Re8) sacrifices the knight to eight black pieces, with each ensuing capture leading to a different mate. 1…Kxe4 2.Re8, 1…Qxe4 2.Qh8, 1…Rxe4 Qxf5, 1…Bxe4 2.d4, 1…Scxe4 2.Rxd5, 1…Sfxe4 2.Sxd3, 1…dxe4 2.Bd4, and 1…fxe4 2.Qe6. The eight-fold sacrifice of the key-piece constitutes a record, and it is achieved in an attractive setting with ideal black economy – every black piece on the board takes part in the thematic play. Another two-mover manages to show nine sacrifices of the key-piece but it requires the first move to be a check.

Only one black move in the diagram, 1…Rb4, has not been given a set mate, and the key 1.Bb5! (waiting) completes the block by providing for it. A Grimshaw interference occurs on b4: 1…Rb4 2.c6 and 1…Bb4 2.Rc4. These two defences are actually correction moves that prevent the mates following the ‘random’ move of each black piece, 1…Ra~ 2.Rc4 and 1…Ba~ 2.c6. Another correction move is 1…Bxc5+, enabling 2.Qxc5. A second Grimshaw takes place on g6: 1…Rg6 2.Sf5 and 1…Bg6 2.Sh7, though here only the bishop has a random defence, 1…Bh~ 2.Sf5. The other rook move, 1…Rxf6+, allows 2.Bxf6. Also, 1…S~ 2.Rd2, and 1…e3 2.Sf3.

A nondescript key 1.Rc2! waits for Black to play the only legal move, 1…c4, whereupon the rook makes a surprising sidestep 2.Rb2 to grant a flight. Two sub-variations follow with 2…Kc3 3.Bg7 and 2…c3 3.Rb4. A pleasant miniature even if the amount of play is limited.

The game blends two paradoxical themes: black pseudo-castling that’s motivated by tempo loss, and a white queen Pronkin. 1.a4 h5 2.a5 h4 3.Ra4 h3 4.Rh4 Sh6 5.e4 Sf5 6.Qf3 Sd6 7.Qf6 gxf6 8.Se2 Bh6 9.Sec3 Be3 10.f4 Bb6 11.axb6 Kf8! 12.bxc7 Kg7 13.cxd8=Q Rf8 14.Qa5 Kg8 15.Qh5 Sb5 16.Qd1. Black avoids castling at move 11 because afterwards neither the king nor the rook would be able to lose a tempo, e.g. 11…0-0? 12.bxc7 Kg7 13.cxd8=Q Kg8 14.Qa5 Kg7 15.Qh5 Kg8 16.Qd1 Sb5 – a single move too long. The Pronkin theme is shown in that the white queen, seemingly on its original square, is in fact a substitute promoted piece.

Three set variations cover every possible black move in the diagram: 1…Sd~ 2.Bb2, 1…Se~ 2.Qc2, and 1…c3 2.Sb3. Simple waiting moves would fail, e.g. 1.Kh1? Sf2+!, and 1.Qg6? Sf5! The nice withdrawal key 1.Qb7! (waiting) shifts the direction from which the queen controls b1, resulting in a complete change of play: 1…Sd~ 2.Qb2, 1…Se~ 2.Rc2, and 1…c3 2.Sd3. Another gem of a mutate.

A good sacrificial key 1.Sxe6! threatens 2.Sxc7+ Rxc7 3.Re5. Six thematic variations follow, each one utilising the b3-bishop and c4-knight to arrange a Siers battery. In this manoeuvre, White moves the front piece of the battery (the knight) to give a discovered check, and forces the black king to a flight-square (e5), after which the front piece moves again to mate from another direction. 1…Bxe6 2.Se3+ Ke5 3.Sg4, 1…Rxe6 (or 1…Rxb5) 2.Sa5+ Ke5 3.Sc6, and 1…Qxe6 2.Sd6+ Ke5 3.Sf7 – these lines are especially interesting in that White exploits Black’s self-pins on the e-file. 1…Sxe6/Sfg6 2.Sxb6+ Ke5 3.Sxd7, 1…Rxe7 2.Sb2+ Ke5 3.Sd3, and 1…Sf3/Shg6 2.Sd2+ Ke5 3.Sf3. “Outstanding,” said the late great William Whyatt who judged the tourney.

The key 1.Be1! threatens 2.Bf2. Black has four defences that unpin the white queen, and the resulting queen mates are skilfully differentiated: 1…Sc6 2.Qc4, 1…Sd5 2.Qd4, 1…Rd5 2.Qb4, and 1…f3 2.Qxe7. There’s by-play with 1…axb5 2.Bb4, 1…Bxe4+ 2.Sxe4, and 1…Se6 2.Sd7. This problem makes an interesting comparison with No.150, which shows the white queen unpinned on an orthogonal line. Heydon’s position here is heavier but presents a more impressive seven variations.

White begins with 1.Bg1!, shifting the bishop across f2 to prepare for a self-interference on that square. If Black aims for stalemate immediately with 1…h5, then 2.Sf2 Kc5 3.Se4+ Kxd5 4.Sxc3, or 3…Kb4 4.Bc5. If Black plays 1…h6 instead, White has time for another critical move, 2.Ra8, crossing over a7. Now 2…h5 is answered by 3.Ba7 – a self-interfering move that’s also a switchback – Ka5/Ka4/Ka3 4.Bc5.

Since 1.Rb5+? permits 1…Kc4!, the white bishop attempts various anti-critical moves that cross over b5 and thus avoid the self-interference. Three such tries threatening 2.Rb5 are defeated, however, when the bishop closes a line needed by the white queen: 1.Bd3? 1…Ra5 2.Qxg1, 1…Rb6 2.Qxh5, but 1…Qe8! 1.Be2? 1…Qe8 2.Qd5, 1…Ra5 2.Qxg1, but 1…Rb6! 1.Bf1? 1…Rb6 2.Qxh5, 1…Qe8 2.Qd5, but 1…Ra5! (Also, 1…c6 2.Sb7 after each try.) The key 1.Bb5! surprisingly creates a new threat of 2.Sb7, and following similar black defences the queen is able to mate unhindered: 1…Ra7 2.Qxg1, 1…Rb6 2.Qxh5, and 1…Qd5 2.Qxd5.

In the diagram position, if the black king had moved last, it did not come from e7 or f7, since on either square the piece would have been in an impossible double-check. If the king just came from f6, it would have been in check from both the a1-bishop and f4-rook, and that’s possible only if the king had captured a pawn on e6, which had delivered the double-check with an en passant capture. So let’s retract 1…Kf6xPe6 2.f5xe6 e.p.+ e7-e5, leading to a position where the king on f6 is in check from the a1-bishop. White could have given this check only by discovery, using the white king. But if we further retract 3.Kd4-e4+, the white king would have been in an impossible check from the e3-bishop, since there’s no square from which the black piece could have played from. Given that no more legal retractions are possible, we have proved that the black king couldn’t have moved last in the diagram. In position (b) without the f2-pawn, however, the same sequence of retractions – 1…Kf6xPe6 2.f5xe6 e.p.+ e7-e5 3.Kd4-e4+ – becomes viable, because now the black bishop could have checked by capturing on e3 from f2 or g1. Thus the black king could have played last in (b).

Most of Black’s moves have been provided with set mates, including 1…Sa~ 2.Qc5 and 1…Sg~ 2.Qh2. The exception is 1…Sf4! which would defeat a simple waiting move, such as 1.Kb6? The try 1.Qc1? (waiting) changes one variation to 1…Sg~ 2.Qf4, but 1…Se3! refutes. The key 1.Qd2! (waiting) produces another change, 1…Sa~ 2.Qb4, with an added line, 1…Sc5+ 2.dxc5. A random move by the other knight now allows a dual, 1…Sg~ 2.Qh2/Qf4, but these mates are separated with 1…Se3 2.Qh2 and 1…Sf4 2.Qxf4. The black rook gives three dual-free variations: 1…Re6/Rf8 2.Re6, 1…Rf7+/Rxg6 2.Sf7, and 1…Rxf5 2.Sxf5.