Weekly Problems 2012-A

Two set lines, 1…B~ 2.Se7 and 1…Qxb4 2.Sxb4, are curiously dropped by the key 1.Sd4!, which threatens 2.Be6. The unpinned black knight initiates the new thematic play, 1…Sxf4 2.Qa5 and 1…Sc5 2.Qc6. These variations, together with the self-blocking 1…Qxd4 2.Qb7, bring about three subtly differentiated queen mates. There is by-play with 1…e3 allowing 2.Bf3.

The splendid key 1.Sd3! (waiting) disrupts the R + S battery, grants a flight, and also enables the black queen to check. A new R + S battery fires directly with 1…Kxd4 2.Sxc5, and indirectly with 1…Qxf4+ 2.Sxf4 and 1…R~ 2.Sb4 when the white rook recovers the d4-flight. 1…S~random leads to 2.e4, while the correction 1…Se4 permits 2.fxe4. Also, 1…Q-else 2.Qxc5.

If the black queen were not on the board, two helpmates in one are possible: 1.Re5 fxe5 mate and 1.Bd5 c5 mate. Simply shifting the queen away to facilitate these mates would not work, however, because White has no waiting move available. Instead, the black queen’s first moves must be aimed at providing White with a spare move. 1.Qxc4 bxc4 2.Re5 fxe5, and not 2.Bd5? here because the d5-bishop would have disabled the 2…c5 mate with a pin. Analogously, 1.Qxf4 gxf4 2.Bd5 c5, and not 2.Re5? here because the h2-bishop would have prevented 2…fxe5 mate. Tempo play with dual avoidance.

After the key 1.Sf7!, any move by either black knight would defend against the threat of 2.Sxe5. A random move by the d6-knight, 1…Sd~, opens the white queen’s line to c5 and allows 2.Rd4. Two correction moves by the knight stop this rook mate, but commit the error of closing a black defensive line: 1…Sb5 2.Qb4, and 1…Sf5 2.Qe6. Moving the e5-knight, 1…Se~, opens the white rook’s line to c5 and again permits 2.Rd4. This knight has three correction moves that prevent the rook mate, and two of them are also self-interferences: 1…Sf3 2.Qe2, and 1…Sc6 2.Rc5. The third correction is a self-block: 1…Sd3 2.Rc2. There’s by-play with 1…Qb5/Qb2 2.Sxd6, and 1…Rc5 2.Rd4. Remarkable for a strategically rich problem, the position is pleasantly open and nearly pawnless.

The key 1.Bf2! threatens 2.Qb1+ Kg2/Kh2 3.Qg1. The thematic defences, 1…e4 and 1..g6, impede the white queen but also render 2…b1=Q ineffective for controlling the white queen. This weakness allows White to activate the half-battery on the h-file. 1…e4 2.S5f4 (threats: 3.Sg5/Sg1) Qe5/Qd8 3.Sg5, or 2…Qxf4+ 3.Sxf4. Not 2.S3f4? because of 2…Qe5! 1…g6 2.S3f4 (threats: 3.Sg7/Sf6) d6 3.Sg7, or 2…Qd8 3.Sf6, or 2…exf4 3.Sxf4, or 2…gxh5 3.Qxh5. Not 2.S5f4? because of 2…d6! Also, 1…S~ 2.Qe4+ Kh2 3.Bg1, and 1…Kg2/Kh2 does not stop the threat, 2.Qb1 and 3.Qg1. Very subtly determined choice between 2.S5f4 and 2.S3f4 in the main variations.

The many white tries include 1.Reb3? Ba3!, 1.Rbb3? Kxa1!, and 1.Rb4? Bxe3! The waiting key 1.Rb6! closes the e3-a7 diagonal in anticipation of 1…Bxe3 2.Qa8. 1…Bd2 permits a dual, 2.Rb2 and 2.Qb1, but the remaining two bishop defences force these mates individually: 1…Bb2+ 2.Rxb2, and 1…Ba3 2.Qb1. When Black takes the flight provided by the key, White gives a model pin-mate: 1…Kxa1 2.Ra3.

Most of Black’s moves in the diagram have set mates arranged for them, and the key 1.Sh3! completes the block. 1…Bb7 2.Qxb7, 1…Bc6 2.Qxc6, 1…Bd5 2.Qd3, 1…Be~ 2.Qf5, 1…Bf4 2.Rxf4, 1…Sb~ 2.Sd2, 1…Sg~ 2.Rf4, 1…d3 2.Qxd3, 1…f5 2.Sg5, and 1…Kxf3 2.Qd3/Bxg2. A waiter with a flight-giving, sacrificial key, and plenty of variations; its only flaw is the dual after the king’s move.

Two obvious first moves, 1.Qxc6? and 1.b8=Q?, fail to 1…Bxe5! and 1…Qxb6! respectively, while a better try, 1.Qd8?, is refuted by 1…Qxb7! If the b7-pawn were missing, White could mate in two with 1.Qa7+, so White’s plan is to induce Black to remove this pawn. The key 1.Qg1! threatens 2.Qxg7. Since short mates result from the lines 1…S~ 2.Qg8 and 1…Bg6 2.Qxg6, the main defence is 1…Qg2. Now 2.Qc5, with the threats of 3.Qe7/Qc7, compels the capture 2…Qxb7. The switchback 3.Qg1 forces 3…Qg2 again, and now that the b7-pawn has been annihilated, White proceeds with 4.Qa7+ Qb7 5.Qxb7. Fine long-range, pendulum-like play by the two queens.

A prominent set variation, 1…Qb8+ 2.Ka4, is discarded by the key 1.Kc5! (threat: 2.Kb6), whereupon 1…Qb8/Qd8 enables 2.Kc6 instead. The thematic key also sees the white king walking into a black battery, which fires with 1…R~+ 2.Kxc4 and 1…Rxd5+ 2.Kxd5. So we have a nice mix of white and black battery play. There’s by-play with 1…Sf7 2.Rxe8 (1…Sg6 2.Rxe8/Qf6).

The key 1.Qf7! threatens 2.Qxd5. A random move by the d5-knight, 1…Sd~, allows 2.Qc4. The knight has three specific moves that disable not only the original threat, but the secondary threat of 2.Qc4 as well. These correction moves, however, entail the error of self-interference and provoke additional mates: 1…Sb6 2.Sxc5, 1…Se3 2.d3, and 1…Sf4 2.Qxf5. Also, 1…Se6 2.Qxe6, and 1…Rd3/Rg3 2.Qxf5. A clear-cut presentation of correction play.

Every possible black move has been provided with a set mate: 1…Sf~ 2.Sd5, 1…Sh~ 2.Rbf5, 1…e3 2.Be5, and 1…d6/d5 2.Se6. The excellent key 1.Se5! (waiting) gives the black king a capture-flight on g5, and generates plenty of changed play. 1…Sf~ 2.Rg4, 1…Sh~ 2.Rf5, 1…Sxg6 2.Sxg6, 1…e3 2.Sd3, 1…d6/d5 2.Se6, and 1…Kxg5 2.Be3. Three mates are changed and two added in this first-class mutate.

The somewhat obvious key 1.Bc6! immobilizes the c7-pawn, so that Black is restricted to shuffling the king between g1 and h1. Now White is free to organise a battery mate with the knight. After 1…Kh1 2.Se4, the g2-pawn is unpinned but 2…g1=Q+? allows 3.Sf2 mate. So 2…Kg1 3.Sg5 Kh1 4.Sh3 – White unpins another piece, but now with the g1-flight attacked Black is forced to open the battery line: 4…Bg1+ 5.Sf2.

From left to right, the four positions are solved by (a) 1.Kb5 Rb3+ 2.Ka6 Sc4 3.Ra7 Rb6, (b) 1.Kb5 Sd4+ 2.Ka4 Rc2 3.Rb4 Ra2, (c) 1.Kf7 Rxe7+ 2.Kg8 Sf6+ 3.Kh8 Rh7, and (d) 1.Kh7 Kh3 2.Kh6 Rg6+ 3.Kh5 Sf4. A curious set employing the same material four times to arrange different one-row asymmetry problems. The point is that despite the symmetrical positions, only one solution works in each case, by utilising the left or right board edge in some way.

In view of the unprovided check, 1…Rxh8+, and the out-of-play g1-bishop, the key 1.Bh2! (threat: 2.Rg7) is easy to find. But this is a task problem with the most number of black rook variations ever shown. 1…Rxh8+ 2.Rg8, 1…Rh6 2.Rg6, 1…Rh5 2.Rg5, 1…Rh4 2.Rg4, 1…Rxh3 2.Rxh3, 1…Rxa7 2.bxa7, 1…Rb7 2.Qd8, 1…Rc7 2.bxc7, 1…Rd7 2.Kxd7, 1…Re7+ 2.Kxe7, 1…Rf7 2.Kxf7, and 1…Rg7 forces the threat 2.Rxg7. Twelve black rook defences are answered by distinct white mates – a record achieved in an unusually light setting.

A great key 1.Qd6! offers two flights to the black king and makes no threat. When Black takes the flights, the d5-bishop becomes pinned (on different lines), leading to two nice pin-mates: 1…Kf5 2.e4, and 1…Kd4 2.Rc4. Moving the bishop lets those flights be re-guarded by White: 1…B~ 2.exf3. And three queen mates follow 1…Se~ 2.Qxd5, 1…Sf~ 2.Qe5, and 1…g4 2.Qf4.

The withdrawal 1.Ke1! is remarkably the only way to solve this in three moves. After 1…Ke4, 2.Qh5 forces 2…Kxe3 3.Qe5. A real problem key is followed by a second-move sacrifice, and then an economical mate – a combination that makes this mid-19th century work very quotable still.

A difficult miniature with many tries. 1.Rg8? threatens 2.Qe4+ Bg2 3.Qxg2, and if 1…Bg2 then 2.Sd3 (waiting) B~ 3.Sf2, or 2…Kg1 3.Qe1, but 1…Bd3! refutes. 1.Qh6? threatening 2.Qc6+ is similar, and it’s defeated only by 1…Bb5! 1.Qh7? has two threats, separated by 1…Bd3 2.Qb7+ and 1…Ba6 2.Qe4+; but now 1…Bg2! works because after 2.Sd3 Kg1, the knight prevents 3.Qb1. The key 1.Qh8! (2.Qa8+) takes advantage of the fact that the black bishop cannot go beyond a6 to guard a8. 1…Bg2 2.Sd3 (waiting) B~ 3.Sf2, or 2…Kg1 3.Qa1. The queen visits three corners in the course of play.

Some problems make use of dual mates in a thematic way, and this is an example illustrating combinative separation. The flight-giving key 1.Bh5! has three threats: 2.Qg4, 2.Qf3, and 2.Qxe3. Black's defences separate or force these mating moves in every possible combination. 1...Rh1 permits all three mates to work: 2.Qg4, 2.Qf3, and 2.Qxe3. Three promotion defences allow different mating pairs: 1…g1=R 2.Qf3, 2.Qxe3; 1…g1=B 2.Qg4, 2.Qf3; 1…g1=S 2.Qxe3, 2.Qg4. Lastly, each queen mate is forced individually with 1…g1=Q 2.Qf3, 1…Kg3 2.Qg4, and 1…Ke4 2.Qxe3. A black AUW is shown, normally not possible in a two-mover.

Black has only two possible moves in the diagram, but the fine key 1.Sd4! (waiting) increases the mobility of that side to six moves. Two flights are created for the king: 1…Kxd4 2.Qd6, and 1…Ke5 2.Qxc5. The knight is also sacrificed to a pawn, 1…cxd4/c4 2.Rg5, while the freed f-pawn enables d4 to be guarded by a white rook: 1…f3 2.Qxe6. Lastly, 1…e5 permits 2.Qd8.

The key 1.Qf7! threatens 2.Sc4 and 3.Sd6. White has two self-pinning moves, 2.Sxe4 (3.Qxf6) Rxe3! and 2.Rxe4 (3.Se7) Rxe4!, that are unplayable until the black rook has been diverted. After 1…Rc1 and 1…Rb1, White must pick the correct capture on e4 in anticipation of new defences by the rook. 1…Rc1 2.Sxe4! Rc6 – stopping 3.Qxf6 but unpinning the knight – 3.Sxg3. Or 2…Bxe4+ 3.Bxe4, and 2…Sd7 3.Qxd7. Not 2.Rxe4? because of 2…Rc7! 1…Rb1 2.Rxe4! Rb7 – stopping 3.Se7 but unpinning the rook – 3.Rxe5. Or 2…Bxe4+ 3.Bxe4, and 2…Sc6 3.Qd7. Not 2.Sxe4? because of 2…Rb6! Lovely dual avoidance strategy.

The diagram is a block position, with every black move having a set mate: 1…S~/Sc2+ 2.S1c2/S1xc2, 1…Sxd3 2.Qxd3, 1…g3 2.Sf3, and 1…fxe1=Q 2.Qf4. With no waiting move available, however, White plays 1.Qh1! with the threat of 2.Qe4. Two changed mates follow with 1…Sc2+ 2.S3xc2, and 1…Sxd3 2.S1c2, while 1…g3 2.Sf3 is as set.

The long-range key 1.Ba7! (waiting) prepares for a self-interference on b6, in anticipation of 1…h3 when stalemate is threatened. Now 2.Rb6 releases the black king and leads to two battery mates: 2…Kd4 3.Rxd6, and 2…Kc5 3.Se6. After 1…hxg3, White ambushes behind the black pawn: 2.Rh3 g2/gxh2 3.Rd3.

The diagram is reached after 1.g3 b6 2.Bg2 Bb7 3.Bh3 Bxh1 4.Bf1 Bd5 5.h3 Bb3 6.cxb3 h6 7.Qc2 Rh7 8.Qxh7 Qc8 9.Qg6 fxg6 10.Kd1 Kf7 11.Kc2 Qe8 12.Kd3 Qd8 13.Ke3. White’s bishop and Black’s queen each executes a 3-move round-trip to lose a tempo. One of the first SPGs to show such a doubling of the theme.

The fabulous key 1.Qg6! (threat: 2.Rxf4) unpins the black queen and concedes a flight, enabling Black to check three times: 1…Kf3+ 2.Rd4 (pin-mate), 1…Qxd2+ 2.Rxd2, and 1…Qxd6+ 2.Rxd6. The black queen forces two more variations with 1…Qe3 2.Rxf6 and 1…Qxf5 2.Qxf5. The by-play 1…Sxd2 2.Rxd2 repeats a white mate. Another fine battery play problem typical of its composer.

Black’s e7-rook and f3-bishop interfere with each other in the set play, 1…Re4 2.Qd5 and 1…Be4 2.Se2. After the key 1.Sd3!, which threatens 2.Qc5, White exploits the Grimshaw interference differently: 1…Re4 2.Qd7 and 1…Be4 2.Be3. A good number of secondary variations occur in this light, Meredith position: 1…Ra5/Rc4 2.Qc4, 1…Re5 2.Qxe5, 1…Rg7+ 2.Bxg7, and 1…Rc7 2.Qe5/Be3.

White mates are set for all of Black’s moves in the diagram, except for 1…Kh4. A nice to-the-corner key, 1.Rh8! (waiting), provides for that move by arranging a battery on the h-file: 1…Kh4 2.Kxg6. Two other diagonal flights lead to 1…Kf6 2.Bd8 and the pin-mate 1…Kf4 2.Qe3. Most of the black knight’s moves result in a dual, unfortunately – 1…S~ 2.Bd8/Sf3, with only 1…Sxb6 2.Sf3 and 1…Sxe5/Sd2 2.Bd8 forcing unique mates.