Problem World > No.21
Line Strategy by Peter Wong

Problem themes of the strategic variety are based on the concrete departure and arrival effects of moves. Such strategic ideas may be divided into two main types, those that involve the occupation of squares (the subject of the previous article), and those that focus on lines, as utilized by the three long-range pieces: queen, rook, and bishop. Line play in comparison offers a greater range of possible effects, and indeed it is a broad category encompassing many different concepts, such as the battery, line clearance and pins. But here we will limit our discussion to the primary ideas of line-opening and line-closing, and look at some directmates that elaborate on their use in striking ways.

121. Gustav Källgren
Tidskrift för Schack 1942
Mate in 2

Requiring only ten pieces, Problem 121 demonstrates intricate line strategy, and shows how a single move can entail multiple line-opening and -closing effects. White starts with 1.Re7! to threaten 2.Rd7. Any move of the black knight will foil the threat by unblocking the black bishop’s path to d5. However, a knight move will also clear the file for the white rook to attack e5 (a potential flight), so that after a ‘random’ placement, e.g. 1…Sd8, 2.Be3 is enabled. The knight can make a correction – stops this ‘secondary threat’ of 2.Be3 – by shutting off the white bishop. But in doing so, with 1…Sf4, the knight also interferes with the black rook, and so permits 2.Qe4. Hence, two lines are opened and two closed by this defence, producing a scheme known as four-way play. Another four-way move is 1…Sg5; again it shuts off the bishop and interferes with the rook, allowing 2.Bg7. (Also, 1…c4 2.Qe3, and 1…Rg5/Rg7/Re4 2.Qe4.)

122. Helmut Pruscha
Deutsche Schachzeitung 1959
1st Prize
Mate in 3

The three-mover 122 illustrates the Novotny, a theme closely related to the Grimshaw. In the diagram, Black’s rook and bishop are each guarding against a knight mate, and their lines of defence intersect on e6. If White places a piece on e6, both lines are shut off, so that the capture of this piece by either the rook or the bishop will still leave one mate undefended. Such a white sacrifice on the intersection of two defensive lines is called a Novotny, and here it appears as the threat after a fine key, 1.Rh7!, viz. 2.Qe6+ forcing 2…Rxe6 3.Sf4 or 2…Bxe6 3.Se8. The knight gives two attractive indirect battery mates. A typical way for Black to answer a Novotny threat is to play one of the line-pieces across the critical square, so 1…Re7 and if 2.Qe6+? Bxe6 stops both mates, but now 2.Sf5+ Bxf5 3.Qxe7. A similar defence by the bishop, 1…Bg4, sets off an even more thematic variation, when White replies with a different Novotny, 2.Se6. This move cuts off the two black pieces again but threatens new queen mates, which are separated by 2…Rxe6 3.Qd7 and 2…Bxe6 3.Qe7. Lastly, Black can take the flight given by the key, 1…Ke5 2.Se6+ Kd6 3.Qe7, or 2…Ke4 3.Sc5.

123. Herbert Ahues
Die Schwalbe 1987
1st Prize
Mate in 2

Problem 123’s play revolves around the closure of two white lines of guard, Qa4-d4 and Bh8-d4. The c5-knight begins with various tries that contain double-threats, but they are handled by Black because one of the threats entails a white self-interference, a weakness that will potentially leave d4 unguarded. The first try 1.Se4? threatens 2.Sc3 and 2.Sf6. Both knight mates are neutral­ised by 1…b4!: it covers c3 directly and also shuts off the white queen, so that 2.Sf6 – interfering with the bishop’s control of d4 – does not mate. An analogous try is 1.Sd3?, which threatens of 2.Sf4 and 2.Sb4. It is refuted by 1…e5!, which defends f4 and prevents the other knight mate by shutting off the bishop, since 2.Sb4 would close the queen’s line to d4. A third try 1.Sa6?, threatening 2.Sc7 and 2.Sb4, is similarly defeated by 1…f6!, which activates the black rook’s defence of c7, and again cuts off the bishop to stop 2.Sb4 indirectly. In the actual play, White’s key 1.Sd7! threatens another pair of mates, 2.Sb6 and 2.Sf6. Remarkably, Black parries them by using the same defensive strategy as that seen in the try play. 1…S5c4 covers b6 directly and shuts off the queen to disable 2.Sf6, forcing a new mate 2.Qa8. And 1…S3c4 thwarts both threats for the same reason, and leads to 2.Qxb5.

124. Herbert Ahues
Hans-Dieter Leiss Memorial Tourney 1996
3rd Prize
Mate in 2

A wealth of line effects, executed by both White and Black, occur in Problem 124. First note how Black is preventing two white mates in the diagram: Rxd4 is stopped by the black knight, and exd4 is stopped by the black queen. The thematic move 1…Sd2 seemingly would admit both mates, by unguarding d4 and interfering with the queen’s line. But in fact neither mate works, because the knight move has also opened two black lines, allowing the a2-bishop to pin the white rook, and the a3-rook to control e3. Now consider White’s play. After moving the f4-knight to open the f-file, White threatens 2.Qf3. A ‘random’ knight move, such as 1.Sh3? because it has no additional effects, is refuted by the thematic defence 1…Sd2! White attempts to improve on this try by picking a square for the knight that will close, in anticipation, a line that Black wants to open. So 1.Sd3? to block the third rank: 1…Sd2 2.exd4. However, 1.Sd3? also closes the c2-e4 diagonal, and consequently it is defeated by 1…Qxc2!, when 2.Bxc2 no longer mates. Another try, 1.Sfd5?, intercepts the pin line: 1…Sd2 2.Rxd4 – a changed mate. But the a8-e4 diagonal is also closed by this try, enabling Black to answer with 1…Ra8!, and White cannot mate with 2.Qxa8. Finally, 1.Se6! works by avoiding the self-interferences: 1…Sd2 2.Rxd4, 1…Qxc2 2.Bxc2, 1…Ra8 2.Qxa8, and 1…Rg3/Rxg2/Rf4 2.Qf4.

125. Nils van Dijk
Die Schwalbe 1961
Mate in 2

More complex line strategy is seen in Problem 125, which brilliantly combines the Novotny theme with white Grimshaws. Black’s thematic pieces are the d8-rook, h2-bishop, and g8-bishop, and initially they prevent the white mates Sd4, Sc7, and dxc4, respectively. By playing to the Novotny squares, d5 and d6, White will shut off two of the black pieces and threaten two mates. However, the white pieces available to do this – the two rooks and bishops – have important duties in controlling c5 and c6, and when they make the Novotny moves, they also interfere with one another’s guard of these potential flights. In three of the four cases, Black is able to take advantage of these white Grimshaws and hence defeats the white moves. The first try is 1.Rd6? (threats: 2.Sd4 and 2.Sc7), which stops the f8-bishop from attacking c5, and it is refuted by 1…Be5!, when Black guards d4 directly and shuts off the f5-rook (2.Sc7+ Kxc5). The second try, 1.Bd6? (2.Sd4 and 2.Sc7), interferes with the f6-rook’s control of c6, and fails to 1…Sf3!, which protects d4 and cuts off the h1-bishop (2.Sc7+ Kxc6). The third try, 1.Rd5? (2.Sd4 and 2.dxc4), disables the h1-bishop’s control of c6, and Black defeats it by 1…Se6!, guarding d4 and shutting off the f6-rook (2.dxc4+ Kxc6). The key is 1.Bd5! (2.Sd4 and 2.dxc4), which interferes with the f5-rook’s line to c5, but Black cannot exploit this with 1…Rd6 (to shut off the f8-bishop), because the a6-knight controls c5 and White’s threats remain effective. The two threats are separated by 1…Bxd5 2.Sd4 and 1.Rxd5 2.dxc4, while 1…g3 stops both and is answered by 2.Sc7.

126. Hendrik Prins
The Problemist 1984
Mate in 2

Have a go at solving Problem 126, which shows line play comparable to that in Problem 124, but achieves it in a marvellously light setting.

Problem 126 solution (To display, hold down your mouse button and select the text below.)

> White’s a6-knight makes two tries and the key, aiming to mate on c6 or b7. Each of the thematic replies, 1…e5 and 1…f2, opens a black line of defence but also closes another one, causing Black to lose control of a white bishop mate. 1.Sb4? (threat: 2.Sc6), 1…f2 2.Bb6, but 1…e5! refutes because White’s own self-interference has disabled 2.Bc3. 1.Sac5? (2.Sb7) is defeated by 1…f2!, when 2.Bb6 is obstructed. The key 1.Sab8! (2.Sc6) avoids closing any white bishop line: 1…e5 2.Bc3, and 1…f2 2.Bb6.