Chess Problems: Solutions and a bonus from Pal Benko
By David Friedgood
The last instalment of problems was presented here. Two had to be solved by our readers. Here now are the full solutions, plus the two enjoyable works submitted by Pal Benko as an addendum.
Milan Vukcevich, 2nd HM, Probleemblad, 1962
Mate in two
According to the hint I gave, there are four Novotnys, two on d6, and one each on e7 and e4. Let us try them in turn: 1.Rd6? threatening 2.cxb5# because the Bf8 can't interpose and 2.Nc6# because the Rg6 has been cut off from this square. But Black has the crafty answer 1...Be4! which gives the desperate king a bolt-hole on d3. This move interferes with the Re8, but 2. Qxe3+ is now not mate because 1.Rd6 has inadvertently cut off the Bb8 and left the e5 square unguarded!
A similar story occurs if we try 1.Bd6? with same two threats 2.cxb5/Nc6 as before. Now, as you'll have spotted, Black refutes the try with 1...Re4! , again creating a flight on d3, but this time taking advantage of the fact that White can't play 2.Rxd5#!
From earlier articles you will recognise the hallmark of the Grimshaw theme being played out here. [Definition of Grimshaw: Two line pieces - usually a B and a R - mutually interfere on the same square.] In this case we have a White Grimshaw on d6, executing a Novotny on that square, being refuted by a Black Grimshaw on e4!
We need to look at 1.Re7? which threatens 2.cxb5# and 2.Qxe3#. This is a non-thematic line and is refuted by 1...dxc4! creating a flight on d5 that White can't cope with. Thus by elimination we arrive at the Novotny that does solve the problem: 1.Be4! This threatens 2.Rxd5# and 2.Qxe3# and now the Novotnys and Grimshaws are turned around: 1...Bd6 2.Nc6# and 1...Rd6 2.cxb5#. Truly a fascinating piece of clockwork!
Milan Vukcevich, Schach-Echo, 1970
Mate in three
The hint here was that Ne5+ is a potential Novotny. If the rook captures the knight then 2.Qxd6 is mate, but we don't have a follow-up if the bishop captures. Doubtless it didn't take you long to find 1.Bd1 threatening 2.Ne5+ Rxe5 3.Qxd6#, or 2...Bxe5 3.Ba4#. Black can defend by avoiding the rook being shut off, while still keeping guard on a4 with 1...Rh4. However, all White has to do is to shift the axis of the Novotny with 2.Nf4! and there is no way to deal with the dual threat of 3.Ba4# and 3.Qxd6#. Similarly, 1...Bg1 avoids having the bishop shut off by 2.Ne5+ and protects d6 from the queen by pinning her. The pin gives a special flavour to the ensuing Novotny: 2.Nc5+! and again either 2.Qxd6# or 2.Ba4# will follow.
One point to note is that 1...Rb5, which looks like a valid defence to the Novotny threat – the rook moves to the other side of the e5 square, thus avoiding being shut off - in this instance fails to work, as after the threat 2.Ne5+ Bxe5 the white bishop equals the rook's agility with 3.Bg4# delivering mate also 'on the other side'!
Novotny by Pal Benko
A pleasing addition to this article is a contribution from GM Pal Benko, who noticed the interest in the Novotny and sent us a two-mover and a study which he had composed on this theme. Certainly the study is a classic and one which every aficionado of chess art should know perfectly.
Pal Benko, Füle, 1972 (2012 version)
Mate in two
1.c6? threatens 2.Nd6# and 2.Bd7# (the two Novotny threats of the problem). 1... Qxd4 is an inadequate defence, as 2.cxb7# follows, but White's move opens the line of the Ra5 which refutes the try by 1...Rd5!
1.Nc6? again threatens the original two Novotny mates and adds 2.Ne7# as a third threat. Black refutes this also with the clever 1...Qxe5! now that 2.Qxb7# is impossible. This stops 2.Nd6 directly as well as removing one protector of c7, so that 2.Ne7 fails to mate as the knight interferes with the other protector, the Rg7.
1.Bc6? threatens 4 mates, 2.Nd6 and three mates on the back rank by the queen and rooks. But Black's knight comes to the rescue with 1...Nf7!
White now brings up the heavy artillery with 1.Rc6? threatening the two Novotny mates plus three by the queen on the h3-c8 diagonal making a total of five mates in all! But now 1...Qxd4! stops them all, as again White’s queen is unable to mate on b7.
As so often happens, the boss has to step in when the underlings fail and after 1.Qc6! there is no escape for Black. A most amusing problem. First the pawn and then officers of increasingly exalted rank make an increasing number of threats until the mighty queen makes the ultimate Novotny sacrifice!
There is an interesting little story behind this problem. Initially, Pal sent us the originally published 1972 version:
Pal Benko, Füle, 1972
Mate in two
I emailed Pal to point out that, in the 1.Bc6? try, there are only three threats (2.Nd6 and one mate by each rook), not the four that he had intended. I mentioned that this seemed a minor issue – the problem was really good and it was surely proper for the bishop’s try to be on a par with the knight’s. But Pal was determined to improve the problem to show the number of threats increasing with the ascent through the ranks. He quite soon produced the following version:
Pal Benko, Füle (1st revision 2012), 1972
Mate in two
I was just about to close down for the night when another message from Pal arrived in my inbox: “Sorry, my wife quite late checked the computer and found a cook 1.Qf8. I will try to correct it, if it is possible at all.” A ‘cook’ is a composer’s term for an unintended additional solution, which renders the problem worthless. In addition to the intended key 1.Qc6! there is 1.Qf8, which threatens discovered checkmate by a move of the Be8 to any square along the e8 to a4 diagonal and copes with attempted defences such as 1...Ng6 with the double check 2.Bd7#.
The following morning, news page editor Frederic Friedel and I were exchanging emails about how we should deal with the situation, when I received another email from Pal, attaching the final version above: “I think I really improved a lot, after I almost gave up. Enclosed my new version in the attachment. I hope you like it.” This time I checked carefully with my solving software and, to my delight, it was completely fine. Not only had he achieved the four threats, but he had even saved a white pawn (in the original version, the Pd2 is needed to prevent Black having a second means of refuting the 1.Rc6? try – by 1...Qd1! as well as 1...Qd3! Thematic tries should have a unique refutation, otherwise they are regarded as being of poor aesthetic standard). Saving a pawn makes the problem even more economical in its use of force, and good economy is something composers are always trying to achieve.
All in all, a quite typical composing story with a happy ending (many such stories end sadly, with the composer having finally to give up trying to set a beautiful idea, because there is no way to get rid of a cook or other unsound element). The one unusual feature is the part played by Pal’s wife – he’s a lucky man!
This problem showed the famously humorous side of Pal Benko. The following study shows his serious side.
Pal Benko, First Prize, Magyar Sakkelet, 1982
White to play and win
1.e7! It is possible to engineer a Novotny by moving the g-pawn forward first, but this ultimately turns out to be a false trail (the equivalent of a 'try' in problems): 1.g7? Rg3 2.e7 Bh5 3.Rg6. The Novotny move. 3...Rxg6! (3...Bxg6? 4.Kf2!) 4.e8Q Rf6+ 5.Ke1 Bxe8 6.g8Q Bd7! and White won't be able to win with best play.
1...Re3. An interesting defence by Black would lead to 'a study within a study': 1...Rf3+ 2.Ke1 Re3+ 3.Kxd1 Rxe7 4.Rc5! (4.Rc4 and 4.Rc3 win more slowly, while 4.Rf6? results in a draw: 4...Re5 5.g7 Rg5 6.Rf7+ Kb6), 4...Kb6 5.Rg5 Rg7 6.Ke2 Kc6 7.Kf3 Kd6 8.Kg4 Ke6 9.Kh5 Kf6 10.Kh6.
2.g7 Bb3 3.Rc7+! Did I say we were getting a Novotny? Yes, but in this position it doesn't quite work: 3.Re6!? Rxe6 (3...Bxe6 4.Kf2!) 4.g8Q Bc4+! Clever play by Black! This way the rook can be kept on the 'e' file with tempo. If instead 4...Rf6+ 5.Kg1 Bxg8 6.e8Q wins easily. 5.Kf2 Re2+ 6.Kf3 Bxg8 7.Kxe2 Bf7.
3...Ka6 If 3...Kb6? 4.Rc3! Rxe7 5.Rxb3+ capturing with check.
4.Kf2 The point of White's preceding move: now that the Pe7 is protected, the white king has time to reach a black square with tempo and avoid Black's saving combination, as seen after 3.Re6.
4...Re4 5.Rc6+ Ka5 6.Re6. Finally, a Novotny that works! 6...Rxe6 7.g8Q Rf6+ 8.Kg1 Bxg8 9.e8Q With a double threat of capturing the bishop or the rook via 10.Qe5+ 9...Be6 10.Qd8+ and wins the rook, as the bishop has interfered with it preventing the saving 10...Rb6.
A glorious study, starting from a 'natural' position with just 7 units and showing winning attempts cleverly foiled by Black, much depth, accuracy and fiendish subtlety and of course no less than three Novotnys, which are brought about without the slightest artificiality.
Any queries or constructive comments can be addressed to me at firstname.lastname@example.org.
Copyright in this article David Friedgood 2012/ChessBase
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