Solutions to our 2009 Christmas Puzzles Part one
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December 25, 2009 – Insoluble studies

The following puzzle was submitted by Manuel Rodriguez from the Dominican Republic. "I saw the core of this position somewhere on the Internet," Manuel wrote. "I made some modifications, and there you are: I think this position is very difficult for computers."

Manuel Rodriguez, 2009

White to play and draw

Unfortunately as the Christmas week progressed it turned out that the study in the above poisiton was flawed. The envisioned solution was 1.Ng4+!! hxg4 2.Nf7+ Bxf7 3.d4+ Kf5 4.Rh1! Qf8 5.Ke1 Qa8 6.Kf1 Qa6+ 7.Kg1 and the black queen cannot penetrate without stalemating the opponent. However, problem experts John Nunn and Noam Elkies found a probably win for Black; and in addition, the problem turned out to have an alternate solution. All this was discussed in subsequent columns, and all the analysis is to be found here.

December 26, 2009 – Building a fortress

W.E. Rudolph, La Stratégie 1912

White to play and draw

The move that computer need to find is 1.Ba4+! Now Black must recapture and allow his opponent to completely lock up the position: 1...Kxa4 2.b3+ Kb5 3.c4+ Kc6 4.d5+ Kd7 5.e6+ Kxd8 6.f5

As is obvious to humans – but not to computers, which evaluate the position as +13 to +15 for Black – the position is a draw, since Black can never penetrate the white defence. Unless, of course, the position is being defended by a computer. You can try winning with black: sacrifice a rook on d7 (the computer will gladly take) and then open up to position to win. Feels good, doesn't it, that there are some areas where we can feel superior to the electronic monsters. [Click to replay]

December 27, 2009 – A thrilling win

M. Matous, 1.hm Szachy 1975

White to play and win

Most computers are content with 1.Qd6+ Kg8 2.gxh7+ Kh8 3.Bxa5, which hardly yields more than a draw. There is, however, a very clear and forced win with a dramatic second move that is thrilling to see. 1.Qc8! Kg8 2.Bc7!! This, says Nordin Tarifit, one of the three readers to submit the study, is the star move. "Why it's hard for a computer to find 2.Bc7!! is because White has for at least 16 ply only a pawn and a bishop against black's queen, knight and two pawns. But Black is in zugzwang!" 2...Qxc8 [2...Nxc7 3.gxf7+] 3.gxf7+ Kh8 [3...Kf8 4.Bd6#] 4.Be5. White is threatening to move his king and discover check and mate. 4...Qc5 5.Bb2 Nc7. Black has the white king contained, but cannot afford to move either the queen or the knight for fear of mate. 6.Ba1 a4 7.Bb2 a3 8.Ba1 a2 9.Bb2 a1Q 10.Bxa1 and now Black is in deadly zugzwang – he must move either the queen or the knight. 10...Nd5+ 11.Ke6+ Nc3 12.Bxc3+ Qxc3 13.f8Q# 1-0. [Click to replay]

Some ingenious readers came up with the interesting technique of removing the black a-pawn from the position above. With the string of zugzwangs gone some programs (e.g. Rybka) find the solution instantly.

December 28, 2009 – The imprisoned king

The problem we gave you arose in a study that might be unsound. This is the original position:

Vitaly Chekhover, Gatchinskaja Pravda, 1954

White to play and draw

The solution given by the author is 1.Rb1! cxb1Q 2.Bxb1 e3! 3.Bxf5 e2, leading to the position given in the next diagram, which is the one you had to solve. However, when checking the problem John Nunn came up with the possibility of an alternative solution: 1.Rh8+ Kg4 2.Rf8 c1Q 3.h3+ Kf4 4.Be6 Ke5 5.Bxf5 Qa3 6.Rf7 Qf3+ 7.Kg1 e3 8.Re7+ Kf6 9.Rxe3 Qxf5, which, he says, looks like a fortress to him.

Now comes the key manoeuvre, which you had to find: 4.Bg4! [4.h3? allows the black King to escape: 4...g4! 5.Bxg4 e1Q 6.Bf5 Qc3 7.Bd7 Qe5 8.Bg4 Qd5+ 9.Bf3 Qg5+ 10.Bg4 Qd2 11.Be6 Qd6] 4...e1Q 5.h3 Qc1 6.Kf3! Qf1 7.Ke3 Qg2 8.Ke2 draw. The black king is trapped, White simply moves around the f2-pawn, with the black queen unable to dislodge him. Even if the bishop is taken by the queen, the pawn ending is still a draw. [Click to replay]

December 29, 2009 – A tale of seven knights

Here are the solutions to the charming knight problems by Ashot Nadanian:

Nadanian,Ashot, Shahmatnaya Nedelya 2003

White to play and mate in three

1.Qe4 Bxe4 [1...Nh4 2.Qe5+ Kg6 3.Nxf8#; 1...N8e7 2.Ne8 Bxe4 (2...Bxe8 3.Qf3#; 2...Bg7 3.N8xg7#) 3.Nf6#] 2.Nxe4 f3 3.Ng3# or 2...Ne5 3.Nxf4#; 2...N8e7 3.Nf6#; 2...Be7 3.Ng7#. [Click to replay]

White to play and win

1.Rg8 Rxg8 [1...Re7 2.N6f5 Re1 (2...Re4 3.Rxg6+ Kxh5 4.Rg1+–) 3.Rxg6+ Kxh5 4.Rxh6+ Kg5 5.Nf3+ Kxf5 6.Nxe1+–] 2.Ne4+ Kxh5 3.Ne6 with the familiar zugzwang and mate. [Click to replay]

White to play and mate in two

The solution to this elegant little problem is the astonishing 1.d8N! The black king cannot move, and whichever knight Black moves, he always gives up the defence of a mating square. [Click to replay]

From a study by Smyslov

The following position was submitted by George Tsavdaris of Thessaloniki, Greece. John Nunn provided us with the source of the original study and a full solution.

Smyslov,V - 64, 1938 [Nunn,John]

White to play and win

1.f5 gxf5 2.Bh3 Re8. The only move, otherwise the c-pawn is quickly decisive; for example 2...fxe4 3.Bxe6 fxe6 4.c7 Rc8 5.Rd8+ or 2...c3 3.exf5 Bxa2 4.c7. 3.exf5. Not 3.c7? Bc8 4.Bxf5 Ke7 and Black defends. 3...Bc8

This is the position we gave in our Christmas Puzzle. 4.f6! The key move, offering a piece to paralyse Black. 4...Bxh3 5.c7 a5. 5...Kg8 6.Rd8 Rf8 leads to more or less the same conclusion, since Black's king and rook are again immobilised; for example 7.Kc2 Bf5+ 8.Kc3 Be6 9.a3 a5 10.a4; 5...c3 6.Rd8 Bf5 is an attempt to prevent the white king attacking the c-pawns, but Black also falls into zugzwang in this line: 7.a4 a5 8.Kd1 c2+ 9.Kc1 c4 10.Kd2 c3+ 11.Kc1 and both Black pawns fall.

6.Rd8. 6.a4? is wrong as White will need a tempo with the a-pawn later: 6...Kg8 7.Rd8 Rf8 8.Kc2 Bg4 9.Kc3 Be6 and White has no waiting move. 6...a4 7.Kb2! [Not 7.Kc2? a3 8.Kc3 Be6 and White has no tempo move.] 7...Be6 8.Kc2. This triangulation puts Black is in zugzwang. If he moves his bishop then White plays Kc3 followed by a3. 8...a3 9.Kc3 Black loses all his queenside pawns after which White wins using the a-pawn. 1-0. [Click to replay]

Frederic Friedel