Solutions to our 2009 Christmas Puzzles
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December 30, 2009 – Improving on Troitzky

The great US/Hungarian problem composer (and world class OTB grandmaster) Pal Benko gave us an improved version of a famous Troitzky study that had turned out to be flawed. Benko used the same idea and produced a properly funtion position.

A. A. Troitzky version Pal Benko, 2007

White to play and win

The solution is 1.Ka1!! Not 1.Kc2? Bh7! 2.Rxh8 Bxg6+ 3.Kb3 Bxh5 and Black wins;
or 1.g4? Bxc4 2.Rxh8 Bd3+ 3.Ka1 Bd2 mates. 1...Ka4 2.g4. This is the only move and the right solution. 2...Ka5 3.g5 Ka4 4.Kb1 Ka5 5.Kc2 Ka4 6.Kc3 Ka5 7.Kd4! and the rest as in the original Troitzky study: 7...Ka6 8.Ke5 Ka5 9.Kf4 Ka4 10.Kg3 Ka5 11.Kf2 Ka4 12.Ke1 Ka5 13.Kd1 Ka4 14.Kc2 Ka5 15.Kc3 Ka4 16.Ra8 a5 17.Rb8 and White wins. [Click to replay]

December 31, 2009 – Compose a position

The puzzles for the final day of the decade were sent to us by Indian GM Sandipan Chanda. The first was a traditional study – but difficult for chess engines to solve – while the second was a special contruction task.

Sandipan Chanda, 2009

White to play and win

Solution: 1.Rd8+ Nc8 2.Rxc8+ Ka7 3.Rxc7+! [3.Kf7 a2 4.Rxc7+ Kb6 5.Rb7+ (5.Bxa2 Ra1–+) 5...Kxa6 6.Rb4 a1Q 7.Ra4+ Qxa4 8.Bxa4=] 3...Kxa6 [3...Kb6 4.a7 Rg1+ 5.Kf7 c1Q 6.a8Q Kxc7 7.Qa7+ Kc8 8.Qd7+ Kb8 9.Qe8+ Kb7 10.Qxe7+ Ka6 11.Qb4+–; 3...Kb8 4.Rxe7 Rg1+ 5.Kf7 c1Q 6.Rb7+ Ka8 7.e7+–] 4.Rxc6+ Kb5. [4...Kb7 5.Bd5; 4...Ka5 5.Kf7] This is where the engines get tricked. 5.Rxc2! Rxc2 6.Bxc2 a2 7.Bd1!! a1Q 8.Bh5 Qh1 [8...Qg1+ 9.Bg6+–] 9.Be8+ Kc5 10.h5+– and White wins. [Click to replay]

The second problem was one that could not be solved with chess engines – except that candidate positions can be checked with the computer.

Compose a position where White has only a bare king and Black has king and three pawns (no double or triple pawns). It is Black to play and the result is a draw.

The solution:

Black to play, draw!

Naturally the position can be mirrored with the pieces on the left side of the board. Also there is a minor dual: the position works with the white king on h3.

Black's best try is 1...Kg7 [or 1...Kh7] 2.Kxg3 Kg6! 3.Kg4! The position is mutual zugzwang. 3...h5+ 4.Kf4 draw. [Click to replay]

January 1, 2010 – A Happy New Year from Pal Benko

The wishes of the incredible GM Pal Benko came in the form on letter problems,
spelling out H-N-Y - 2-0-1-0 - P-B and F-F (for the editor). Each is White to play and mate in three.

1.Bf5 Bg6 2.Nd7+ Kf7 3.Be6# and 1.Bd5 cxd5 2.Nc3 d4 3.b4#

1.Kf1 Kxe3 2.Bf5 Kf3 3.Rd3# and 1.Nab6 Kb5 2.Nc8+ Kxa6 3.Rb6#

1.Re3 hxg5 2.Be6+ Kxf4 3.Nd5# and 1.b3 axb3 2.Ra4+ Kxa4 3.Rxa6#
(or 1...Nxc3 2.R4b5+ Bxb5 3.b4#; or 1...Bb5 2.R6xb5+ Nxb5 3.Rxa4#).

1.Nf3+! [not 1.Nf6? Kf4 2.Ne2+ Kg5 3.Rd5+ Kh6] 1...Kf5 2.Bh5 Ke4 3.Bg6#
1.Ng6! [not 1.Ng3+? Kg5] 1...Kg4 2.Nf2+ Kg5 [2...Kf5 3.Re5#; 2...Kh5 3.Re5#] 3.Re5#.

Click to replay all of Pal Benko's letter problems

The final puzzle is a unique creation by a great mathematician and chess composer:

Noam Elkies, 1991

White to play and draw

There is a unique point to this study, one that has made it famous in problem circles – and one that you are most unlikely to encounter anywhere else. White draws by expoiting the 50-move-rule! This states that that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves (fifty moves by each side).

1.f6! Qb3 2.f7! White must be careful: If he plays 2.Kh6? the drawing idea of the main line fails by one move. 2...Qd1 3.f7 Qf3 4.Kg7 Qg4+ 5.Kh8 Qf5 6.Kg7 Qg5+ 7.Kh7 Qf6 8.Kg8 Qg6+ 9.Kf8 Ka4 10.Ke7 Qg7 11.Ke8 Qe5+ 12.Kd7 Qf6 13.Ke8 Qe6+ 14.Kf8 Kb3 15.Kg7 Qe7 16.Kg8 Qg5+ 17.Kh8 Qf6+ 18.Kg8 Qg6+ 19.Kf8 Kb2 20.Ke7 Qg7 21.Ke8 Qe5+ 22.Kd8 Qf6+ 23.Ke8 Qe6+ 24.Kf8 Kc1 25.Kg7 Qe7 26.Kg8 Qg5+ 27.Kh8 Qf6+ 28.Kg8 Qg6+ 29.Kf8 Kd1 30.Ke7 Qg7 31.Ke8 Qe5+ 32.Kd7 Qf6 33.Ke8 Qe6+ 34.Kf8 Ke2 35.Kg7 Qe7 36.Kg8 Qg5+ 37.Kh8 Qf6+ 38.Kg8 Qg6+ 39.Kf8 Kf3 40.Ke7 Qg7 41.Ke8 Qe5+ 42.Kd7 Qf6 43.Ke8 Qe6+ 44.Kf8 Kf4 45.Kg7 Qe7 46.Kg8 Qg5+ 47.Kh7 Qf6 48.Kg8 Qg6+ 49.Kf8 Ke5 50.Ke7 Qg7 51.Ke8 Ke6 52.Kd8 Qxf7 and Black has made a capture just in time to avoid a 50-move draw.

2...Qd1+ 3.Kh6! Qf3 4.Kg7 Qg4+ 5.Kh8 Qf5 6.Kg7 Qg5+ 7.Kh7 Qf6 8.Kg8 Qg6+ 9.Kf8 [9.Kh8? Qxf7 10.Nc2 dxc2] 9...Ka4! 10.Ke7! Qg7 11.Ke8 Qe5+ 12.Kd7 Qf6 13.Ke8 Qe6+ 14.Kf8 Kb3 15.Kg7 Qe7 16.Kg8 Qg5+ 17.Kh8 Qf6+ 18.Kg8 Qg6+ 19.Kf8 Kb2 20.Ke7 Qg7 21.Ke8 Qe5+ 22.Kd8 Qf6+ 23.Ke8 Qe6+ 24.Kf8 Kc1 25.Kg7 Qe7 26.Kg8 Qg5+ 27.Kh8 Qh6+ 28.Kg8 Qg6+ 29.Kf8 Kd1 30.Ke7 Qg7 31.Ke8 Qe5+ 32.Kd7 Qf6 33.Ke8 Qe6+ 34.Kf8 Ke2 35.Kg7 Qe7 36.Kg8 Qg5+ 37.Kh8 Qf6+ 38.Kg8 Qg6+ 39.Kf8 Kf3 40.Ke7 Qg7 41.Ke8 Qe5+ 42.Kd7 Qf6 43.Ke8 Qe6+ 44.Kf8 Kf4 45.Kg7 Qe7 [45...Qd7 46.Kf6!] 46.Kg8 Qg5+ 47.Kh7 Qf6 48.Kg8 Qg6+ 49.Kf8 Ke5 50.Ke7! Qg7 [50...Qe6+ 51.Kf8 Kf6 52.Kg8=; or 50...Qd6+ 51.Ke8 Ke6 52.Nc2!=] 51.Ke8 Ke6 52.Kd8! With this move, White can claim the draw by the fifty-move rule since move two no piece has been captured and no pawn moved. Incidentally 52.Nc2 is also a draw by the 50 move rule. [Click to replay]

The composer of this unique chess problem Prof. Noam Elkies