Problem chess with Noam Elkies

by Frederic Friedel
1/2/2019 – On Christmas day we published an article by Frederic Friedel, describing the process of composing a chess problem. It was based on his own effort to generate a proper helpmate back in 2002. A number of readers followed his invitation and send in amateur compositions themselves. We also received feedback from a remarkable personality: Noam Elkies is a professor of mathematics, a musician and music composer, chess master and problemist. He explained how to use an online problem database to assist in such tasks. We share his instructions with our readers.

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A helping hand from a friend

On Christmas day I published an article on helpmates. It included a description of a problem I had composed in 2002, as an amateur, and the process that led to the final version. Both are given in the replay board at the bottom of the page. My initial attempt resulted in a nice helpmate, but it had a number of cooks — alternate solutions that were not intended. Here are the mates to which it led:


The first diagram is sound: the moves 1...Rc5 2.h5 Re6 3.h6 Kc6 4.h7 Kd6 5.h8=Q Rc6 6.Qd4 are the only ones — in exactly that sequence — that lead to mate in five. The second diagram is an earlier stage of composition and contains a number of cooks. As you can see I was able to solve the difficulty by moving the black king in the initial position from b4 to b7.

Above are three mates that result from different move sequences from the second diagram. You can move the pieces in the two diagrams above, but also replay both positions in the ChessBase game viewer at the bottom of this post.

I received a number of comments on the article, and amateur submissions with readers trying to compose their own valid helpmates. This will be the subject of a later report — you have until the end of January to send in your compositions. Today I would like to quote an exchange I received from someone I have known for ages.

Noam ElkiesNoam Elkies is a truly remarkable person. At the age of fourteen, he won a gold medal at the 22nd International Mathematical Olympiad, one of the youngest ever to do this. At sixteen he won the Putnam competition, making him one of the youngest Putnam Fellows in history.

After graduating as valedictorian at age 18 with a summa cum laude in Mathematics and Music, he earned his PhD at the age 20 under the supervision of Benedict Gross and Barry Mazur at Harvard University.

At 26 he became the youngest full professor ever to receive tenure at Harvard and has worked there ever since (designing explicit models for Shimura curves associated to rational quaternion algebras and for the special K3 and abelian surfaces that they case you were wondering!).

Noam is an accomplished musician and music composer. If you have time, take a look at him performing (with Prof. Young Hyun Cho) just a few weeks ago. He is also a USA National Master and an accomplished chess composer. Watch this video interview:

At the start he describes his chess (he is an NM in the USA, "which is like being a black belt in martial arts") and problem composing career. From 1:34" on it is all about music — baroque flute compositions specifically — where he is also a master

The day after Christmas Noam wrote me:

Hi Frederic, I enjoyed your "helpmate challenge" column today. I expected that there'd be a helpmate that combines two or more of the mating pictures that turned up in the alternative solutions to your first attempt; indeed these days most published helpmates have at least two solutions, each with a unique move sequence (though some helpmates in 5 or more do have just one). That's a tall order for beginning helpmate composers but possibly some of your more experienced correspondents have already sent you such an example (which may already be in the "literature").

Merry New Year's Eve Eve Eve Eve Eve Eve Eve

First of all, it is edifying to note that Noam, like me, is a fan of XKCD. But secondly, he set me off on a mission to find a position that would allow all three mates shown above to be achieved from a single starting position in dual-free lines. I did not succeed and so asked him for help. He replied that this was beyond his skill level, and he could only find such a position by accident, or possibly by setting up a computer search, which would also take him a while. Instead, he taught me how to query a very useful database of chess problems. I share this very valuable lesson with our readers.

Die Schwalbe (translates to The Swallow) is a German society for chess problems, founded in 1924. They have a magazine and stage composition and solving tournaments, meetings and congresses on an international basis. Most importantly (for me) is that they maintain a database of chess problems, which does not seem to be a link on the main page. For this reason, I had missed it, and certainly did not immediately know how to query it. The database contains to date 418,063 problems, and the total number of queries since launch is 6,874,063. That number has increased by maybe a dozen since Noam showed me how to use it. This is how it is done: first, you go to the database of chess problems. There you type in:

piecelist = 'KkBtt' AND wpieces = 2 AND bpieces = 3

... and bingo, you have over 90 problems with the two kings (Kk), a white pawn (B for the German "Bauer") and two black rooks (tt, for Turm). Number 55 turns out to be my 2002 helpmate problem, with a number of examples with the two unwanted mating pattern that occurred in my first attempt — dozens with the epaulet mate (middle diagram of the three shown above). There was only one problem, as far as I could see, that had my main mating pattern (left, above).

[Event "Jugendschach"] [Site "?"] [Date "1983.12.??"] [Round "?"] [White "Bartel, Erich"] [Black "h#2, White to play, 3 mates."] [Result "*"] [SetUp "1"] [FEN "8/5P2/3r4/4k1K1/4r3/8/8/8 w - - 0 1"] [PlyCount "3"] [EventDate "1983.??.??"] [SourceVersionDate "2018.12.28"] {This simple problem demonstrates three different mating patterns.} 1. f8=Q Re6 (1... Rd5 2. Qf6# {[#]}) (1... Red4 2. Qf5# {[#]}) 2. Qc5# {[#]} *

While I was in the Schwalbe database I thought I might as well look up something else: I typed in "A='Elkies'" and immediately got 99 problems he had composed. A large number are "proof game" puzzles, like the ones Pal Benkö sent us for Christmas 2016. But Noam also has a few retros, series movers, selfmates, helpmates, direct mates and studies. Here is one I remember from Lubomir Kavalek's 2010 chess column in the Huffington Post.

[Event "sp.p Chess Life & Review#1468"] [Site "?"] [Date "1984.??.??"] [Round "?"] [White "Elkies, Noam"] [Black "White to play and win"] [Result "1-0"] [SetUp "1"] [FEN "4B2k/4P1p1/8/3p4/8/8/bb1K2p1/8 w - - 0 1"] [PlyCount "11"] [EventDate "1984.??.??"] 1. Bg6 $1 ({After} 1. Bd7 $2 Bc1+ $1 {White cannot win:} 2. Ke2 g1=Q 3. e8=Q+ Kh7 4. Bf5+ (4. Qh5+ Bh6 5. Bf5+ (5. Qf5+ Qg6) 5... g6 {Black will win.}) 4... g6 5. Qe7+ Kh6 6. Qh4+ Kg7 7. Qe7+) 1... Bc3+ $1 (1... Bc1+ 2. Kc2 $1) 2. Kxc3 (2. Kc2 $2 Bb1+ $1 3. Kxb1 g1=Q+ {wins for Black.}) 2... d4+ 3. Kb4 $1 { The only square.} ({The king cannot move to the second rank because} 3. Kd2 $2 g1=Q 4. e8=Q+ Bg8 5. Bh7 Qh2+ {allows the black queen to capture the bishop on h7.}) 3... g1=Q ({After} 3... Bf7 4. Bxf7 g1=Q 5. e8=Q+ Kh7 6. Qg8+ Kh6 7. Qh8+ Kg5 8. Qxg7+ {wins.}) 4. e8=Q+ Bg8 {[#]} 5. Bh7 $3 Kxh7 6. Qh5# 1-0

The other study Kavalek showed in his column was one in which Elkies extended and improved on a windmill puzzle by Ladislav Prokes, making the white queen chase the black king around a white pawn in counter and clockwise direction. Really astounding:

[Event "Huffington Post"] [Site "?"] [Date "2010.??.??"] [Round "?"] [White "Elkies, Noam"] [Black "White to play and win"] [Result "1-0"] [SetUp "1"] [FEN "8/4pq2/6p1/3Pp2p/8/3pQP1k/5P2/5K2 w - - 0 1"] [PlyCount "31"] [EventDate "2010.??.??"] [SourceVersionDate "2018.12.31"] {Comments by GM Lubomir Kavalek.} 1. f4+ Kg4 2. Qg3+ Kf5 3. Qg5+ Ke4 4. Qxe5+ Kf3 5. Qe3+ Kg4 6. Qg3+ Kf5 7. Qxd3+ $1 {Preparing to spin the windmill the other way.} Kg4 ({After} 7... Kxf4 {White wins the black queen with either} 8. Qg3+ ({or with} 8. Qe3+ Kg4 9. Qg3+ Kf5 10. Qf3+) 8... Ke4 9. Qe3+ Kxd5 10. Qb3+) ({Trying to escape with} 7... Kf6 8. Qc3+ {transposes to the main line.}) 8. Qg3+ Kf5 9. Qh3+ $1 Ke4 10. Qe3+ Kf5 (10... Kxd5 11. Qb3+) 11. Qe5+ Kg4 12. Qg5+ Kf3 13. Qg2+ $1 Kxf4 14. Qg3+ Ke4 15. Qe3+ Kxd5 16. Qb3+ 1-0

And here's a problem for you to solve. Move the pieces on the board and see if you can find a forced mate in three moves. Try to figure out why there is a white pawn on b5. Afterwards you can look at the full solution in the replay board below.


A wonderful puzzle — in my opinion, Noam should put those Abelian surfaces aside and compose more chess problems (and baroque music). The world would thank him for that.

So that's it, lesson learnt and new problem database found.

Your turn

I still ask our readers to take part in our challenge:

For the best helpmate by an amateur reader, we have two special signed programs as prizes. Submissions must be accompanied by a statement assuring us you have never published a helpmate before. Use "feedback to the editors" below to send us your compositions. The competition closes on January 31st, 2019.

Replay all problems from this article

Editor-in-Chief emeritus of the ChessBase News page. Studied Philosophy and Linguistics at the University of Hamburg and Oxford, graduating with a thesis on speech act theory and moral language. He started a university career but switched to science journalism, producing documentaries for German TV. In 1986 he co-founded ChessBase.


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