A Happy New Year from Pal Benko... January 1st, 2010
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... and from your ChessBase team! The positions below spell H-N-Y - 2-0-1-0 - P-B and are
letter problems composed by the incredible GM Pal Benko. Each is White to play and mate in three.

You can print out all the three-moves on the page from this PDF file.
The problems are ideal for anyone recovering from festive day excesses, lying on the sofa doing
penance for culinary over-indulgence – or simply for people who like chess puzzles.

A unique puzzle by Noam Elkies

The following problem was submitted by Themis Argirakopoulos and by Ioannis Georgiadis, both from Athens, Greece, as well as by Joshua Green, Laurel, MD. Themis wrote: "My Fritz 9 took more than an hour working but was unable to solve it. The secret is in the second move." Ioannis says: "This puzzle is simply impossible for a computer to solve. Actually I doubt any 'normal' human being would solve it either."

Noam Elkies, 1991

White to play and draw

The source of the above position is usually given as "The Internet, 1994", but we have tracked it back to an email sent by the author to colleagues in mid-November 1991. In it Noam Elkies wrote: "This is a joke study using the same K+Q vs. K+P (c/f) battle that I've based some of my more serious compositions on. In the Queenside jumble only the Black King and Queen are active; the Knights and Pawns are immobile and only serve to delay Black's pieces."

When solving this problem it is important to know the theoretical draw Elkies refers to above.

In the above position, with Black to move, White can draw because of a stalemate threat: with his king on h8 the pawn cannot be taken due to stalemate. In the study above, however, the stalemate resource fails because White has a suicide move with his knight on a3. So everything looks pretty straighforward: 1.Kh6 Qb3 2.f6 Qd1 3.f7 Qf3 4.Kg7 gives us the position in the analysis diagram, with the white Na3-c2 move always available to break the stalemate. So Black should win. There are a number of permutations of the first three moves, and computers will tell you: they are all equivalent. Or are they?

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. Your task is to imagine what it might be, and then work out the details with a (once again) more or less clueless computer. On the other hand: with the search extending to incredible depths these days, who knows when a program will come up with the key moves and a 0.00 evaluation, while giving anything else a losing score.

About the author

Noam D. Elkies, 43, is an American mathematician and chess master. At 14 he received a gold medal with perfect score at the International Mathematical Olympiad, and at 16 he won the Putnam competition. He graduated as valedictorian at age 18, in Mathematics and Music, and earned his Ph.D. at the age of 20 at Harvard University. In 1987 he proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes, and in 1988 he disproved Euler's sum of powers conjecture for fourth powers. His work on these problems won him recognition and a position as an associate professor at Harvard in 1990. In 1993, he was made a full, tenured professor at the age of 26. This made him the youngest full professor in the history of Harvard, surpassing the record previously held by Alan Dershowitz and Lawrence Summers (who were made full professors at age 28).

The winning team from Israel at the World Problem Solving Championship 2004:
Paz Einat, Ofer Comay, Aharon Hirschenson, Noam Elkies.

Noam Elkies is an accomplished composer and solver of chess problems. He is also renowned for his knowledge of the connections between mathematics and music

For the editor of the ChessBase news page and this Christmas Puzzle section Pal Benko sent two more letter problems, twins, spelling F-F. Once again both are mate in three.

It took us a while to figure out why the same position, moved one row to the right, should make a difference. It does – both solutions are unique and show little resemblance to each other. It is at least as interesting as solving the problems to find out why each solution does not does not work on the other position.

Frederic Friedel