Building a fortress December 26, 2009
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Yesterday's position, which was constructed from memory by the submitter, had a couple of flaws – one relatively minor and one very serious.

Manuel Rodriguez, 2009

White to play and draw

The envisioned solution runs as follows: 1.Ng4+!! hxg4 2.Nf7+ Bxf7 3.d4+ Kf5 4.Rh1! Qf8 5.Ke1 Qa8 6.Kf1 Qa6+ 7.Kg1 draw.

The reason is clear: the black queen cannot penetrate without stalemating the opponent, and so must retreat back to a8. Naturally the computer will still evaluate the position as winning for Black and potter around forever behind the pawn barrier. We humans know there can be no progress, the position is a draw.

Now to the flaws: the less serious one is that the first two moves can be inverted: 1.Nf7+ Bxf7 2.Ng4+ hxg4 3.d4+ etc. works just as well as the solution given above. That devalues the position as a classical study, but it would still serve its purpose in our Christmas theme: to baffle computers and demonstrate our superior understanding in some areas of chess.

The second flaw is serious and was pointed out by two readers, both problem experts: Dr Noam Elkies and GM Dr John Nunn. The latter had accepted our solution on the 24th evening, but then woke up on Christmas day in a cold sweat. "What if we sacrifice the queen on b5?" he muttered. A quick check showed this to be feasible. The line runs as follows: 1.Ng4+ hxg4 2.Nf7+ Bxf7 3.d4 Ke6 4.Rh1 Qf8 5.Ke1 Qa8 6.Kf1 Kd7 7.Kg1 Be8 8.Kf1 Qa6+ 9.Kg1 Qb5 10.axb5 cxb5

Now it looks as though Black can win, e.g. 11.Kf1 b4 12.Ke1 Kc6 13.Kd2 Kb5 14.Kc2 a4 15.Kb2 a3+ 16.Kb3 Ka5 17.Rb1 Ba4+ 18.Ka2 Bb5 19.Ka1 Ka4–+ (line provided by Elkies). That pretty much ruins the position as a study or even for a test of the perspicacity of chess playing computers, which may concievably be avoiding the knight sacrifices because they see that this strategy does not help anyway. [Click to replay]

A number of readers recognized the position in its original form and sent us the following study that is simpler but does not have the above defects:

J. Hašek, Národní Listy 1951

White to play and draw

Here the solution is clear, only one move draws (and really does so): 1.Ng4+!! If the computer does not play this it has not seen or even smelled the draw. Perhaps some of our readers can leave a quad or oct system running for many hours to see if the solution comes up. One should also try the Monte Carlo feature of Rybka, to see if that produces the key move. The rest of the line is clear: 1...hxg4 2.d4+ Kf5 3.Rh1! Qh8 4.Ke1! Qa8 5.Kf1 Qa6+ 6.Kg1 draw as above. [Click to replay]

Puzzle 2 – December 26th

Li Wu of Cambridge, UK, wrote to us: I have a puzzle that computers cannot solve. He was not able to give an author or source, but that we know will be quickly supplied by our readers. [It has been, ten minutes after we went live, by the aforementioned Noam Elkies].

W.E. Rudolph, La Stratégie 1912

White to play and draw

The solution to this problem will pose no great challenge to our readers, given the discussion of the previous submission. However it is fun to experiment with computers. If you let them play with the white pieces you will be able to win on any level – unless they are able to find the one drawing mechanism which saves the game. It would be interesting to know if any of the six white moves are found by a program when the previous are manually entered, naturally against the will of the machine, which believes that White is lost and only seeks to minimize the damage.

Frederic Friedel

Addendum

Chess historian Edward Winter (where would we be without him?) has sent us a precise source for the above position. "The composition," he writes, "was given on pages 174-175 of Pawn Power in Chess by Hans Kmoch (New York, 1959), headed ‘W.E. Rudolph, La Stratégie 1912’. The French magazine published it on page 156 of its April 1912 issue (with White’s king and bishop on e3 and c2 respectively, and not d2 and d1). It was stated that the study came from the Chess Amateur. That earlier publication (also with the king and bishop on e3 and c2) was on page 184 of the March 1911 Chess Amateur, in T.R. Dawson’s ‘Endgames’ column. The caption was ‘White plays and what?’. Dawson described it as ‘a most ingenious composition with an amusing denouement’. The solution appeared on page 224 of the April 1911 Chess Amateur. William E. Rudolph of Brooklyn, NY was a regular contributor of problems and studies to magazines of the time."

Now we know everything about the problem. We have modified the original diagram in light of this historical documentation (originally we gave White’s king and bishop on d2 and d1).