Djaja study: how humans and computers solved it

8/19/2009 – Remember the study we showed you in one of our Chess Classic reports? The one which top grandmasters failed to solve, while the program Rybka succeeded in just over a minute? We promised to give you the astonishing solution, which we now do, together with a number of interesting – and sometimes delicate – anecdotes describing how the humans fared. 1-0 for the computers on this one.

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Djadja problem and its solution

In our report on the Livingston Chess960 Computer World Championship in Mainz earlier this month we showed you a problem which human beings and computers were not supposed to be able to solve.

We got the position from the Computer Championship arbiter Hans Secelle of Belgium. He gave it to us on a sheet of paper, which we dutifully showed to the chess players who wandered by. It was from a study by an unknown (to us) composer, with the initial play left out. Here is the position:

D. Djaja 1972

White to play and draw

In his book "The King" GM Jan Hein Donner writes: "White makes one more move and it’s a draw! Keres, the two Byrnes, Lothar Schmid, Bisguier and I sat staring at this position for more than half an hour. We couldn’t find it. Can you?"

Hans was convinced that computers would also fail miserably. So Frederic Friedel bet him a glas of whisky at the bar that Rybka would find the key move. "Not necessarily understand why it holds the draw," Friedel said, "but it will find the move by discovering that all other moves lose badly and quickly." Hans lost his bet, Rybka found the right strategy in one minute and two seconds.

Before we give you the very interesting solution (and release a large number of readers from their suffering) here are some of the top grandmasters who wrestled with the problem in Mainz, and some cute little stories surrounding their efforts.

One of the first players we showed the problem to was Levon Aronian (on the right in the above picture) between his games in the GrenkeLeasing Rapid World Championship. He solved it instantly, but with a little confession: "I know this position, I have read the Donner book!" Lev had a prediction: "Show it to Gabriel Sargissian," he said [Gabriel is his second, left in the picture above]. "That guy is a problem solving wonder. He gets any study and any problem immediately. It's a miracle." No he doesn't. Gabriel was unable to find the solution, and after some taunting by Levon and us he asked for us to reveal it. Which we did.

Next we showed the problem to Evgeny Najer, rated 2663, Daniel Fridman, 2665, and David Navara, 2709 (left to right in the picture above) – and to any number of GMs in the hall. None solved it on the spot. Late that evening Fridman, who spent a lot of time working on it, came up with the solution.

That evening at the Champions' Dinner everyone got to try: in the above picture it is Vugar Gashimov, rated 2740, his brother and manager Sarkhan, IM elect rated 2351, and Viktor Bologan, 2689. At the same table was also Ivan Sokolov, 2655, Ordix Open winner Shakhriyar Mamedyarov, 2717, and other passing GMs.

Guess which of the Gashimov brothers solved the puzzle. The one who is weaker at over-the-board chess, by almost 400 Elo points! Sarkhan is a project manager of Hewlett-Packard in Azerbaijan, speaks excellent English and has a great sense of humour. He spells his surname "Hashimov", but that is a Russian thing. We must remember to keep in touch with him.

Shakhriyar Mamedyarov was another Super-GM who solved the problem – after a number of local tap beers and some intense brooding over our sheet of paper.

Another episode needs to be narrated, but we will keep the protagonists anonymous, for obvious reasons. One top GM we showed the puzzle to – not necessarily one of those mentioned above – worked for a while on the problem and then gave up. Some time later he asked to see it again, and this time, after a few minutes of thinking, a smile broke out on his face and he gave us the correct solution. Very nice. Except that later that evening a young and somewhat distraught lady told us the following: "He came outside and asked us for the solution, and the whimp (Gabriel) told him! He said not to tell you, but I can't allow it to pass." Very devious – but hey, we like that in a man.

Finally there is Garry Kasparov, enjoying a vacation on a Mediterranean coast, but still keeping up with the chess news. He called and told us that he had solved the puzzle in a minute or two. "But only because of the big hint you included in the story!" Garry said. His reasoning, as he explained it, was the following: "if Rybka takes over a minute – that long! – to find the solution, in an open position, then there is only one possibility: it must be a perpetual! Once you know that the solution is easy to find...". Good thinking, Garry Kimovitch!

Well, here at last is the solution for all our patient and long-suffering readers. The study is taken from Donner's book and can be found on this Chessville review page. Donner says that the Djaja study was circulated in the Skopje Olympiad, 1972, and brought many of the participants to despair. Here it is in its entirety:

Study by Yugoslav composer Djaja

White to play and draw

White’s position appears hopeless as there is no way of stopping the Black pawn’s march to become a queen. For example, 1.Nf5+ Kd8 2.Nxd4 a2 3.Nc2 Rb2 and Black wins. Our computers tell us that White can probably defend with 2.Nxd4 a2 3.Rb7 a1Q 4.Rxb6 Qxd4 5.a7. However, let us concentrate on the main line: 1.Nf5+ Kd8 2.Ra8+Kxd7 3.a7 Ra4 4.Rg8 Rba6 brings us to the position we were circulating in Mainz:

In this position you have to find a single white move, and then spend a few seconds explaining why it is a draw. The solution is 5.Nh6!! The words you must add are "...and now White has perpetual check along the g-file!" Check it out: the rook is proctected on every square the black king can use to approach: g1-g3 by the white king, g4 and g8 by the knight, and g6 by the pawn. The only unprotected squares, g5 and g7, cannot be used by the enemy king, since f5 and f7 are attacked by the knight. [Click to replay the study]

Isn't that a clever little puzzle? But how are computers able to solve the problem? When we took our bet with Hans Secelle the intention was to use the "Monte Carlo" function of Rybka, in which the program plays thousands of games against itself at high speed and discovers that, although it may not understand why, one move simply does not produce wins for the black side (while all others do). However Rybka does it on a normal level as well:

Above is Rybka running on a standard quad system: the solution pops up in just 28 seconds, and remains permanently the main line of the program. But what about other engines?

This is good ol' Fritz, running on the same quad (at close to ten million positions per second). The program comes up with the solution and stays with it after just 32 seconds.

Send us an insoluble study!

That's that. Are there any studies that these monsters cannot solve? Anyone who sends us a nice puzzle – something as elegant as the position above – which chess engines cannot figure out, can win a Deep Fritz 11 signed by all the players of the Dortmund tournament. Maximum three. Please use the feedback button on the left side of this page and give "Computer puzzle" as the subject line (anything else may cause your letter to be ignored). And please give us the position and solution in PGN.

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