None of the chess players in Mainz were able to solve this position either, and Hans was convinced that computers would also fail miserably. So I bet him a glass of whisky at the bar that Rybka would find the key move. "Not necessarily understand why it holds the draw," I 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.

In Mainz we showed the problem to some of the best players in the world, with mixed results. Some actually solved it, others cheated! Garry Kasparov, who at the time was enjoying a vacation on a Mediterranean coast, 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!

For the Djaja puzzle you have to find a single white move, and then spend a few seconds explaining why it is a draw. The solution is 1.Nh6!! and 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 with the introductory play from the original]

Richard Forster, the author of the new (and awe inspiring) Lasker biography, told us that he had published the Djaja study eight years ago as a readers' competition in the Swiss newspaper Neue Zürcher Zeitung. Naturally a lot of readers used computers to solve such problems, and Forster had hoped that in this case it would be fruitless. "But later I learnt from a correspondence player that with the right hardware the puzzle was not a serious problem for computers." And Peter Stephenson from Kempton Park, South Africa told us that adding a white pawn on h3 in the above position makes no difference to humans "but baffles every computer I have tried it on, even those that eventually home in on the drawing move Nh6 when there is no pawn on h3." The puzzle with the extra pawn was given in BCM October 1999, submitted by Jonathan Mestel. We were unable to confirm that it poses graver problems for Fritz or Rybka.

Insoluble studies

"Send us an insoluble study," we told our readers. We wanted to know if there are positions which our silicon friends cannot solve. The puzzles must be elegant and the solutions readily comprehensible to humans. But they should cause a major headache (chipache?) to computers. The best submission will receive a Deep Fritz 11 signed by the players of the 2009 Dortmund tournament. Incidentally you can still participate: 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, not Word, Exel or Cuneiform. A proper description of the solution will help you enter the circle of potential winners. Whom you, dear readers, will in the end be choosing.

Our first impossible puzzle designed to haunt computers was submitted by Manuel Rodriguez from the Dominican Republic. "I saw the core of this position somewhere on the Internet," Manuel wrote. "I made some modifications, and there you are: I think this position is very difficult for computers. Some time ago I left Deep Rybka 3.0 on my second laptop, dual core 2.0 GHZ with 3 GB RAM and Windows Vista 32 bit) to analyse it for 36 consecutive hours. Rybka didn't find anything. I haven't tried the Monte Carlo function yet – maybe that will produce the correct first move?!"

Manuel Rodriguez, 2009

White to play and draw

The way to handle this position is to play against the computer (yes, we are explicitly asking you to switch on your machines!) and find a way to hold a draw. It will tear you to pieces if you do not play precisely the right and only strategy to do so. The computer may not realise that it can never win the position, but you as a human will. While your opponent is generating and evaluating millions of positions, and showing a giant plus score for Black (plus seven to more than plus ten!) you can read a good book and sip your Christmas glühwein, executing countermoves with hardly a glance at the board.

Frederic Friedel

A final request: please do not send in any solutions yet. We will ask for them at the end of the puzzle sessions. You should keep notes, though, since we will be asking you to vote for your favourite position and thus nominate the winner.