Christian Hesse explained the theory of such logical puzzles in his book "Achtung Denkfalle" (English: "Careful: thought trap"):
The Zen Chess Puzzle illustrates, in chess context, the idea that knowledge is not merely knowledge. Knowledge about a certain fact in a group of two people can mean that each person knows the fact. But it can also be the case that each person also knows that the other person knows the fact, and even that each person knows that the other person knows that the other person knows the fact. This is possible not only for knowledge, but also for the lack of knowledge and even for the impossibility of knowledge of a certain fact.
Our Zen Chess Logical illustrates that a transition can take place from the impossibility of knowing something (namely which piece the Zen Master is talking about) to the possibility of knowing this, paradoxically by someone merely stating the impossibility of this particular knowledge.
If you have difficulty with the solution to our Zen Logical, here's a little warm-up task that might help you understand the process:
Two logicians go to a cafeteria. The waitress comes to their table and says: "Coffee for both of you?" The first logician says "I don't know," and the second says "Yes." What does each want, and how did they figure it out?
The Zen Chess Logical
The logical problem we published two weeks ago was created by Christian Hesse, and is typical for his way of thinking. A Zen master visits a chess club and sees two students studying a chess position with the following material on the board:

The Zen master thinks of one piece and whispers some information into each student's ear. He tells Kaito which piece type he is thinking of, and Toshi the colour of the piece. Toshi is the first to react: "There is no way either of us could deduce which piece you mean." To which Kaito says: "Okay, now I know which piece it is!" Toshi: "Aha, then I know as well."
The chess logical was a task for our readers: find out which piece the Zen master meant, and how Kaito and Toshi could deduce it. So here's the solution:
- Both Kaito and Toshi know that Kaito has been told the type and Toshi the colour of the piece.
- Toshi immediately says nobody can know which one it is.
- From this Kaito deduces it must be white, because otherwise Toshi had to consider the possibility that it might be a knight or a queen, in which case Kaito would know which piece the Zen master was thinking of.
- Since Kaito now says he knows which piece it is, Toshi deduces it must be the white king, because bishop or pawn would not specify the exact piece. So now Toshi also knows it was the white king.
|
A number of readers got it right, while we can tell you that so far many world-class players have been unable to find the answer to the Logical. With that they have helped us collect data for our attempt to answer the question: Are chess super-talents generally smarter than regular kids? So far only two young talents have given us the correct answer. And grown-ups? John Nunn solved it almost immediately, Ken Thompson too, followed by Vishy Anand. But not many more.

Professor Christian Hesse with one of the successful solvers
The Yakimchik study
The second task for our readers was to solve the study on the chessboard. It was given to us by Dr Karsten Müller (to match the Chess Logical material) and is cleverer than it looks at first sight. Here is the full solution, nicely annotated by our problem expert Siegfried Hornecker:
1.e4 | 1,184,215 | 54% | 2421 | --- |
1.d4 | 958,932 | 55% | 2434 | --- |
1.Nf3 | 286,327 | 56% | 2441 | --- |
1.c4 | 184,722 | 56% | 2443 | --- |
1.g3 | 19,884 | 56% | 2427 | --- |
1.b3 | 14,598 | 54% | 2428 | --- |
1.f4 | 5,953 | 48% | 2377 | --- |
1.Nc3 | 3,906 | 50% | 2384 | --- |
1.b4 | 1,790 | 48% | 2378 | --- |
1.a3 | 1,250 | 54% | 2406 | --- |
1.e3 | 1,081 | 49% | 2409 | --- |
1.d3 | 969 | 50% | 2378 | --- |
1.g4 | 670 | 46% | 2361 | --- |
1.h4 | 466 | 54% | 2382 | --- |
1.c3 | 439 | 51% | 2425 | --- |
1.h3 | 289 | 56% | 2420 | --- |
1.a4 | 118 | 60% | 2461 | --- |
1.f3 | 100 | 47% | 2427 | --- |
1.Nh3 | 92 | 67% | 2511 | --- |
1.Na3 | 47 | 62% | 2476 | --- |
Please, wait...
1.e8Q+! 1.cxd7? Qe4+ 2.Kh2 Qf4+ 3.Kg2 Qd2+ 4.Kf3 Qd3+ 5.Kg4 5.Kg2 Qe2+ 6.Kh1 Qf3+ 7.Kh2 Kf4-+ 5...Qe2+ 6.Kg5 Bd2+ 7.Kg6 Qd3+ 8.Kg7 Qg3+ 9.Kh7 Qxh3+ 10.Kg8 Kf6 11.e8N+ Kg6 12.Nxd6 Qe6+ 13.Nf7 Qxf7+ 14.Kh8 Qg7# 1...Qxe8 2.cxd7 Qa8+ 2...Qh5 3.Kh2 Bd2 3...Kf4 4.d8Q= 4.Bxd6+ Kd4 5.d8Q Qe2+ 6.Bg2 Qh5+ 7.Bh3 Qe2+= 2...Qg6 3.d8Q Qe4+ 4.Kh2 Qf4+ 5.Kg2 Qd2+ 6.Kf3 Qd3+ 7.Kg2 Qe2+ 8.Kh1 Qf3+ 9.Kh2= 3.Kh2! Ba5! 4.Bxa5 4.d8Q Qxd8 5.Bxd8 Bxd8-+ 4...Nb7 4...Nf7?! 5.d8Q 5.Bc3+= 5...Nxd8 6.Bc3+ 5.d8Q! Nxd8 6.Bc3+ Kf4 7.Bd2+ Ke5 8.Bc3+ Kd6 9.Bb4+ Kc7 10.Ba5+ Kb8 11.Be1! 11.Bg2? Nb7-+ 11...a5 11...Ne6 12.Bg2= 12.Bg3+ Ka7 13.Bf2+ Kb8 14.Bg3+ ½–½ - Start an analysis engine:
- Try maximizing the board:
- Use the four cursor keys to replay the game. Make moves to analyse yourself.
- Press Ctrl-B to rotate the board.
- Drag the split bars between window panes.
- Download&Clip PGN/GIF/FEN/QR Codes. Share the game.
- Games viewed here will automatically be stored in your cloud clipboard (if you are logged in). Use the cloud clipboard also in ChessBase.
- Create an account to access the games cloud.
Yakimchik,V | - | White to play and draw | - | ½–½ | 1956 | | 3.c Shakhmaty v SSSR#38 | |
Please, wait...
Have you seen this kind of drawing mechanism before? We hadn't.