Chess Logicals – an experiment

by Frederic Friedel
5/5/2021 – Two students are studying a chess position. A Zen master watches and tells them that one of the pieces will play a very deep move. "Which one?" the students want to know. The Zen master whispers the piece type to one student and the colour to the other. From their reactions they are able to deduce which piece it is. You can help us in a book project by solving the problem. And hopefully have some fun in the process.

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You all know Christian Hesse. He is a professor of mathematics with a chair in Stuttgart University (and sometimes Santa Barbara). He is also a prolific author who has published some of the most popular books on mathematics in Germany. Christian has also written a couple of well-received books on his special hobby, chess. And he has contributed to a large number of articles on our news page. On the right you see him, chatting with a friend.

Me? I started editing this news page in its database form twenty years ago, incidentally on September 12, 2001. On page 734 of our index you can see how it all started – and perhaps read the first article there. Very poignant.

Before I edited a German language magazine on computer games and chess. Computerschach & Spiele ran from 1983 to 2004, with over 120 issues. In it, I penned many hundreds of articles, many of which today have historical value. A number of the most interesting ones will flow into the book  Christian and I are writing, of course with careful editing and updated bring them into current times.

Another thing we will do is to make all the games, moves and analyses replayable on your smartphone. For this we use QR codes, as described in this article: The future of chess books. Christian has already tried and tested the technology in his book "Damenopfer".

Naturally there will also be a lot of new material, fresh articles written directly for the book. And this, dear readers, is where you come in. We will be conducting experiments on this news page to see how people react to our chess problems, puzzles and stories. Today we start with what we call "Chess Logicals", problems that merge chess and logic in general.

The Zen Chess Logical

This logical problem 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:


After watching for a while the Zen master says: "I see that one of the men on the board will, in the course of the solution, make a very deep move!"

"Which one," the students want to know.

"I'll tell you, Kaito, the piece type, and you, Toshi, the colour." He whispers this into their ears.

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 is for our readers to find out which piece the Zen master meant, and how Kaito and Toshi could deduce it.

An important note: the process of deducing the piece has nothing to do with the chess content of the position. Kaito and Toshi could have deduced it even if the pieces were not standing in a meaningful position, but simply lined up on the table, next to each other.

Having said that the study on the board happens to be very meaningful. One of the people we tested the Chess Logical on was John Nunn, who solved it in just a few seconds. "Pity about the actual position, though," he said. "It could at least have been an interesting study." But an hour later he wrote "Actually, I was a bit rude. I didn’t see Black’s main attacking idea. It’s actually quite a nice study."

So here is the second task for our readers: in the diagram position above, which was given to us by Dr Karsten Müller (to match the Chess Logical material), it is White to play and draw. Warning: the solution is quite hard, especially if you see the best black attack.

Currently, a number of very strong players, as well as young super-talents, are working on the logical part of the problem, so please do not post the solution in the feedback section below – just whether you were able to solve it (and the study), how long it took, and whether you like this kind of puzzle.

The solution to the Logical and the study will be published next week. Until then: have fun!


Editor-in-Chief emeritus of the ChessBase News page. Studied Philosophy and Linguistics at the University of Hamburg and Oxford, graduating with a thesis on speech act theory and moral language. He started a university career but switched to science journalism, producing documentaries for German TV. In 1986 he co-founded ChessBase.
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crispyambulance crispyambulance 5/23/2021 06:01
Ah when Kaito says I know which piece he means the exact piece on a particular square rather than a generic eg "a white bishop" ? If that is clear then it does make sense
crispyambulance crispyambulance 5/23/2021 05:19
Hmm can now see why it has to be white but still no further about the piece
crispyambulance crispyambulance 5/23/2021 05:05
I still don't understand this. Could you please give a better explanation? I can see that it can't be a queen or knight but I don't see how you get further. If it had been the black king wouldn't T have stated the same " neither if us can know"?
dostroot dostroot 5/8/2021 01:23
I think I have it. We’ll see. Fun problem. Right up my alley.
mdamien mdamien 5/7/2021 09:20
Solved the logical pretty quickly and I enjoy such puzzles; one small hitch slowed me down a few moments in the thought process. After a few minutes of the study, I landed on what I would try, but didn't reach a concrete solution where I'm sure of it.
malfa malfa 5/7/2021 06:32
@frederic: speaking of feedback, I forgot mine! So it took to me more than few minutes, maybe 15-30 overall, but I cannot be more precise, since my mind repeatedly returned to the puzzle in random "chunks" during the day, rather than concentrated on it once and for all without thinking to anything else. Instead I found the chess problem not so difficult as announced, at least not after I guessed the drawing idea in reply to Black's winning attempt (no spoilers...)
Frederic Frederic 5/7/2021 05:59
@Zdrak: "... please do not post the solution in the feedback section below..." For this reason I have removed it.
malfa malfa 5/7/2021 05:16
@ Michael Jones: thanks for mentioning that puzzle. I recall that it was made famous by Martin Gardner as "The Impossible Problem", but he was not the original author. Gardner had even to later provide an amendment, since his readers proved that his version of the puzzle was really an impossible one :-)
Pedrix Pedrix 5/7/2021 04:04
It wasn't hard for me, but I've met a much more difficult logical puzzle of this kind - this is a longer version of the puzzle mentioned by Michael Jones:

I thought of two whole numbers greater than one.
I have two friends: P(roduct) and S(um). (Or, because this is a chess site: Peter and Svidler. :))
I whispers the product of the numbers to P, and the sum of the numbers to S.

I ask them to try to guess the numbers without informing eachother of the number I whispered them.
They are very logical thinkers and they never lies.

Here is their conversation:

S1: I don't know the numbers.
P1: Neither do I.

S2: I don't know the numbers.
P2: Neither do I.

S3: I don't know the numbers.
P3: Neither do I.

S4: Now, I know!
P4: So am I!

And now anybody could know the two numbers! Do you know?
(I read this logical exercise in a hungarian amatour physics forum - reportidly the source of the exercise was a Nobel prise winner physicist from CERN, in 1986.)
Michael Jones Michael Jones 5/7/2021 01:04
I was able to solve the logic part of the puzzle fairly easily, partially thanks to having come across a similar one before. Mr Sum knows the number A+B, Ms Product knows the number AB. The only information they have restricting the possible values of A and B is that both are integers, strictly greater than 1 but less than 100. Their conversation goes like this -

Mr Sum: "I don't know what A and B are, but I know that you don't know them either."
Ms Product: "Now I know what they are."
Mr Sum: "Now I know what they are too."

What are A and B? It's a similar type of puzzle to the one above, but more difficult because there are many more possible combinations of A and B from which one is required to narrow it down than there are chessmen in the diagram position. If you've already come across that puzzle and know how to solve it, the chess one is comparatively trivial.

@malfa - Toshi could perhaps have worded his statement a little more carefully. What he meant is that "*Based on the information each of us currently has*, there is no way either of us could deduce which piece you mean" - a statement which would be entirely correct, since deducing the piece relies on each of them providing the other with further information. Since he didn't specify that, one could indeed argue that the statement as he actually phrased it was incorrect.
malfa malfa 5/6/2021 05:34
Frederic: thanks! Actually there is a whole class of problems like these two, based on one guy gathering further (hidden) information from what the other says. However it seems to me that, whereas in the double coffees case both statements by the friends are correct, in the present problem Toshi's initial statement, though necessary for Kaito to deduce the solution, proves itself to be a posteriori wrong, doesn't it?
stikmat stikmat 5/6/2021 03:30
could it be a piece that is acquired by minor promotion?
Frederic Frederic 5/6/2021 02:08
@malfa: yes, it is not (necessarily) the piece that makes the first move. BUT: the Chess Logical should be solved without any concern with the study position itself. For those of you who (like me initially) are struggling, here's a simpler Logical: two friends enter a café and sit down at a table. The waitress comes over and says: "Coffee for both of you?" The first friend says "I don't know," and the second says "Yes!" How come?
malfa malfa 5/6/2021 01:51
I suppose that by saying "in the course of the solution" the Zen master implies that the "very deep move" is not necessarily the first one, is it?
ScorpionC ScorpionC 5/6/2021 08:30
Bf5 is the move I think, how logically pupil understood that it`s that Bishop I don`t know.
JoshuaVGreen JoshuaVGreen 5/6/2021 01:42
I solved the Logical fairly easily. I have no idea where to begin on the endgame study, though I suppose the solution to the Logical should provide a bit of hint.
Hdlh Hdlh 5/5/2021 07:26
Yes I could solve, in a few minutes. Nice problem.
Frederic Frederic 5/5/2021 06:57
@gatogo: The Zen Master is thinking of a specific piece and has told one student its colour and one its type. If he thought of a pawn it could be the pawn on a7 or the one on b5, or c6, d7 or e7. In the end both students know exactly which piece the master was thinking of.
gato90 gato90 5/5/2021 06:08
Just to make sure I understand the question, are they trying to find out the exact piece that makes the move or only the piece type+color combination?
Let's say for example that the Zen Master refers to a black pawn: black has two pawns, would they have to determine which one of the pawns makes the move, or just knowing that it is a black pawn is enough?
I assumed the former, and then I believe I solved it in a few minutes.

As for the chess position itself, I might need more time since black seems to have a lot of alternatives and I cannot say I found such a surprising or interesting idea as suggested.
Frederic Frederic 5/5/2021 05:49
Great stuff, brian8871 (I'm promoting you to 8872). Thanks for not telling everyone the solution. Are you sure you solved the study as well. There is a black attack that requires a very clever white defence. Most people I discussed it with did not see it. Even John Nunn needed many minutes to do so.
brian8871 brian8871 5/5/2021 02:13
It wasn't hard for me to figure out which piece. I just had to spend a bit of time viewing the situation from each person's perspective. The actual puzzle wasn't difficult either.