try this without using a program


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Normajean Yates    (2008-07-11 02:41:24)
try this without using a program

White to play and mate in 4. There is a unique first move. Find it. Make a guess.
[I thought this one up a few years ago - i want to see how difficult it is for humans. Any good program will solve it in a few seconds.] ChessPosition (see diagram)

a b c d e f g h

Svante Carl von Erichsen    (2008-07-11 15:26:09)
first move

I think that the first move has to be 1.Qaxf7 or 1.Qfxf7.
Reason: In order to complete the task in 4 moves, we have to keep the king in check, otherwise Black can stall with checks of his own; so, one of the Queens d7, e7, or f7 has to be captured. Capturing e7 results in immediate counter-check, and capturing d7 has no continuation. Also, f7 is the only candidate under double threat.
However, I find no forcing continuation afterwards when the black King just moves to d8.

Normajean Yates    (2008-07-11 21:33:22)
that's damn good!

yes, the first move is Qaxf7!. (Qfxf7 doesn't work).

There is no forcing continuation, but from your response ( :) ) i now feel humans can 'heuristically' conjecture that Qaxf7 begins a mate in 4, while Qfxf7 and others don't. I don't really know - looks like a computer problem for me as far as proof is concerned - too many variations.

Normajean Yates    (2008-07-11 21:44:53)
The other one fails to:

Qfxf7 fails to Qxf7. No mate-in-3-or-less after that. In fact there is no mate in 4 either.

Normajean Yates    (2008-07-11 22:07:23)
but i dont agree with your last sentence

if 1. Qaxf7+ Kd8 2. Qhxc7+ Qbxc7 (only legal move!) 3. Qexe7+ Kc8 (only legal move!) 4. Qdxd7# (or Qexd7#).

On, 1 Qaxf7+ Qgxf7 (the only other legal move) 2. Qh8+! [unique move which gives mate in 3], now 2.. Qxh8 (forced, since the only other move is 2..Qf8 3.Qfxf8# (or 3.Qhxf8#)); now 3. Qxh8+ Qff8 (or Qfg8) 4. QxQ # (choice of two Qs here to mate with).

Svante Carl, now that you have guessed the solution (or narroed it down to two moves), and since the above is quite forcing; so it looks human-solvable to me after all!

Normajean Yates    (2008-07-11 22:09:20)

Svante Karl and my joint research shows that this problem is human-solvable after all, it seems!