Is this position legal?

Perhaps he believes some of them are illegal because of the unusual positioning of the pieces (with respect to a sensible chess game.) But again, that's not an issue here. All trivially legal.

I'm sure the guy has no idea whether or not they are legal. :)

Is this legal? I think someone else might have posted this.

Actually, it was pretty easy

Tip: solve your own 'puzzle' before posting it. :P

I'll just hope this problem is correct.

Here's one I composed today. Very easy on the solving side, but it was a composing exercise I set myself. Inspiration for the story drawn from Raymond Smullyan's The Lady or the Tiger?, an excellent non-chess logic book. Adapted from Chapter 18, "The Machine That Never Got Built". Many apologies for the many logical loopholes in the dramatisation. Entirely fictional.

I once had a dream. Working on chess retroanalysis puzzles, it eventually dawned on me that nobody had yet taught a computer how to solve proof games. And why not? All it would take would be brute-force lines of move retractions, like Houdini in reverse. By repeatedly retracting moves, or playing "retro-chess", one could empirically construct proof games for all legal chess positions. A vast portion of the literature could be at last absolutely solved! So I tried to engineer one.

Finally the code was written, the dedicated hardware assembled. For the moment of testing, I chose the following position, for it contained the main features of classical retros:

(a) White can castle 0-0.
(b) Black can castle ...0-0-0.
(c) Black can capture ...exd3 en passant.

If my machine could construct a proof game to allow all 3 scenarios at once, it would be a perfect proof of its power. So I input the position, and set all 3 moves to be legal, and the machine spouted an error!

I had previously checked: The machine could handle (a) and (b), (b) and (c), (a) and (c) together, but it could not process all 3 together! I spent much time troubleshooting... and then I woke up.

When I woke up I immediately recalled the position, and saw how silly I was. Of course this machine would fail here, and it would be too silly to see why!

The puzzle: Are (a) and (b) together legal? (a) and (c)? (b) and (c)? Finally, (a), (b) and (c) all together?

@Arkhimeedes: There's a knight on h1.

Oh yeah Sorry I missed it :)

#384: So by some stupid thought I kept thinking that the piece blocking on d8 will be a promoted c2. Oops. I need more practice huh.

#382:

Everything together: Since Black can capture exd3 e.p., White must have just moved d2. So Bc1 is captured at home. In addition, Black's Rh5 must be a promoted rook; Black's queenside rook hasn't moved and the kingside rook cannot go out. Also, there is a promoted dark bishop. This promoted dark bishop can only occur on g1 (everything else is blocked), after performing five captures dxexfxg3xh2xg1=B-h2 (dxexf2xg1 checks White's king, and so must be captured, otherwise White cannot castle). The promoted rook must be axbxc, performing two captures. This sums up to seven captures, plus White's dark bishop captured at home, giving eight captures, too much.

When White cannot castle, Black's dark bishop might be from dxexfxg1. When Black cannot castle, Rh5 might come from Rh8. When Black cannot capture exd3 e.p., Black's dark bishop might be from dxc.

chaotic_iak: Correct! dxc1 I'll take to mean "d-file to c-file", since specifically Pd2xc1=B would have been checking white's king on d2.

Also, it's fine to have cooks, especially with promoted pawns (they're hell to deal with.) For instance, the twin on #322 was a derived from investigating why that solution wouldn't work in the original problem. #381 is already pretty well-designed, especially the lower right sequence.

Who said "dxc1"? *goes to edit post* :P Yeah, minor typo there.

I think I intended #381 to be illegal. Something like "cxdxc takes two captures, so Ph2=Bh8 doesn't capture, so Bd8 comes by hxgxhxg-g1=B, and then Ra1 is captured by Black's king, too many captures". I should have kept pieces instead of pawns; something like this:

Don't we all hate cooks. Especially with the many varieties of pawn movement: here black only needs one capture, and it so happens g1 is dark:

...pawn f2 -> g2. I botched it up so much.

And also if this still turns out to be solvable, basically you know what I intended but clearly I didn't test it properly (or I simply can't read every possible variation).

B & C are cannot be at one time, because you either have to promote your second blackfield bisshop on either c1 or g1. When you promote on c1 it is impossible to move the bisshop to the right position whitout moving the pawn on d2 first. If you want to promote on g1 you must come over h2 because otherwise you check the King when you are on f2 and the king has to move.