Is this position legal?

Legal/ illegal? (Not a particularly hard one)

illegal

Why?

#2 is yes it's legal

(b) and (c) can be legal together. The black bishop was promoted on g1 from d7, capturing dxexfxgxhxg, capturing 5 times. The 5 pieces taken were the 2 knights, f1-bishop, f-pawn, and promoted (or just displaced to the e-file by 2 captures) c-pawn.

#393: wPf2->g2 seems to fix it, yes. Illegal I think.

#405: Legal. Black retracts a capture like 0...Ra1xQe1. Or white can retract 0. Kh2-h1 Nd4x(Q)f3 and either way, both sides have many moves.

Uh wPe2 -> g2, since otherwise wBf1 can't go out and counting captures is more trivial. But...eh, nevermind. Throw that one away.

Here's a rather easy one. I think it's inspired from some earlier post in this thread or something.

So this thing came to my head.

Out of all Chess960 starting positions, how many of them can lead to the following positions?

Problem 1:

Problem 2:

I'll answer anyway. It doesn't take too long. Hope I'm right.

Problem 1 - 60 games. 6 x 5 x 4 / 2.
Problem 2 - 8 games. 2^3.

It's not that long, although sure it feels more mathematical instead of chess-y. (Not to be confused with cheesy, which the above problems might be.)

In both cases, the set is full, so there are no promotions and captures; the pieces are original. Bishop on a,b,d-files cannot leave Black's pawn structure, while bishop on e,g,h-files cannot leave White's pawn structure, so the bishops are on c,f-files.

For the first problem, this is enough; remove the bishops and the knights out, and it's easy to shuffle the rooks/queen/king to the desired arrangement. Now, knowing that there are 60 ways to put the remaining pieces after all bishops are put (6 ways for queen, 5 ways for first knight, 4 ways for second knight, divide by two as they are identical, the remaining spots are always rook-king-rook in order), we easily get the answer.

For the second problem, the bishop on c-file in Black's position restricts the starting arrangement: a rook must be in the northwest cage (the one that is on a-file), and there's no more rook/queen/king in that cage (they cannot get out). So the other one is a knight. Similar with southeast. This means there are two arrangements for the queenside rook/knight, two arrangements for the kingside rook/knight, and two arrangements for the queen/king (they can be exchanged by first letting the queen out). They are independent from each other, so there are 2*2*2 = 8 ways.

Now back to the regular program.

I hope I did it properly.

a) Is the diagram legal?

The publication of the remaining parts depends on whether this problem is successfully made. :P

No because the only square the rook could have put a check from is e1, which is still a check.

I agree.

Legal?Illegal?

Ah, the classic colour of capture squares. I second mashanator's analysis (and unfortunately, sentiment. Retroanalysis does not appear to be in most chessplayers' repertoire of skills.)

@ghostqiuyu #420 trivially legal, after retracting, say, -1...Rh8xQh2 -2. Qb8xBh2 and both sides have as many moves as they need. Impossible-looking checks are not necessarily impossible, at least once you know the capturing and en passant tricks.

I thougt it would be possible to get the f1 rook by g2 x f1=R, but it is not possible to get the Bisshop from c1 to g1 whitout moving the pawns on b2 or d2. I thougt then to promote a pawn by a7x b8=B but that's impossible because you either don't get the Bisshp away from a7 and b8, or you will have to move the pawn on b6. Then I had the to get the white pawn from a2 like xb3 ... xc4 ... xd5 ... until he gets on xf7 and then f8=B but I was not able to do that because ther were too few black pieces to capture on his way. (I got the pawn to e6, then there were only the black pawns, and the Kight on h2 left.)