This pins the knight. If white follows 3. BxN, then we have 3 … KxB, and while white is still in control, the position has fallen apart. (I think black can last long enough to force white to harvest some pawns before mating)
I think the best move after 2 … Nd7 is
3. QxR Na3
4. QXN+ Kb1
5. Qa2++
But I could be wrong. I’m doing this in my head, too.
Well, I just played it out, and 3. QxR leads to
3. QxR c7xb6
4. BxN+ NxB
5. Qa8+ Nb8
6. Bd6 Kd7
7. QxN e5e4
8. Qc7++
but 3. BxN led to
3. BxN+ KxB
4. b6xRa7 c6-c5
5. axb8=Q e5-e4
6. Qb8d8 ++
I played against “Carrie” (rating 651) on Chessmaster 8000, so both sets of moves are probably full of mistakes.
Correct me if I’m wrong (I suppose that goes without saying): while not strictly correct in a “purist” sense, couldn’t you get away with having black on the right simply by having black go first?
I looked at it, and got the King to d4 mate, then started thinking, no, that one black pawn covers covers that square. Then I read about the board orientation/rotation angle.
(This far in, this late spoilers are unnecessary, no?)
Since the problem is a mate in one, you don’t need to go past “Of course, this isn’t mate in one”. Most mate-in-n problems are an easy win for one side (though not all).
Took me less than thirty seconds to spot it - once you have eliminated the impossible, whatever is left must be true (and only then did I notice the orientation).
“Helpmate” doesn’t entail a refusal to move out of check when you can - even in a helpmate problem, the final move must be checkmate according to the laws; the defender cooperates only on the previous moves.
Yes, but … She won’t play me at chess any more, because I always win. I think she’s better at seeing the ‘big picture’, or ‘thinking outside the box’, or something.
This problem is driving me nuts. I think I might have two solutions:
Is it that the board is upside-down? White’s last move was pushing a pawn up and promoting to a bishop? Black’s king would have been on h2 and moved to h1. What are the other solutions? I guess one would be a white pawn capturing a black piece on g1. Then the third?
[spoiler]It’s solvable with the board the right way round, so that the black king would have just moved to a8.
There is more than one way to deliver check…[/spoiler]
Unlike the first one, this is not a trick.
The board is the right way round and both sides have played legal moves.
Here is a hint:
Black has just moved. It could have been a capture!
Yes. Solution in spoiler. Black played KxN, White had just played N-R8+ (discovered check)
The second position is nice too - two solutions each entailing a subpromotion, on different squares for each. 
I thought about the discovered check, and I thought about black capturing a piece, but somehow never managed to combine the two. So what are the other two solutions? Are they the ones I suggested?
There’s only one basic solution.
Black must have just played Ka7 x Na8
I suppose they mean that White’s last move could have been either:
Nb6 x Ba8 or
Nb6 x Na8 or
Nb6 x Qa8
Not really interesting enough to be separate solutions in my eyes.
I’ve found an extract from the book of the Smullyan problem, plus another beautiful retro problem:
Yay. Looks like my original solution was presented as well. 
I should have been more precise with my wording. ( I will admit that I thought there was a mate-in-one on the original set up, but I was obviously wrong.)
In my experience with Chess puzzles, it is often the case that the answer does not end up with one side mating or the game even ending. With that in mind I think a valid answer would be:
White gets the Queen and a kNight for a Rook and a Pawn. I’s not a mate-in-one, but I’ve seen similar puzzles that have been titled “White to move and win.”
I haven’t had a chance to look at the other links provided, but thanks in advance anyway. I’ll bookmark all of them. I’m a big fan of Chess puzzles despite having lost my last two contests against my 8 y.o. son.
And had this one said “White to move and win” you’d have been good to go. But when the stipulation is “Mate in X” then any win in more than X doesn’t count. Denial of this will cause you to lose more against your eight-year-old son in future. 
[chess geek ON]Chess problems are composed positions that involve a checkmate in a stated maximum number of moves.
The vast majority are mate in two, but you can also see:
and some other variants…
Here’s a simple one - White to move and mate in 2 moves
White: King f8, Rook h1, pawn g6
Black: King h8, Bishop g8, pawns h7,g7
Chess studies are composed positions that require accurate play to achieve a clear win (or to reach a solid draw from a desperate-looking position). Play stops when a ‘known’ position is reached.
Here’s a simple looking one (it’s not!)
White to play and win
White: King c4, pawn e4
Black: King e8, pawn e6
[/chess geek OFF]
Here is a problem that does not involve checkmate, and I have seen plenty of others like it. I’m not sure where problem and study are defined as you indicate, but I don’t believe there has to be a mate involved. I have even played out problems titled, white (or black) to move and win where the solution does not end with mate and found myself unable to beat a computer using the final arrangement.
Somewhere around post #19 there was some consideration as to how the incorrect set up might be played out and I was commenting on that. I can see that my scenario is not a mate-in-one and that white hasn’t won the game.
I realize the question is moot since it’s an illegal set up but, FWIW, I once played an opening with a friend only to realize that I had interchanged the knights and the bishops when I set up the board. He told me that when he was learning to play, if he didn’t notice a set up like that then he had to play with the pieces as they were.