## Friday, October 02, 2009

### White to play, and mate in two

Today's puzzle is a special three-parter. You are asked to provide:
(a) white's first move
(b) proof that this is the only key move possible (that's to say, proof that the puzzle isn't cooked)
(c) the relevance (a) has to the Streatham and Brixton Chess Blog today.
Much kudos and cake to the reader who can provide us with three satisfactory answers. All will be explained soon . . .

Jack Rudd said...

Suppose white can castle. Then the white king has never moved, and so the rook from h1 cannot have got out of the bottom-right corner. What, then, is the rook on d4? It is not the king's rook (which never escaped), nor the queen's rook (which is still on a1), so it is a promoted pawn.

Now where did this pawn promote? If it did so on e8 or h8, the relevant black piece has obviously moved and so black cannot castle. If it did so on anywhere from a8 to d8, it got out via d8, and so must have displaced the black king along the way. And if it did so on f8 or g8, it must have either got out via f8 (again displacing the black king) or h8 (displacing the black rook).

So if white can castle, black cannot, because either his king or his rook has moved. So the key-move is 1.O-O-O! with an unstoppable threat of 2.Rd8#.

Anonymous said...

Yeah, I'd got that far as well, but two questions are still bugging me:

(1) Why isn't 1. Rxa7 just as good?
(2) What happens if White can't castle, and the rook on d4 is the original h1-rook?

It appears quite possible that the last moves were 1. ... Nc6-d4 2. Rd3xd4 b7-b6, for example, meaning Black can still castle and that is his defence to all three key-moves.

Anonymous said...

Actually, I think I sort of see now. If White were to start 1. Rxa7, then Black would claim 1. ... 0-0 as a defence. But because we are allowed to assume in problems that castles is legal unless proved otherwise, White must play it (1. 0-0-0) to prevent Black from castling in reply.

Relevance to S&B blog? Sorry, that one escapes me.

Jonathan B said...

Jack Rudd and our anonymous friend have the answer to the first move - as to the justification as to why it has to be 1. 0-0-0 I'm not qualified to judge (Morgan did exlpain it to me but I'm afraid the answer just didnt stick in my brain)

That leaves the relevance to our little blog. As a clue ... might I suggest you compare the solution to the question what's the first move with the title to the previous post?

Anonymous said...

1000 blog entries! Congratulations.

PG

Jonathan B said...

We have a winner. Today's blog entry - amazingly - is our 1000th post. To quote that great thespian Sir Vincent Jones, it's been emotional, but here's to the next 1000.

Morgan Daniels said...

Thanks Jack for the exegesis. It means I don't have too much left to add about a puzzle that really is spectacularly complicated in conception.

It's all about proving that both sides are not allowed to castle. If the Rd4 originally came from h1, then white can't; if it's a promoted rook, then it must have dislodged the black king along the way.

So to prove that he can castle, white castles! 1.0-0-0 makes 1...0-0 illegal.

This is why, Anonymous, 1.Rxa7 and 1.Rad1 are both no good--- because then black castles to prove that he can castle, meaning that white can no longer give mate in two.

Jack: you're going to have to share your prize with PG. Would you prefer the kudos or the cake?

Morgan Daniels said...

By the way, the puzzle is Armand Lapierre's baby, and it was published in Themes in April 1959.

Jack Rudd said...

Cake, I think. A nice Victoria sponge, or something.

Anonymous said...

Oh I wanted the cake as well. Maybe a chocolate gateaux.

PG

BlueRaja said...

"posted by Tom Chivers @ 10:00"
clever.

Tom Chivers said...

Well spotted BlueRaja; there's also another clue in the post.

I think PG deserves the cake!

Michael Goeller said...

Fantastic puzzle. I have to drop by more often.

Tom Chivers said...

I predict that about 999 posts after this one, there'll be one to which the solution involves 2.O-O-O.