Saturday, March 15, 2008

Cecil's Saturday Puzzle - March 15, 2008

from the Winnipeg Free Press, March 15, 2008

White to mate in 3 - Healey

It's been a long time since I last tried these mate in 3 composed problems. The Saturday problem has a long tradition in the Winnipeg Free Press; the first one I attempted was in 1971.
But they go way back.

Anyway, on to this one. Let's look at the basic features.
The Black king has no squares, it just needs to be checked without block or capture.
Black's knight can't move because of the mate on d6.
The Bishop has to cover the mate on c6, so only Bd7 and Be8 avoid immediate checkmate if it was Black to move.
The knight on b6 is protecting the pawn on d5, otherwise I would like to try moving the knight and delivering mate on b6.
The bishop on a1 is bothering me - what is the relevance of this piece ?

My first try is
1. Rxf4 threating Rxc4+ and then Qc6 mate
then 1...Bd7 2. Nxd7+ Kxd5 3. Rd4 mate, but 1...Be8 is ok
2. Rxc4+ Kb5 and the king runs away via the square vacated by the bishop.
Then I spent half an hour trying other ideas that didn't get too far; I ran out of moves. Then I gave up.
I checked the position with an engine that just happened to be handy and it did not find a mate in 3, but a few mates in 4 which I had already discovered on my own. Concerned, I checked with the author of the column; he suggested 1. Rh1. Sure enough , if I show this to those engines, they say, yes, that would be a mate in 3.
So I tried it with some other engines; Shredder 10 and the old Fritz 5.32 both find 1.Rh1 instantly.
I would like to hear from anyone whose engine does not find 1.Rh1.

Anyway, the point of 1. Rh1 is that White will play 2. Qb1 threatening mate on b4 or 3. Qg1 mate. If you saw this "triangulation" idea without assistance you are quite clever !

So what about the bishop on a1 ? Well, if you remove it, Rg1 still mates in three. But the bishop's absence would introduce a "cook", or alternate solution, in this case 1. Ra1. Note the bishop is the only piece that can be placed on a1 !


Anonymous said...

This problem is very famous as it the first problem that implemented the now infamous Bristol Theme. D. Langner

Chess Manitoba said...

Interesting ! Thanks, David.
Do tell more ! Why infamous ?

Anonymous said...

I think one of the best explanations is here

If you notice the 2nd diagram down is the problem from Cecil's Column. The beauty of the problem is that the rook is in the way of the queen to get to g1 hence the bishop on a1 to remove any cooks. There are many more problems that use this theme. I'd say infamous for that and because of the ascetic beauty of the rook moving to a seemingly useless square in an apparently non-sensical way.

Dave Langner


Anonymous said...

My Fritz can't see it. :(