Chess Online

Really liked this puzzle, as one has to find all the responses black has to all of white's threats. So many close calls, it's one of the things that makes a great puzzle, IMHO.

Yes, there are multiple ways to mate after some of black's moves. That's simply because white creates so many threats with his first move, that black cannot defend them all. Depending on what black responds, white can mate with Qf3, Nd5, Bf6, Bd6, Rf3, Bd4. I don't think that's unusual for a great puzzle. What's generally important for a good puzzle is that the first move is unique, and in multi-move puzzles, that the main line also requires unique moves for the mating side. Obviously if the "opponent" plays less optimal moves, there will be more than one way to mate. I think that's generally understood. In this puzzle, there is only one first move by white that will allow mate on the following, no matter what black does. It's not easy to find, but is logical once you study it.

Nice day to you as well!

By multi-move (which precedes the quote about the main line), I mean generally 4+ moves, or even more so, endgame studies. In a 2-mover, the idea is often to create multiple threats in such a way that one response cannot defend against all of them or without creating another weakness. Bxe8 does not deserve a "!", as it does nothing against the 3 mates you rightly list. To me, the idea is 1. Ba6! which introduces Q or R f3 as the mate threat. The main reply (to me) would be 1...Bc6, cutting the coordination of Q+R. But now, white's bishop is eyeing the square e2, allowing a mate with the bishop.

With a two-move solution, I'm not sure we can really talk about "main-line", as it's so short. Yet there are clearly some tries for black that are better than alternatives (for instance Rg6, or R6h5 are just silly and allow multiple mates). But I don't think that that takes away from the greatness of the puzzle in requiring an absolutely precise first move.

www.theproblemist.org

See everything, especially page 6 onwards.

Apparently in 1932 they didn’t worry so much about duals on the mating move.