Chess Online

Also check puzzle #1762

I visited puzzle #1762 which was composed in 1959. It was exactly similar other than the composer added a rook and two pawns.

Could it be considered plagiarism?

1.Qxb5 Kxa3 (only legal move for black) and then wut?

Of course it's a winning position for White even after 1.Qxb5 Kxa3, but I don't find any checkmate in the next move

It took me a bit, here's how I narrowed it down:

In the initial situation the Black king could take either of the knights. However, the knights need to stay where they are because they prevent the Black king from escaping to the c-file. If White allows the Black king to escape to the c-file, the king is out in the open and there's hardly any chance to deal a mate in the second move, regardless of what the first move by White was.

Hence, the knights have to remain where they are in the first move.

This implies that the Black king will have the option of taking either knight after White's first move unless White's first move protects one of the knights (but White can't protect both knights). From the initial position, if you remove the knight from a4 in your mind and place the Black king there, there can be no mate in the second move even if the white queen could teleport herself anywhere, because from a4 the Black king has three escape squares: a5, a3, and b3, and there is no square from where the White queen can control _all_ of a5, a4, a3, b3 -- except for the square b4, but that is unprotected and White has no first move that allows to protect the queen on b4 if we don't allow the knights to move:



Hence, it is clear that White's first move has to disallow the Black king from taking the knight on a4, i.e., White's first move has to control the square a4.

(Note that if you do the same exercise but picture the Black king on a3 instead, then you don't get that problem. Here, if the White queen can teleport herself to a2, she controls all relevant squares and it's a mate:



So you could imagine the line 1. Qd5+ Kxa3 2. Qa2# as a possible line of the putative solution for example.)

Once you know that you can't move the knights in the first move and that your first move has to control the square a4, only four possible first moves remain: Qa8, Qa7, Qa6, and Qxb5. From each of those you have to consider the responses Kxa3, bxa3, and bxa4 and deliver a mate in one from there. That's basically 4*3=12 possible lines and it's easy to see that only Qa6 works for all three possible responses by Black.

A bit of a twisted train of thought I admit, but it worked for me.