Mate In 3

I was recently challenged by this problem and, I must recognize, it is really really hard and inscrutable. I don't know who has created this master piece, but it is completely impregnable and mysterious, and undoubtedly, a piece of art, because of its tricky solution.

All the moves you have thought will make checkmate in more than $3$ moves, or even won't, as Black plays $optimally$ . It is difficult to see how Black can avoid checkmate in $3$ moves, but, in fact, Black $can$ ... if you think about another variant that will give checkmate in exactly $3$ moves, post it as a reply and I will answer it.

As I said, all the moves that you have thought will make checkmate in more than $3$ moves... except this one:

$1.\quad Rh3\quad \quad \quad \quad b3$

$2.\quad Rh1\quad \quad \quad \quad bxh1=Q+$

$3.\quad Qxh1$ . Checkmate.

Thus, $Rook=5=V$ , $\left( { x }_{ 1 }=8 \right)$ and $\left( { y }_{ 1 }=3 \right)$ . The answer is $5\cdot 8\cdot 3=120$ .

I hope you appreciate the beauty of this problem as I did when I discovered the solution.

If you're overwhelmed, I invite you to search "The Dance of the Elephant" and Petrov puzzle "The Retreat of Napoleon I from Moscow".

What about moving the Rook to the square (2;2)? You will then get eaten by the enemy pawn. Then you move the Queen one to the left, the pawn eats the other pawn, queen moves diagonally to the white square to threat the King.

Alessio: If you move Rc3, the black pawn does not need to take the rook. And it shouldn't. Black would move b3. Rh3 looks like the only move to force mate in 3.

It is important to note two things:

1. Black is stalemated unless the white move unblocks or unpins one of black's pieces.

2. If the white Q had access to the long white diagonal it would be mate in one.

Turning the B loose has a problem since Bh2+ will provide a flight square if the Q captures or force the white king to move after which the black pawn promotes, or if the white king captures the pawn the B remains free to interpose or block, in all cases extending into too many moves. One might consider Rg3 allowing the pawn move and blocking the B check after a Q move. Unfortunately all those lines lead to blocks or interposition by the B that take an extra move for the mate on the long white diagonal. However, if the B has NOT moved the black king has no flight square. The answer then is to keep the B pinned and move 1. Rh3 to allow the pawn to move, 1...c3 then with 3. Rh1, force black to capture the rook at h1 with the B still pinned at b8, still blocking the flight square while black is otherwise stalemated.. After 2....gxh1=<anything> 3. Qxh1 is mate on the long white diagonal now that the pawn is out of the way.