Interesting Puzzle from Anime: Kakegurui

From Season 2 Episode 10, the Tower of Doors. Among many puzzles Sayaka encountered, one of them is this interesting chess puzzle. With white to move, what is the quickest checkmate, and in how many moves?

Although there are many ways to checkmate within five moves, the correct answer can be rather surprising as it involve a move that is hard to spot. Can you find it out?

Credit: The original puzzle was created by Thomas Taverner. It was published on Dubuque Chess Journal on 1889 and won the first prize for chess puzzle. Visit https://www.uschess.org/index.php/May/Sam-Loyd-s-Organ-Pipes-and-Benko-s-45th-Anniversary.html for more similar puzzles

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Analysis:

Before diving into the solution, let's analyze the position first. White is up two knights, and has no king security concerns. On the other hand, black not only has an exposed king, but the rook on e8 is hanging. With no counter play from black, white is obviously winning. 

From a practical standpoint, 1. Nxe8 Bxh7 2. Qxh7 Rxe8 3. Qf7+ Kg5 4. Qxe8 helps white to win both black's rook and the bishop with the cost of a bishop and a knight. If black choose to take the knight, then 2. Qxe8 Bxh7 3. Rxh7 isn't significantly better - white still wins two rooks with the cost of a bishop and a knight.

Of course, our goal is to go for checkmate. One way to think about it is to find a check. The only safe check on the board is Qh6+. If black blocks with 1... Bg5, then 2. Rh4+ Ke5 3. Re4# is mate. The bishop could not take the rook due to the pin. When black went for Ke5 instead, then Rh4# is mate. The knight controls the escape square .

Another option for black is 1... Ke5. Then white can go for 2. Rh5+ Bg5 3. Qxg5+ Rf5 4. Qf5#. A faster mate is 2. f4+ Rxf4 3. Qxf4#

So far we have achieved mate in three. Which seems to be a good answer. However, upon engine analysis, I've found an even faster checkmate, in merely two moves. How come?

It is tempting to suggest 1. Nxe8 Rxe8 2. Qf5#. But white can defend by 1... Bg5 2. Qg4+ Ke5 3. Qe4#. 

To find the quickest checkmate, we have to look closer. Notice the black king has no escape square. In some ways, black is in Zugzwang. When black plays a move, it has to give up control on at least one square or blocking one escape square for its king, allowing white to play a move that would not have been mate. Let's say white play a waiting move that does not affect the position, like 1. Re1. If black plays 1... c3, then we have Nd3#. If black plays 1. ... Bxc7, then we have 2. Rh4#. If black plays Re5, we have Qg4#. Seems like if black plays any move, we have many different ways to checkmate it in the next turn. But does it means Re1 is the answer?

After analyzing all possible moves from black , we come across the only tricky move: 1... Bg5. White can only mate by 2. Qh2#, but there's a problem: we have a white rook there. 

It seems that we are getting very close to the answer. We simply play a waiting move that vacates the h2 square, allowing Qh2#. And that waiting move is 1. Rh1!!. 

After Rh1, whatever black plays, you should be able to find a way to checkmate it, and if 1... Bg5, then 2. Qh2# follows. So white can mate in two.