This is problem 156 from The Ultimate Chess Puzzle Book: 1001 Original Chess Puzzles to Challenge All Standards of Player, from Beginner to Grandmaster, by John Emms. Black to move.
In many cases, king and queen versus king and queen is going to be a draw unless there are extenuating circumstances or one side blunders. This is a classic example in which both sides queen a pawn at the same time but one side is able to mate.
Let’s suppose that we are not familiar with this type of position and let’s see if we can reason out the win.
It’s clear that if white gets a chance to check black’s king, then this is most likely a draw, unless black is in a position in which any check of black’s king results in the loss of white’s queen.
Were it white to move, white could check black’s king with Qc8, Qf8, Qh7, Qh5, and Qh3. Black cannot cover all these squares, so black must check the white king in order to avoid a draw.
Black can check with Qa1, Qd4, Qd7, Qg4, and Qg1. Which move do we assess first? Let’s start with options where the queen moves relatively close to white’s king, since such moves tend to limit options for white. Candidate moves include Qd4, Qd7, and Qg4.
Which move do we prioritize? We generally want to be certain of three things:
- We want to restrict the mobility of white’s king by keeping it closer to the corner; this also tends to reduce the mobility of white’s queen while it’s on h8
- We want to ensure that the queen’s mobility is not hampered by the king
- We want to ensure that we can check black’s king after it moves, especially checks which allow black’s queen to move closer; generally, having more checks gives us more options
After 1. …, Qg4+ 2. Kf8, the only reasonable check is Qb4, which moves the queen further from white’s king and allows white’s king to reach e8. We’ll rule out this move for now.
Let’s look at 1. …, Qd7+. Black’s king and queen work well together to restrict black’s king.
White has Kf8, Kg8, and Kh6. With any of these, we can get the queen closer to white’s king:
- 1. …, Qd7+ 2. Kf8, Qd8+ 3. Kg7, Qe7+
- 1. …, Qd7+ 2. Kg8, Qe8+ 3. Kg7, Qe7+
- 1. …, Qd7+ 2. Kh6, Qe6+ 3. Kg7, Qe7+
Black has mate in two after 4. Kh6, so 4. Kg8 and now the key move is 4. …, Kg6! This is the key position. White cannot check black’s king without losing the queen.
We can see that white has no reasonable option. If the white queen were not on the board, then black can mate in one with Qe8, Qd8, or Qg7 or mate in two starting with Qf7 or Qh7. It is simply not possible for white to guard against all such options.