This is problem 24 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.
Black wins a pawn with 1. …, Rxf2. What is the best response for white in this setting?
First, suppose that the queens and rooks were removed from the position. Both sides have passed pawn; black has the pawn on c3, and now, because the f2 pawn is gone, black has a passed pawn on e5. Who wins the king and pawn endgame? Black should win. Why? Because black’s pawns can take care of themselves without the help of black’s king. Black can plan f5 and e4, and then black has a pawn chain with the h7 pawn at the base. If the white king moves past the e4 pawn, and assuming that white’s passed pawn cannot queen, then black advances his pawn up the board and will queen the e-pawn.
So black only needs to ensure that he can blockade the c-pawn with his king. Meanwhile, black can play a waiting game and gain additional advantages in his position.
We deduce that white probably wants to keep at least the queens on the board.
Let’s look at one option straight away: 1. …, Rxf2 2. Qxf2, Qxc1+ 3. Qf1, Qxf1 4. Kxf1 and black should win the king and pawn endgame. So 2. Qxf2 is not an option.
White has to move his queen. Let’s look at all options: Qa6, Qb5, Qc4, Qd3, Qd1, and Qe1.
2. Qc4 loses the queen outright.
2. Qa6 and black can pick up another pawn with 2. …, Rxg2+ 3. Kxg2, Qxc1. For this reason alone this is not a good option, but note that white also has the very strong 2. Qe3.
We can rule out Qa6 and Qb5 based on this same analysis.
2. Qd3, Rxg2+ 3. Kxg2, Qxc1 loses another pawn and the king is woefully exposed, but this keeps the queens on the board. This is the best option thus far.
2. Qd1, Qe3, and we saw above the challenges this poses for black. 2. Qd2, Qe3 3. Kh1, Qg5 4. Qg1, Rxg2 5. Qxg2, Qxc1+ 6. Qg1, Qxg1 7. Kxg1 and black wins.
So unless Qe1 is better, we are left with Qd3 as the best move for white.
2. Qe1, Re2 3. Qxe2, Qxc1+ 4. Kf2, Qxc3. The queens are there, but white has lost two pawns.
We have a choice between two evils. White appears to lose an additional pawn regardless of his move, but he can keep the queens on the board.
I might lean toward Qe1 if only because white’s king will not be as exposed since the g and h pawns remain on the board and are connected. Black will have to work hard to win.