By the way, I forgot to include the alternative solutions for the first puzzle in this thread.
Don't cheat!
Moving the Queen to g5 actually expedites the checkmate by a full move, thus:
1. Rxe5+ Qg5
2. g4+ Kh4
3. g3#
Using the Rook to defend against the checkmate results in mate in the same four moves, as in the original puzzle, thus:
1. Rxe5+ Rf5
2. Rxf5+ Qg5
3. g4+ Kh4
4. g3#
One variant will lead to checkmate in five moves, thus:
1. Rxe5+ fxe5
2. g4+ Kh4
3. Qe7+ Rf6
4. Qxf6+ Qg5
5. g3#
Since all possible responses result in checkmate, it's strange that Nona Gaprindashvili decided to go for a draw instead.
Here's the layout of the board, as given by Forsyth-Edwards Notation (FEN). Just copy and paste, then go to
ChessUp.net and enter it there and try to figure out the solution online.
7r/4R1Qp/p4p2/4p2k/P3P3/4q1PP/6PK/5r2