2 edited body
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This question really needs a diagram with this position:

[FEN "8/8/4P3/3p4/2p3p1/1pP1kPPp/1P5P/R3K2R w KQkq - 0 1"]

White to mate in 3.

Tim Krabbé and Max Pam found the loophole in the rules that you are asking about -- when they composed this problem in 1972, the promoted rook did indeed enable castling, as the rules only talked about a rook that hadn't moved yet! The rule was changed because of this problem.

The solution is beautiful as there are three different castlings involved:

  1. 1.e7 Kd3 2.e8=Qe8=R gxf3 3.0-0-0#.
  2. 1.e7 Kxf3 2.e8=R d4 3.0-0#.
  3. 1.e7 Kxf3 2.e8=R Kg2 3.0-0-0-0#!.

This question really needs a diagram with this position:

[FEN "8/8/4P3/3p4/2p3p1/1pP1kPPp/1P5P/R3K2R w KQkq - 0 1"]

White to mate in 3.

Tim Krabbé and Max Pam found the loophole in the rules that you are asking about -- when they composed this problem in 1972, the promoted rook did indeed enable castling, as the rules only talked about a rook that hadn't moved yet! The rule was changed because of this problem.

The solution is beautiful as there are three different castlings involved:

  1. 1.e7 Kd3 2.e8=Q gxf3 3.0-0-0#.
  2. 1.e7 Kxf3 2.e8=R d4 3.0-0#.
  3. 1.e7 Kxf3 2.e8=R Kg2 3.0-0-0-0#!.

This question really needs a diagram with this position:

[FEN "8/8/4P3/3p4/2p3p1/1pP1kPPp/1P5P/R3K2R w KQkq - 0 1"]

White to mate in 3.

Tim Krabbé and Max Pam found the loophole in the rules that you are asking about -- when they composed this problem in 1972, the promoted rook did indeed enable castling, as the rules only talked about a rook that hadn't moved yet! The rule was changed because of this problem.

The solution is beautiful as there are three different castlings involved:

  1. 1.e7 Kd3 2.e8=R gxf3 3.0-0-0#.
  2. 1.e7 Kxf3 2.e8=R d4 3.0-0#.
  3. 1.e7 Kxf3 2.e8=R Kg2 3.0-0-0-0#!.
1
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This question really needs a diagram with this position:

[FEN "8/8/4P3/3p4/2p3p1/1pP1kPPp/1P5P/R3K2R w KQkq - 0 1"]

White to mate in 3.

Tim Krabbé and Max Pam found the loophole in the rules that you are asking about -- when they composed this problem in 1972, the promoted rook did indeed enable castling, as the rules only talked about a rook that hadn't moved yet! The rule was changed because of this problem.

The solution is beautiful as there are three different castlings involved:

  1. 1.e7 Kd3 2.e8=Q gxf3 3.0-0-0#.
  2. 1.e7 Kxf3 2.e8=R d4 3.0-0#.
  3. 1.e7 Kxf3 2.e8=R Kg2 3.0-0-0-0#!.