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I suspect that the correct answer, "Rhf1" would be impossible for the viewer to show. That being so, I also supect that the reason TraglorfBob said to "move the rook from g2 to h2" was merely to provide a move (any move would do) that would expose the hint below the puzzle.
Think outside the box I suppose. The only 1/2 move available on the chess board.
I can see how if the king was in the middle of castling, there would have been 1/2 a move made when the king moved from e1 to g1. The second 1/2 of that move would be Rhf1, completing the castling move.
I guess the viewer must have at least one move for the designer to enter a message. The actual Rgh2 move has nothing to do with the solution, rather, it's a method of allowing the view to provide a message to the reader.
Creative, yet the viewer confuses things. I spent a bit of time trying to understand how Rgh2 was 1/2 a move and how Rgh2 could be considered checkmate.
I have another solution! It's a King's move. Lifting the King off the board is a 1/2 move. it's a discovered check by the Rook in h1. Checkmating in 1/2 move!
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