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11171 --- why doesn't the king just take the rook (Kxd7) when the rook attacks?---
Because 1. Rxf7+ ...Kxf7 2. Rf2+ ...Qf5 ( ...Kh8 3.Qe6# ) 3. Rxf5+ ...Kh8 4. Qe6#
still an mateinfour
Why doesn't black play Kg7 on the return of the first move?
I do not understandthat that after the first move of white, why the black king spare the rook?
Nice checkmate !
He doesnt take the rook becasue then rg2+ forces kh8 which leads to qf6#
why did the king not eat the rook on the first attempt?
If Black played Kxg7, as you suggest, what would you play next ?
I got the answer - if black played Kxg7, then mate in 3 - Rg2+, Kh8, Qf7#