Figure[White to move]

Now a variation on the current logic. Exchanging on d7 in front of Black’s back rank rook doesn’t work, but White looks for any checks he can give and finds one: QxN. If Black recaptures with his d7 rook, the resulting pattern should look familiar from the last few studies. White then plays RxRd8+, forcing Black’s other rook to interpose at c8; and now White mates by playing RxR with either of his rooks. Notice that Black does no better by replying to the original 1. QxN+ by moving his king to a8, because then White mates with 2. QxRd8+, RxQ; 3. RxR#.