So After Rc8+, Rxc8, Rxc8, Bxc8, the queen goes to d8 giving mate.
Bobby Fischer teaches Chess wrong exercise?

Yeah but what if Bxc8 first instead of Rxc8? Then Black would have a rook at the end of White's combination, right?
Yeah but what if Bxc8 first instead of Rxc8? Then Black would have a rook at the end of White's combination, right?
No because white would not play Rxc8 if black took with the bishop first he would just mate with Qd8. See first variation posted by Roger438 above.

Oh, now I got it LOL, thanks for the patience and explanation guys, i hadn't seen that the bishop would block the way and allow the mate

Bobby Fischer Teaches Chess...a book review...
https://www.chess.com/blog/RussBell/bobby-fischer-teaches-chessa-book-review

Oh, now I got it LOL, thanks for the patience and explanation guys, i hadn't seen that the bishop would block the way and allow the mate
Now I get it too. Thanks for asking the question, I had the same wrong thinking as you.

So I was passing through this page at Bobby Fischer teaches Chess and I think this exercise is wrong, because the book says that the mate here is possible, but gives a bad explanation.
If Black captures the first rook with his bishop and then white captures the bishop with his rook, black will capture the second white rook and still have a rook protecting the back rank. Am I wrong or missing something?
No. Well. Qd8# after al white rooks are captured.
If Black captures the first rook with his bishop and then white captures the bishop with his rook, black will capture the second white rook and still have a rook protecting the back rank. Am I wrong or missing something?