mate in 3

Nice puzzle but black does not have to take the rook there are different moves black can do.

then we have just d5!

But then it's not mate in three. Its a nice puzzle

I don't think it's a mate in three:

1. Rc5 b5....

I beleive Black can stretch it to a mate in five, but it's still inevitable.

It is a mate in three if white plays 1. Ra5+

How so?  The Black king will be able to flee to c5.

 1 Rc5 b5 2 axb5+ Kb6 3 Nc4#

You are correct, I missed it.

i think the puzzel is intended for pvp instead of pvcom....computer would never make such moves.

Good puzzle, somewhat unrealistic because there's the possibility of the mate in five variation.  But variations are inevitable in chess puzzles...