so.. why did the black rook not take the knight on the first move?

The best puzzle I have tried 

I didnt get this one....... how this worked

Very good.

perfect moves

cause checkmate is then faster a fact

after knight c8, black can move pawn to f6 and he will prolong the game

good puzzle

nice!!!!

I tried many moves, finally got it, the hardest part, where to move the Queen,it was sacrifice..to smother.

The logic behind 1.Nc8 is that white cuts off the black rook from defending d8 threatening checkmate.  The logic behind 1..., Nd5 is to prevent white from having a direct shot at d8 as 1..., Rxc8 loses to 2.Qd8+, Rxd8, 3.Rxd8#.  The logic behind 2.Qb4+, is that black cannot play 2..., Nxb4 because of 3.Rd8#.  The logic here is not readily visible, but the moves played are the best for black unless you consider massive material loss as better than losing to checkmate.  Try looking through some of the earlier posts with diagrams to see how that is.

Cool mate.

nice one

Brilliant!!

rxnc8?

there is no way to avoid this mate and every move is forced.  if you deviate in any way it will cause a faster checkmate. yes

Not necessarily.  Black could play something like f6 as his first move and avoid immediate mate, but would lose material as a result.