So, did you solve the problem? Unlikely, but the following description of how I arrived at the solution will perhaps be of some interest to you.

The first thing you have to do is find a mating position. You need something to work towards, otherwise you will just wander off into the forest and, not having any breadcrumbs, end up lost.

So, what is a likely mating position? Black’s King in the corner would be the easiest way of getting checkmate. What about putting the Rook on a2, almost mate. If Black’s knight were on b1 it would be mate. But, if the knight goes to b1 (a white square) it must do so in an even number of moves (2) which would mean that Black’s King would have to move too.

What about N on c3, R on b1 or a2. That is mate. But can you achieve that position? Answer is no, the N can get to c3 in 2 moves, but the R can’t move to b1 in one move because Black is in check.

eg. 1…Kb2 2.Na2 Nd2 3.Nc3 Nb1 4. Rxb1 and the King is on b2, not a1.

What about a discovered mate? Move White’s King to c2 and play Nb3, doesn’t work. If the Black knight is on a2 it can always block the check with Nc1.

So if that doesn’t work, what if the King is on the edge of the board? You can quickly see that a simple idea like putting Black’s King on a3, White’s King on c3 and the R on a8 would be mate. This takes 4 moves again. You can’t get your King and rook close enough in only 3 moves.

Rule #1 in all endings is to get ALL your pieces into the attack. So, we need to use ALL our pieces, including the King. We saw that White doesn’t have time to bring his King to attack Black. Can we bring him to us? Ahh…there is the answer!

1…Kb2 2.Rd5 Kc3 3.Rc5+ Kd4 4. Nb3++