Mate in 4 (from a real game)...with a cook :(

When I first arrived at this position, I thought the mate was forced.  Then I noticed that there is a way out (and only one) for White.  I'm still posting it though, because it's unusual to find a (nearly) unique solution in an actual game (and also because the final mate is rather nice).

At first, forgetting we should look for mate in 4, this was my idea:

I haven't considered 1... Rc6 probably because I thought it was inferior. But I didn't even see the possibility for that mate, which is brilliant.

Like you say however, 1... Rc6's weakness is that it does not cover white's escape route on the d file.

From the beginning you can clearly see that black has a deadly hold with that knight, blocked pawns, and the help of the rook. Immediately patterns of many knight and rook checkmates come to mind - of course, black being a knight and a rook up doesn't leave white with much counterplay.

In your line it probably goes 3. Kd1 Rd6+ 4. Kc1 e3 or something similar. Black queens and checkmates soon, so it might not even be inferior to 1... Rd6. Although 1... Rd6 has the satisfaction of keeping white inside the mating net.

Once again, I solved this one:  using my usual "Infinite Number of Monkeys" strategy.  Then, I was glad to see, in the alternate version, that One of my ideas Could have actually been successful, even though that annoying red "Incorrect" thing kept shooting me down--- you know, when you've seen that thing flash at you 10 or 12 times, you start to get irritated, even when you keep telling yourself "It's Just a computer-programmed message -- it doesn't Hate you.  What's the matter with you?!  There's nothing "personal" about it!  Chill out, why don't you?  for God's sake, what's the matter with you?!"

Perhaps I've said too much.  Thanks for the post ....