Took it not much time for the first and second moves but the third one ( involving the white King) was very tricky since I was trying hard to continue with the Knights duo. Very clever puzzle.
4 stars
@ jcOle: the mate is possible in 7 moves. I am not sure why you posted a 10 move mate?

Did you finally find out the solution?

although it's one of those that looks like common sense when you finally solve it.

Building the cage by controlling f7 and f8 was my first idea, but I didn't think Ne5-d7 was the way to do this. Even though I saw that the threat of Nf6+ and Nf7# would be there if the king could help out, I managed to convince myself that the king would get there too slowly.

Like jc0le, I then decided that White needed to sacrifice a knight and promote a pawn, and spent far too long trying to make 1. Ne5 Kg8 2. Ng6 work (the king escapes just in time). But I returned to the correct idea in the end.

jc0le, when you wrote "Once you realize the pawns are irrelevant", did you mean "Once you realize the pawns don't go anywhere"? For me, the point is to realize that the pawns are already doing an excellent job by denying Black's king access to g7 and h7, although working out how to exploit this is far from easy.

kicorse, yes i meant they don't go anywhere. Irrelevant wasn't the right word, but I was typing my thought process... I said irrelevant simply because after I worked out the 10 move mate above I realized worrying about the pawns was a distraction and they had to be left untouched in order to get mate in 7. As for the Troitzky line, it's what a lot of these 2 knight end game puzzles are based on. That's why I brought it up. When I said unfamiliar that was also not a good use of the word. I understand the concept but I'm not well polished on how to take advantage of its basic principles...

There's another website I use to play tactical puzzles that has thousands archived and it just hits you one after another with various puzzles. There's a good one on there with 2N 1K vs 1K and pawn. When I first saw this puzzle I thought I was going to have to work out a way to take advantage of the same premise that the Troitzy line is based on. I realized quickly that wasn't going to be the case. Basically, I got long winded and was explaining my thoughts with little detail.... similar to this post. heh