Mate in 3. Cannot solve

Hey all. I was helping a friend with his chess problems. I cannot figure out how white mates in 3. Can anyone help?

Took me a while but managed to solve it eventually. The first move 1.Nd4! threatening 2.Ne2 is not too hard; what's hard is figuring out how to continue after 1...Qc2, since either 2.Ndxc2? (for 3.Rd1) or 2.Nexc2? (no threat) is defeated by 2...Nd2. It turns out that because the Q is needed on c2 to stop both N mates on e2 and b3 (not to mention Rd1 mate), White can M2 from here by putting Black in zugzwang, and the only pure waiting move is 2.c5!! Then the Q must unguard one of the mates, e.g. 2...Qxd3 3.Nb3, 2...Qa4 3.Ne2, 2...Qd1 3.Rxd1. 2...Nd2 also allows 3.Ne2. There's no other waiting move for White besides 2.c5!!, e.g. 2.Kh7? Qxd3+!, 2.Kg8/Kg7? Qg2+!

Oh my gosh. You are an actual genius! THANK YOU! haha, been racking my brain for days now. What an awesome puzzle! 

I have that book.

That's such a cool puzzle. Shows zugzwang in its true form

wow that's was hard thx to rocky64

there is mate in 2!!! 1.a8=Q+ Qe8 2.QxQ# kappa

a8=Q is not legal...

Why not??

1. The square you are looking at is h1, not a8. I know, confusing. 

Therefore, white promotes on h8 and a8, which is on the "top" corners. 

how do you know this tho? there is no coordinates on a given diagram

The OP is 1600. 

If it were that easy, he wouldn't be spending 3 days to solve this problem. Also, if it says "white mates in 3 moves," there is a mate in 3, and not any faster. 

so u saying that both kings traveled to opposite sides of the board?!? TRAVESTY

Many positions are just studies, and not from real games. 

That was a cool puzzle.

It is simply a convention. This diagram is a composition and the field of chess compositions has some rules of its own. One of them is: Never give coordinates; white is always on the lower side of a diagram.

Note that the Daily Puzzles follow this convention as well. They even switch colours in real chess games to make sure you always play white and white always plays bottom up. They do add coordinates though, which is redundant.

Another composition convention is that white always starts except in some defined cases. It is sufficient to state #3 (checkmate in 3 moves) since it is always white's duty to perform. 

There's a zuzgwang in the puzzle

Nd4 Qc2

c5 Nd2

Ne2#

That's what Rocky64 wrote in post #2. Plus other interesting tidbits.