Is My Tactics Book Wrong?!

Hey everyone, the start of summer has given me the drive to break out some of my unfinished tactics books. Currently I am going through "303 Tricky Checkmates" by Fred Wilson & Bruce Albertson. Problem #245 (on page 142 if anyone has the book) is supposedly a "White to Move & Mate in 3" problem, yet I believe white can do it even easier in just two moves. Here is the problem with the book solution which is 1. Kf6 cxd6 2. Ke7 dxc5 3. Nf6#:

My question is, couldn't this problem be solved in just two moves with 1.Ne6 cxd6 (forced) 2. Nc7#. That is what I saw at first and was confused when I read through the book answer. Have I outsmarted the masters? (Jokes!) But I believe that's a simple, legal checkmate that occurs an entire move faster. Am I mistaken somewhere?

1. Ne6 allows black to defend in a new way by playing 1...c5. After that, the black king can escape to c6, so there will be no mate in two.

This has happend to me alot in that book. It's really tricky to see everything in some positions.

Ahhh duh! How did I not see that before? I swear, tunnel vision sometimes...Thank you very much CM ilmago. AtahanT, it really does live up to it's title of "tricky" checkmates doesn't it?!?!

I remember this position. Isn't it composed by R. Zangger or something like that

Also, a book with a bunch of composed problems isn't really about tactics training more about "seeing" nice things on a chess board

I'm not sure heinzie, I don't think it says where they get the problems from.

It's a good way to train visualization and calculation accuracy. You really need to calculate accurately to solve many of these.