mate in 2 moves puzzle(s)

I have a puzzle that I have been struggling to solve on and off for months now. The challenge is to deliver a checkmate to the king in two moves. I am not kidding around here. Apparently, there is a solution, but I cannot seem to figure it out and thought I should seek out assistance from chess.com community.

BLACK
NG8,  PE7,  BG7,  PF6,  PC5,  KF5,  NH5,  PC4,  BG4,  PF3, PH3

WHITE
NC8,  BH7,  PG6,  PD5,  PH4,  BC3,  QE3,  PD2,  KH2,  NF1

The challenge is surprisingly difficult: If you are white, can you deliver a checkmate to the black king in 2 moves?  

Here it is in puzzle form

Alright. Cool!

I meant to do that, but how do bring the chess board into the forum thread like that?

here is one

The white knight on C1 should be on C8. 

This it a correct puzzle by ROLF__ which was completely corrupted by Tjornan's diagram.  I will change it slightly to turn it into a nice twin problem. The only difference between the next two diagrams is the position of the white king!

A.

B.

Kh2 on the first one

Bxf6 on the second

I don't know for sure. I added the white pawn f2 as an improvement to ROLF__'s version to get the B-diagram. I suspect that was the original problem, but in any case the solution is the same and correct!

The A-diagram is just my concoction but it is the logical partner of B.

I looked some more at this problem and found an even better zugzwang setting. This one clearly differs from the original, even though the solution remains more or less the same. Examine the "tries" in the analysis column!

Yes, I prefer to omit the 2nd move in a twomover since there are many variations of equal value. Solving just one of them is insignificant. You can read them all in the analysis column.

By the way, in formal solving contests, you are only required to provide the key move for twomovers. Unlike three- and more-movers which you must solve including the checkmate moves.

Interestingly, couple of years ago I bought an oldish set via an on-line auction. Written on the bottom of one of the knights was the name 'Feast', (well I assumed it was a name and not part of some bizarre eating game based on chess!).

When I researched the 'name' I discovered a book for sale in the USA by a certain 'Frederick Bonner Feast'. According to http://chesscomposers.blogspot.co.nz

Frederic Bonner Feast (12-02-1872 - 28-03-1941) British composer

A specialist of two-movers, Feast wrote a book about "Simple Two-Move Themes" together with Alain C. White and George Hume in 1924 as well as "Chess Cameos. A treatise on the two-move problem" in 1936.