This is tactical origami with fold upon fold of variations. Amongst the heavy artillery I liked the following scuffle:
1.Rg6 f6+
2.d5 e6
3.Nxe6#
Treasure everywhere in this one.

I found this one mystifying. Could someone enlighten me, starting with the purpose of Rg6?

The purpose of 1.Rg6 is to guard g4 so the black king doesn't have an escape square after 2.Nh3+, forcing 2...gxh3 & then mating with 3.Bg3#
Of course Black can always capture the rook but there's no defence from mate in 3...
1...fxg6+ 2.Nd5+ Bxd5+ ( 2...Rxd5 3.Qf8# ) 3.e6#

It was obvious that at some stage a white piece would move to d5, blocking both the black R and B. The question was, which piece? I could not see how to make it work.

In the end all three - the B, N and P - get the chance to do the deed, depending on Black's line of play.

I think the key to solving the puzzle (which I failed to do) is noticing that, unless the first move is a check, g4 needs to be guarded, and there are not many ways to do that.