The Power of Checks and Captures

I was doing some group coaching last night at my chess club, and the first position up for discussion was the one shown on the right. It is Black to move and win.
This position comes from the game Fish-Abrahams, 1929, although my source was The Power Chess Program by GM Nigel Davies.
Now a problem like this is normally pretty easy to solve, but a position like this may not be. So let me explain.
If you are shown a position like this the act of it being shown to you is a big clue that some cleverness is afoot. And often knowing there is a solution is half the battle in problem solving. So armed with the knowledge that this is a "problem" trying anything and everything until you find the right move isn't a huge strain.
Now there are a couple of other interesting things about the solving process. My intention with this problem (and the others that followed) wasn't to see who could come up with the quickest or cleverest solution, but to aim for a systematic approach. In this case I impressed the need to look at all checks and captures. While most players know the importance of this rule, due to mental laziness we often look at "some" checks and captures. This is because we either dismiss some moves as "stupid" and don't even try them, or more commonly, we look at the first couple of checks or captures and then decide that the third capture (out of 6 or 7) "must" be the right move and proceed to ignore everything else.
Interestingly enough it was the more experienced players who fell into this trap, and it was a newer player who said "lets try 1... Qxf3", which turns out to be the correct move. Nonetheless this was also an exercise in calculation and while they found that 2.gxf3 Bh3+ 3.Kg1 was forced, they hit a wall at this point, mainly because they weren't allowed to move the pieces. After that restriction was lifted, they quickly found 3... Nxd4 4.Qd1, although it then took a little time to spot 4. ... Re1+ 5.Qxe1 Nf3#
As an exercise in Checks and Captures it was great, as every Black move is either a check or a capture. As an exercise in disciplined thinking it was also good, as the key move was a move that the casual observer may discard (although the experienced chess player might find simply because it is a chess problem).
But there is a small sting in the tail. While trying to impress on the players that Black won by choosing a "less obvious" move, we gave White no such leeway during the solving process. The trap that the group (including myself) fell into was assuming that 2.gxf3 was forced for White, when the non-capturing 2.Ne2 leaves 2 Black pieces still under attack. Of course Black can emerge with an advantage with 2... Nxd4 3.Nxd4 Q runs away, but it isn't the forced mate/win that the combination seems to be.