Chess Online

Not so hard if you can envisage the mating scenario and work backwards from there.

The B turns out to be useless because it's on the wrong colour square. In a mating position, a1 must be covered somehow, but only the N can do that. In the mating position the N must be on b3 or c2 to cover a1; the white K must be on the other of these two squares so as to guard b2; that will leave either a2 or b1 that White has to cover somehow, but the B can't do that because the N will be blocking it. Since we have established that it must be the N that gives the coup de grace, the move sequence must end with the black K on a1 and the white N on b3 or a2.

The next thing to realise is that, to avoid stalemate, there must be at least two squares that Black can oscillate between, while White sets up the mating position. Suppose the other square is a2 (the reasoning is the same if the other square is b1). Then White's second last move must attack a2 with the N, while also threatening mate with the N next move. So black's K can't actually be on a2 at this point, because if it were, it would move off that square leaving a2 as a flight square after the next move of the N. The black K must be on a1 on the penultimate move, and must stay there; we require a means of closing off a2 as an escape square, and a little thought will show that this can only be done with the black P. Hence the B sacrifice, to force the P onto the a file.

The above paragraph sounds very convoluted on reading it back, but the conecpt is simple.