1.
[{B:4r1b1/1p4B1/pN2pR2/RB2k3/1P2N2p/2p3b1/n2P1p1r/5K1n}
{V:This is one of the most famous problems ever composed, and I apologize to those who have seen it before, but I am sure they will appreciate the pleasure it will give to those who do not know the solution. White to play, mate in three.;f1e2;Surprisingly, the many discovered checks available from rook and bishop don't lead anywhere, since the black king can escape by moving to d4 or e4. Solving this problem requires a massive suspension of disbelief.;Incorrect.;A typical solver, 'I've tried just about every legal move, and nothing seems to work. All those checks with the rook and the bishop don't seem to lead anywhere ... well, since I've tried all the sensible moves, I might as well look at the ridiculous ones. What about 1 ***? No, that's just too stupid - Black can simply reply 1...*** and I'll just have to go back again. Hang on a moment, maybe I don't have to go back  ... no, that can't possibly work, it's absurd ... but I don't see exactly why it doesn't work. Perhaps it does work ... yes, unbelievable!' Now all you have to do is fill in the blanks.}]

2.
[{B:4r1b1/1p4B1/pN2pR2/RB2k3/1P2N2p/2p3b1/n2P1p1r/5K1n}
{S:f1e2}
This is the stunning key. White not only allows Black to promote his pawn, but to give double check at the same time. The threat is 2 Rf7+ (or, indeed, anywhere else on the f-file) Kxe4 3 Bd3 mate. If Black doesn't promote his pawn, then the influence of the active white king proves the straw that breaks the camel's back, for example 1...Nxb4 2 Bd3+ Kd4 3 dxc3 mate, 1...Kxe4 2 Bd3+ Kd4 3 Rf4 mate, 1...Kd4 2 Rf4+ e5 3 Nxg3 mate, 1...Nc1+ 2 Ke3 Bf4+ 3 Rxf4 mate or 1...Rd8 2 Ke3 followed by mate from rook or bishop.]

3.
[
{S:f2f1}{P:BQf1}
1...f1Q+
Who could resist this move? At first sight White has to play 2 Kxf1, but then any chance of a mate in three has gone right out of the window.]

4.
[
{S:e2e3}
2 Ke3!!
From surprising to totally unbelievable. White just ignores the new queen, and leaves Black's pieces to do their worst. Someone glancing quickly at the position might think that Black should be able to mate in one, but in fact Black can't avoid a mate in one himself! Despite having ten different checks available, in every case White can mate by discovery with either the b5-bishop or the f6-rook.]
