1.
[{B:8/8/8/2N5/B1p1Q3/4n3/p3R3/B1kn2K}
{V:White to play and mate in two. Try your solution on the board.;e4b7;Correct;
That is incorrect.;A close look at Black's possible moves shows that in every single case White can reply with an immediate mate. It follows that a waiting move would solve the problem. But this is another typical example of deception by the composer. The solver is tempted to look for a way of preserving the status quo, but the solution depends on abandoning preconceived ideas and finding alternative ways of coping with Black's defenses.}]

2.
[{B:8/8/8/2N5/B1p1Q3/4n3/p3R3/B1kn2K}
All Black's moves allow immediate mate, for example if the d1-knight moves, then Bb2, or if the e3-knight moves then Qc2. Finally, 1...c3 allows 2 Nb3 mate. A waiting move would solve the problem, but there are no waiting moves, for example 1 Kh1? Nf2+, 1 Kh2? Nf1+, 1 Rg2? Nf2 or 1 Qg6? Nf5. The composer has arranged it so that the solver's natural inclination to preserve the existing mates leads to a dead end, and only some lateral thinking can provide the answer. White must retain control of b1, or else ...Kb1 prevents a mate, so it isn't too hard to find this move, even though it gives up all the mates already prepared. Now Black's moves are answered by a completely new set of mates, if the d1-knight moves, then 2 Qb2 (instead of 2 Bb2), if the e3-knight moves, then 2 Rc2 (instead of 2 Qc2) and finally if 1...c3, then 2 Nd3 (instead of Nb3).]