1.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
{V:White to play and mate in four. Try it on the board.;c6b4;Correct;
Incorrect.;White's main plan is to transfer his knight to c7. After 1 Nd8, for example, he threatens 2 Ne6 and 3 Nc7. At this stage it isn't obvious why 1 Nb4 and 1 Ne7 might be different, but of course it will turn out that only one of these three moves works. Black defends by 1...***, but White has the surprising reply 2 ***!, which appears to give White the time he needs to complete his knight maneuver. But then Black produces the truly imaginative defense 2...***!, which forces White to abandon his plan of playing the knight to c7. Now it suddenly becomes clear why White's first move is unique, because he needs to have the option of 3 *** with mate next move. Now just fill in the blanks.}]

2.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
Solving this problem is like peeling the layers off an onion. Attempting to bring the queen into the attack doesn't mate in four, for example 1 Qg3? Rg1! or 1 Qh4? Rh1! 2 Qd8 Rh7!, so White's main idea is to play his knight to c7. There are three possible routes, 1 Nd8, intending Ne6-c7, 1 Ne7, intending Nd5-c7 and 1 Nb4, intending Nd5-c7. At this stage it isn't clear why these three moves aren't equally good. This is the first layer.]

3.
[{B:k1K5/p7/P1N5/1P6/4pP2/2p1P3/pp6/r3Q3}
{S:c6b4}
1 Nb4!
Later on we will see why only this move works. Whichever knight move White chooses, Black has only one possible defense.]

4.
[{B:k1K5/p7/P7/1P6/1N2pP2/2p1P3/pp6/r3Q3}
{S:c3c2}
1...c2
If Black promotes with the check, then White's mating plans will be completely disrupted, so White must do something extraordinary to prevent 2...c1Q+.]

5.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/ppp5/r3Q3}
{S:e1c1}
2 Qc1!
This spectacular move is the second layer. White simply blocks the c-pawn, preventing the check. Now it seems that Black's resources are at an end because neither 2...bxc1Q nor 2...b1Q stops White's knight tour to c7.]

6.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/ppp5/r1Q5}
{S:b2b1}{P:BBb1}
2...b1B!
The third layer. This imaginative defense incarcerates Black's rook and sets up a stalemate. If White had chosen one of the other first moves, his knight would now be on either d8 or e7. In neither case would it be possible to mate in two, but with the knight on b4 there is one final layer ...]

7.
[{B:k1K5/p7/P7/1P6/1N2pP2/4P3/p1p5/rbQ5}
{S:b4d3}
3 Nd3!]

8.
[{B:k1K5/p7/P7/1P6/4pP2/3NP3/p1p5/rbQ5}
{S:e4d3}
3...exd3]

9.
[{B:k1K5/p7/P7/1P6/5P2/3pP3/p1p5/rbQ5}
{S:c1h1}
4  Qh1 mate.]