1.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
{V:White to play and mate in three. Try your solution on the board.;d7h3;Correct;
Incorrect.;Black threatens to play ...Kc7, when White's bishop will be attacked. If White spends a tempo saving the bishop, then he will have little chance of mating in three. So suppose White plays 1 Bf5, for example. Black replies 1...Kc7, and after 2 Qxa6, threatening mate on c8, the king just runs away by 2...Kd8. How can White improve on this line by again aiming to mate on c8, but at the same time preventing 1...Kc7 followed by 2...Kd8?}]

2.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
White's main problem is to deal with Black's defense 1...Kc7. The temptation is to prevent ...Kc7 directly by playing 1 Qxe5, but then Black replies 1...a5 and, even though White's pieces appear very menacing, there is no mate in two. 1 Qh5 is a cunning idea, so that 1...Kc7 can be met by 2 Qe8 and 3 Qc8 mate, but again 1...a5 is a satisfactory defense. This leads to the idea of transferring the queen to c8 by another route, but after 1 Bf5 Kc7 2 Qxa6, for example, Black slips away by 2...Kd8.]

3.
[{B:8/pk1B4/p7/2K1p3/8/8/4Q3/8}
{S:d7h3}
This surprising move clears the way for 2 Qg4 and 3 Qc8 mate. It also copes with the defense 1...Kc7 2 Qg4 Kd8, because White has the mate 3 Qd7 ready. Black has only one way to meet the threat.  1...a5  If now 2 Qg4, then 2...a6 and Black has created a flight square for his king on a7. While the move 1...a5 has prevented one mate, it has opened the door to another, far more spectacular, possibility.  2  Qa6+!  White suddenly changes plans and sacrifices his queen.  2...Kxa6  Forced, or else Qc8 mates.  3  Bc8 mate.]
