1.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
{V:White to play and mate in four. Try your solution on the board.;h3f5;Correct;
Incorrect.;White would like to play Ra2+ followed by Qb4 mate, but the immediate 1 Ra2+ fails because 1...Qxa2 pins White's queen. On the other hand, White has no time for the cautious 1 Kf8, because then Black can bail out with 1...Qb2!, which delays mate beyond the fourth move. White must remove his king from the a2-g8 diagonal 
with gain of tempo. How?}]

2.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
The combination which leaps to the over-the-board player's eye is 1 Ra2+ Qxa2 2 Qb4 mate, but this doesn't work because ...Qxa2 pins White's queen. If White plays the preparatory 1 Kf8 (1 Kg7 is met the same way), then 1...Qb2! prevents Ra2+ and delays mate beyond the fourth move. Another idea is 1 Bg2, intending 2 Bd5 and then 3 Ra2+, but Black plays 1...b5 and White has to waste time moving the queen. White must move his king off the dangerous a2-g8 diagonal with gain of tempo, and this is where the bishop on h3 comes into the scene.]

3.
[{B:8/1p3K1p/8/5p2/2Q2P2/k1P4B/3R4/1q6}
{S:h3f5}
1 Bxf5!
The solution to White's dilemma, if Black doesn't take on f5, then the bishop has entered play with gain of tempo. Then White's attacking force is too much, for example 1...b5 2 Qc5+ Ka4 3 Bxb1, 1...Qb3 2 Be6! Qxc4 3 Bxc4 and 4 Ra2 mate, or 1...Qb2 2 Qc5+ Ka2 (2...Ka4 3 Rxb2 and 2...Kb3 3 Qb4+ also lead to mate) 3 Qa5+ Kb3 4 Be6 mate. And if Black does take on f5 ...]

4.
[{B:8/1p3K1p/8/5B2/2Q2P2/k1P5/3R4/1q6}
{S:b1f5}
1...Qxf5+]

5.
[{B:8/1p3K1p/8/5q2/2Q2P2/k1P5/3R4/8}
{S:f7e7}
2 Ke7!
Despite the open position, this careful choice of square leaves Black without a reasonable check. Black can give up his queen, but this only delays mate by one move. Consequently, there is nothing better than to stop the threatened mate on a2.]

6.
[{B:8/1p2K2p/8/5q2/2Q2P2/k1P5/3R4/8}
{S:f5b1}
2...Qb1
And now the original idea appears in full force.]

7.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/3R4/1q6}
{S:d2a2}
3 Ra2+]

8.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/R7/1q6}
{S:b1a2}
3...Qxa2]

9.
[{B:8/1p2K2p/8/8/2Q2P2/k1P5/q7/8}
{S:c4b4}
4 Qb4 mate.]