Figure[White to move]

Again you want to see all of White’s threats and not stop with the first you see; for the ideas taken together are more powerful than any of them individually. First the queens are faced off against each other; and Black’s queen is pinned but protected by its rook, whereas White’s queen has no protection at all. Second, there is the hint of a back rank mate: Black’s king is stuck there; since White’s rook seals off f7, Qb8 almost mates—but not quite. Black has two pieces—his queen and rook—coordinated on c8; so White’s Qb8 is met with the interposition Rc8. Finally, with White’s rook aimed at f8 and his dark-squared bishop still on the board, White has the beginnings of a classic bishop and rook mate; if his bishop were aimed at f8, Rf8 would mate.

What to do with all this? Size up the impediments to each of these ideas and see if they somehow overlap. Your goal is not to make all of them work, of course; it is to put enough threats into motion to require Black to make sacrifices to stop them. For White to play QxQ, he would need to get rid of the protection Black's rook supplies to its queen. For White to mate on the back rank, he would need to stop either the rook or queen from guarding c8. For White to play the bishop and rook mate, he would need to get his bishop onto the a3-f8 diagonal. Any of these ideas—and certainly any two of them seen together—should cause you to toy with 1. Bd6. See the conundrum it creates for Black:

(a) If he replies with QxQ, White mates with Rf8.

(b) If he plays 1. …RxB, he no longer has two pieces coordinated on the same back rank square, so his interpositions there become useless and White mates with 2. Qb8+, Qc8; 3. QxQ+, Rd8; QxR#. (If Black were able to reply to Bd6 with QxB it would work better for him, since then his queen would guard b8 directly; but Black can’t play this because his queen is pinned.)

(c) Black could reply to 1. Bd6 with 1. ...NxB; but this interrupts the protection that Black's queen had been receiving from his rook, so now White has QxQ+ and mates promptly.

(d) Black's best bet is to let go of his queen and play 1. …h7-h5, creating a flight square—“luft”—for his king. When White plays 2. QxQ+, Black thus has 2. …Kh7. Now White has won Black’s queen—and still has a forced mate. One way it can go is this: 3. QxN+ (think in checks when you are closing in for the kill; this forks Black’s king and rook), Kh6; 4. QxR, Kh7 (Black has no pieces left); 5. Qe4+, Kh6; 6. Bf8 (pinning the g7 pawn), d4-d3 (nothing Black can do with his king makes it any safer); 7. Rf6+, Kg5; 8. Qf4#.