knight knight: Sunday. Ok black's 35...Qxf1# threat means we can eliminate a lot of moves, the only ones that don't lose immediately are:
35. h3, 35. h4, 35. Rxe1, 35. Rc7+, 35. Qg7+, 35. Qh7+
and I'd say the solution is white to draw by perpetual check.
a) 35. h3 Qxf1+ 36. Kh2 Qg1+ 37. Kg3 Rxf3+:
ai) 38. Kxf3 Re3+ 39. Kg4 Qxg2+ 40. Kh5 Qxh3+ and 41...Qxh8 queen + three pawns ahead
aii) 38. Kg4 Qxg2+ 39. Kh5 Qxh3+ 40. Kg6 Qxh8 41. Rxe1 queen + three pawns ahead
b) 35. h4 Qxf1+ 36. Kh2 Qh1+ 37. Kg3 Qxh4+ 38. Qxh4 gxh4+ 39. Kxh4 Rxc1 two rooks ahead
a) 35. Qg7/h7+ Rf7 36. Rc7+ Kd6! no more decent checks
b) 35. Qh7+ Rf7 36. Qd3 Rxc1 no more perpetual and Q/Rxf1+ on the next move
c) 35. Qg7+ Rf7 36. Qxg5+ Kd7 37. Rc7+ Kxc7 no more decent checks
a) 35. Rxe1 Qxe1 36. Kg1 (if 36. Qh7+ Kd6 is now possible) Qe3+ 37. Kh1 Qf2 the bishop is lost... 38. h3/h4 Qxf1+ rook ahead, white has no perpetual
b) 35. Rc7+ Kd6:
bi) 36. Qd8+ Ke5 white's rook gets in the way... 37. Qh8+ Rf6 no more decent checks, white must play 38. h4 Rxf1+ 39. Kh2 Qxh4+ 40. Qxh4 gxh4 41. Rxb7 black is a rook ahead, or 38. h3 Rxf1+ 39. Kh2 Qg1+ 40. Kg3 R(1)xf3+ 41. Kg4 Qxg2+ 42. Kh5 Qxh3+ and 43...Qxh8 with mate very soon
bii) 36. Rd7+ Kxd7 37. Qg7/h7+ Kd6 no more decent checks
biii) 36. Rc6+!! this has to be the move, found by process of elimination, but it works as follows:
a) 36...Ke7 37. Rc7+ repeating
bi) 36...Kd7 37. Rd6+!! Kxd6 38. Qb8+ this is the position we want, will call it 'Position A' and discuss it more in a mo
bii) 36...Kd7 37. Rd6+ Kc7?? 38. Qd8#
bii) 36...Kd7 37. Rd6+ Ke7?? 38. Qd8+ Kf7 39. Rd7+ Kg6 40. Qg8+ Kf6 (40...Kh5/h6 41. Rh7#) 41. Qg7#
c) 36...Kxc6 37. Qc8+ (37. Qc3+ Kd6) Kd6 38. Qb8+ the same 'Position A'
d) 36...bxc6 37. Qb8+ this we'll call 'Position B'
Ok, in Position A we see the black king can't find refuge on the queenside, e.g. 38...Kc6 39. Qc8+ Kb6 40. Qd8+ and the king must return to c6.
Let's try the kingside, 38...Ke7 39. Qc7+ Kf8 40. Qd8+ Kg7 41. Qe7+ Rf7 42. Qxg5+ the queen checks along the d8-h4 diagonal and also the h6 square if need be. Black's rook actually gets in the way of his king here.
The other try is to escape via e5, but this fails to a skewer trick. 38... Ke7 39. Qc7+ Kf6 40. Qd8+ Ke5 41. Qc7+ Kd4?? 42. Qc5+ picking up the queen with a winning material advantage
In Position B the queenside escape is impossible, the kingside escape fails as in Position A, plus the king still cannot escape via e5... 37...Ke7 38. Qc7+ Kf6 39. Qd8+ Ke5 40. Qc7+ Kd4?? 41. Qxa7+ c5 42. Qxc5+ again picking up the queen.
I'd better be right after an hour of analysis!!