johnlspouge: Sunday (Insane): White to play and win.
Material: Down N for B+P. The Black Kh7 has 1 legal move, to h8. White has a c-file battery, Rc1 and Rc7, with Rc7 on the same rank as Nd7, Bg7, and Kh7. The Black Nd7 might be embarrassed if it has to retreat. Other than diffuse pressure against the Black position, however, the only immediately obvious strategic theme is a heavy piece invasion. The White Nf3 and Ba3 are relatively inactive. The White Qb5 is threatened by Ba3, requiring an immediate response.
Candidates (31.): Qxd7, Qc6
31.Qxd7 Rxd7 32.Rxd7, threatening
33.Rcc7 34.Rxg7+ winning 2Ns for R.
The threat also includes winning Pe5, so the resulting passed Pe4 would give White the initiative and a winning advantage.
Black can try to counterattack.
32…Qb3 [or Qa2] 33.Rcc7 (threatening 34.Rxg7+)
cedes White a winning attack. The heavy pieces Ra1 and Qb3 must now defend Kh7 from a swarm 2Rs+2Ns, which can avail itself of powerful attacking moves like Ne8 and Nh4-Nxg6. Black has no feasible defense, e.g.:
(1) 33…Qxa3 34.Rxg7+ Kh8 35.Nh4 then 36.Nxg6#
(2) 33…Rg8 34.Ne8
(threatening 35.Nxg7 or 35.Rxg7+ 35.Nh4 36.Nxg6#)
34…Bb5 35.Rxg7+ Rxg7 36.Nf6+ Kh8 37.Rc8+ Rg8
38.Rxg8+ Qxg8 39.Nxg8 Kxg8
and White has N for P. Other moves 32… by Qg8 make no difference, because doubled on the 7-th rank, the White Rs can force the Black Q to lose contact with e8 and h4, permitting the variations above.
Black can try to frustrate the White plan of doubling Rs on the 7-th.
32…Bc8 [or Rd8] 33.Re7
and the Rs will double. Finally, Black can try to prepare a defense to the doubled Rs and the pin on Bg7.
To avoid the original threat (on move 31., losing B+N for R), Black can move Bg7.
(1) 33…Bf6 34.Nf7+ Kg7 [or Kh7]
35.N7xe4+ Kh8 [else, drop Qg8 to avoid mate]
36.Nf7+ Kg7 37.N7g5+ Kh8 38.Rh7+ Qxh7+ 39.Rxh7+ Kg8 40.Rxh6
and White is up 2Ns+P for B. A similar maneuver is successful against 33…Bf8.
(2) 33…Bf8 34.Nf7+ Kg7 [or Kh7] 35.N7xe4+ Kh8
36.Nf7+ Kg7 37.N7g5+ Kh8
38.Bxf8 (threatening 39.Bg7+ 40.Bf6+ 41.Bxg5+ 42.Rh7+ and mate)
38…Qxf8 [Rxf8 permits the finish above] 39.Rh7+ Kg8 40.Ne6
threatening 41.Rcg7+ 42.Rh8#, so Black must sacrifice Qf8 for a R.