Friday’s chess tactics quiz

“Believe in the existence of that combination and seek to discover it. And if you have searched in vain a hundred times, continue. Possibly the advantage that you think you hold is only an illusion; your valuations may be at fault: prove them and improve them. But, first of all, search diligently; work, for such work is rewarded.” (Lasker’s Manual of Chess; p215)
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The following examples are all taken from the Sant Marti International Open tournament that just finished yesterday. Just click the previous image to find all the tournament information and results. Or HERE.

From the 8th round. Position after 29 moves of play. White has played a brilliant game, completely outplaying his talented rival. Even though White is a whole Rook down, his three passed pawns, dominant pieces and Black’s exposed King are more than full compensation. HOWEVER, the game is complicated and White must still prove his advantage…Here White should probably play 30.d5!? (threatening Be3+ winning). After 30…RxB 31.QxR(d8)! White would have excellent winning chances.
IN THE GAME continuation, probably short of time, Peralta completely lost his head, and with it, all of his advantage:
30.QxB?

This obvious move gives Black the opportunity to cleverly turn the tables on his rival…
30…RxB! 31.PxR?!

BLACK TO PLAY AND WIN!
31…Qe2!!

0-1.
After 32.Rf1 Rd1! is more than sufficient.
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MORE EXAMPLES

Black had just played 22…Nxc2, trying desperately to gain some momentum for his counter-attack on the Queenside. I suppose the idea is that if 23.KxN Ba4!? would follow…but it is hardly forced. White has better; much better!
WHITE TO PLAY AND CRUSH!

If I had a dollar for everytime I see this tactic in praxis…
WHITE TO PLAY AND MATE IN 3!

The game is just starting. White played 20.Nd5 and Black immediately resigned! WHY? Can someone please explain this to me?
