Abdel Irada: <<•> Converging vectors <•>>
This is an interesting sort of position. At first glance, White's advantage is minimal; Black's sole weakness appears to be his rather congested minor pieces.
Then we note points, and experience points to a focus: g7. This is a matter of vectors.
We already have one rook bearing down on the target square vertically, and the other is poised to line up against it horizontally.
Since this *is* a puzzle, the first thought is to sacrifice the exchange. But this doesn't work out after (a) 34. Rxg7?, Kxg7 35. e6†, f6 36. Rb7†, Kg8, when White has nothing and plenty of it.
But now another idea comes: What, then, if we reverse the order of rook moves?
<<•> 34. Rb7! ... >
This isn't a spectacular sacrifice, although it does offer a pawn. But does Black really threaten to take it?
< (1) 34. ...Rxa2†?!
35. Kb3, Ra6 >
Also possible is (b) 35. ...Rf2 36. Rf4, Rd3 37. R4xf7†, Ke8 38. Rxg7, R2xf3 39. Rb8†, Rd8 40. Rxd8†, Kxd8 41. Rxh7 , when White has an extra piece.
< 36. e6 >
This move is cyanide. Black perishes after (c) 36. ...Bxc3? 37. Rxf7†, Ke8 38. Rg8†, Nf8 39. Rgxf8#, (d) 36. ...Nf6 37. Rxf7† (also good is 37. e7†), (e) 36. ...Rd3 37. Rxf7†.
This seems to suggest that Black doesn't have time to grab the pawn, so what else can he do?
< (2) 34. ...Re6?! >
This is meant to stop the tactics by holding back White's e-pawn. But it allows
< 35. Rxa7 >
Having offered an a-pawn, White now wins one of the same. This outside passed pawn might or might not suffice to bring home the victory, but White has another threat that will force material off the board advantageously: 36. Rf4.
Combined, these advantages in the hands of a Kasparov are daunting.
< (3) 34. ...Re8 >
This is intended to stop White's e6 without losing the a-pawn.
< 35. Rxg7, Kxg7
36. e6†, Kg6
37. Rxf7, Nf8 >
Not (f) 37. ...Raxe6?/Rexe6? 38. Rg7† and White wins a piece.
< 38. Ne5†, Kh5
39. Rf5†, Kxh4
40. Rxf8! >
White wins a piece after 40. ...Rxf8 41. Ng6†
Sometimes the merit of the first idea can be seen only in the outcome of the second.
But in all cases, to the vector goes the spoils.