Puzzle of the week #33

Chess Diagram: 


Link: http://www.suttlesbook.com/
Buy "Chess on the edge" regardless of your level (if any)! It will offer you countless moments of intellectual pleasure and maybe it will influence your play as well...
There are moments in a chess game when all acumulated advantages (both positional and material) need to be converted into a win. If you don't do it, the opponent will and there will not be a second chance. Let's look at the following position from a game between Wachtel - Suttles, Vancouver 1975 (part of the book; used with permission); after the move 32.c6-c7 Ra8-a7 we arrived here (see diagram). Questions:
a) Analyse the position. (3 points)
b) Was 32... Ra8-a7 a good and necessary move? Explain. (3 points)
c) Give the most probable line for both sides (no longer than 10 moves) and the result (4 points)
Total available points for this puzzle is 10. The answers will be published next week together with puzzle #34.

Puzzle #32 solution:
Sorry for the delay in posting this solution and following puzzle! It was nice to get 5 detailed responses, each one of them with unique solutions for questions "b" and "c". Everyone agreed White had a decisive advantage, even being down a piece; this is a good thing! Here are 3 nice solutions I received:
Jeremy: "38... Ne8 39.fxe7 Bg7 40.Rd8 Rc8 41.Nd6 ... 1-0"
John (did not agree with 38.f6...; compressed version): "38.Nd5! Nc8 39.Rd8 e6, this is really the only good move to start counterplay {if 39... Kf7 then 40.Nxg5+ and Black gets nowhere} 40.Nc7 Ra2+ {if 40... Rb8 41.Nxg5 and xe6 wins} 41.Kf1 Ra1+ 42.Ke2 Ra2+ 43.Kd1 Ra1+ 44.Kc2 Ra2+ 45.Kb1 Rg2 46.Nxg5 exf5 47.Rxc8 followed by any Knight to e6, winning Bf8."
Joshua (did not agree with 38.f6... either; compressed version): "38.Nxg5 Nc8 39.Nce4 Ra2+ 40.Kg3 Rc2 (40...Ra3+ 41.Kh4 Nxf5+ 42.gxf5 Bh6 43.Rd8+ Kg7 44.Ne6+ Kh7 45.Rxc8) 41.f6 exf6 (41... Ne8 42.f7+ Kg7 43.fxe8Q wins) 42.Nxf6+ Kh8 43.Nf7#"
In the game Duncan saw a nice mate in case Black decided to hold onto his extra piece: 38... exf6 39.Nxf6+ Kh8 40.Nce4 Nc8 41.Nxg5 Nd6 42.Rxd6! Bxd6 43.Nf7# Any other Black move would win the piece back for White; also White could still have a crushing position.

Correct solutions:
Joshua and Jeremy - 9 points
John - 8 points
Nathaniel - 3 points
Wilson - 2 points

57.0 John
52.0 Joshua
43.0 Wilson
40.0 Jeremy
15.0 Karl
13.0 Nathaniel
10.0 Jacob


Passed pawns