Puzzle of the week #385

Submitted by Eugen on Mon, 04/05/2021 - 22:22
L-shape setup
Chess Diagram
[Event "Puzzle #385"][Date "2021.04.05"][Result "1-0"][SetUp "1"][FEN "8/4k3/1p2n3/p3PB2/7P/5K2/5P2/8 w - - 0 1"]
After a long battle in this correspondence chess game white has been rewarded with this endgame. Black's last move was "Nc7-e6". Your tasks:
a) Was this the best move black could play? If the answer is not, please provide a better move and line
b) Why is white winning here?
c) Show the fastest way to win for white

Total available points for this puzzle is 30. The answers will be published next time together with puzzle #386.

Puzzle #384 solution:
Game GM Magnus Carlsen - GM Brandon Jacobson, online bullet Mar 2021. This week's best answers are by the top scorers:
b) Because the back rank (the 1st rank) was weak and vulnerable to back-rank mate, due to the pawns on h2 and g2 blocking the white king's escape, and the potential Bc5+ or Qxd4+, blocking the king's access to f2 by controlling the square. Another reason the combination was possible was the presence of two major pieces, and major pieces (queens and rooks) are capable of back rank checkmates (or checkmate patterns).
[Event "Puzzle #384"][Date "2021.03.16"][Result "0-1"][SetUp "1"][FEN "r2r3k/p3b3/q4NQp/5P2/3B4/1P6/5RPP/6K1 b - - 0 1"]1...Qa1+ 2.Rf1 (2.Bxa1 Rd1+ 3.Rf1 Bc5+ 4.Kh1 Rxf1#) Qxd4+ 3.Kh1 (3.Rf2 Qa1+ 4.Rf1 Bc5+ 5.Kh1 Qxf1#) Qxf6

Correct solutions:
Zhengyu - 20 points
Joey, Lucas - 15 points
Walter - 10 points

Zhengyu - 35 points
Joey, Walter - 25 points
Lucas - 15 points