board games - Stepladder Puzzle 2: Edge Surfing (small target version)

Continuing the Stepladder Game puzzle series, here's

Stepladder Puzzle 2: Edge Surfing (small target version)

If you haven't played the Stepladder Game^* before, you should first take a look at the rules, which can be found in the introduction part of the first stepladder puzzle.

_{*: You may already know this game by another name}

In puzzle 2, the target area is split into two parts along the edge of the grid. Your task is to colour in the minimum number of squares in the target area(s), (using either white, black, or both colours), so that with optimal play (formally defined in puzzle 1) from both players, the stepladder hits the lone black square at the top of the diagram and terminates there.

Here is the text version of Puzzle 2. "X" is black, "O" is white, "." is an empty square, "_" marks the target area, and "|" is the edge of the grid.

    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|
    . . . . . . . . X . . . . . . .|
    . . . . . . . . . . . . . . . .|

    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|

    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|
    . . . . . . . . . . . . _ _ _ _|

    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|
    . . . X X X X X . . . . . . . .|
    . . . X O O O O O X . . . . . .|
    . . . X O X X X O X . . . . . .|
    . . . X O X . X O X . . . . . .| 
    . . . X O X . X O X . . . . . .|
    . . . X O X X X O X . . . . . .|
    . . . X O O O O O X . . . . . .|
    . . . X X X X X X X . . . . . .|

    . . . . . . . . . . . . . . . .|
    . . . . . . . . . . . . . . . .|

Answer

Here's the solution (squares in target area is the solution:

Here's the explanation (sorry for it being blurry):

when white plays, black presses and therefore white only has one choice to move. When white plays O (and hits the lone black square), black plays X and wins the game.