Stepladder Puzzle 2: Edge surfing

Question

Continuing the Stepladder Game puzzle series, here's

Stepladder Puzzle 2: Edge Surfing

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

Daily Hint (2018-01-11):

I accidentally posted this puzzle with the targets one column narrower than here. That ruined the "Wow, that's cool!" solution I had in mind.

Daily Hint (2018-01-12):

The solution for the upper target is extremely simple to set up.

Daily Hint (2018-01-13):

While the solution itself is extremely simple in terms of the coloured squares, the optimal play arising from it is somewhat tricky. So this puzzle is not so much about figuring out which squares to colour, but rather about finding the proper optimal play.

Daily Hint: (2018-01-14):

Not everything is lost even if white catches a single square.

Daily Hint (super hint, since I missed yesterday’s hint): (2018-01-16):

The intended solution has 4 squares coloured in. The bottom part has three of them.

Daily Hint (actually, the solution; just add the optimal play sequence): (2018-01-17)

Solution for the bottom part has already been found. Solution for the top part is a single black square in the 5th column.

Daily Hint (well, not really) (2018-01-18)

There is nothing left to hint. The entire answer is already given, you only need to write it out, and follow the instructions to add in the optimal play.

Honestly, I do not see how, by adding a column, we could find a solution with fewer squares. So good luck to those who will try it! (Maybe I'll try it myself a little later...) — Alix Eisenhardt, Commented Jan 11, 2018 at 16:32

Alix Eisenhardt · Accepted Answer · 2018-01-14 11:57:03Z

2

+100

Since I found 4 for the other version, I think it's applicable here

Here's the path:

answered Jan 14, 2018 at 11:57

Alix Eisenhardt

1,2577 silver badges15 bronze badges

$\begingroup$ This variation was exactly the reason why I made the mistake with the targets. I of course checked the solution of the other problem too, and everything seemed to work just fine. But black wouldn’t play like this, since he has a shorter win: playing b-46 at 47 ends the stepladder without reaching the target square. $\endgroup$
– Bass
Commented Jan 14, 2018 at 12:37

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Stepladder Puzzle 2: Edge surfing