Stepladder Puzzle 2: Edge Surfing (small target version)

Question

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

With terminates, you mean that one of the players can secure a win? — Lolgast, Commented Jan 11, 2018 at 10:55
I believe you left some Xs at the second last row of the text version. — paper1111, Commented Jan 11, 2018 at 11:37
@Lolgast yes, exactly. And since the target square is black, it's going to be black, of course. (Free hint :-) — Bass, Commented Jan 11, 2018 at 11:47

paper1111 · Accepted Answer · 2018-01-11 12:21:40Z

4

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.

edited Jan 11, 2018 at 12:21

answered Jan 11, 2018 at 12:09

paper1111

1566 bronze badges

$\begingroup$ Great work on the lower part! After 52 though, white can catch the black square above 45. This threatens to catch 48 next, so white wins. $\endgroup$
– Bass
Commented Jan 11, 2018 at 12:17
$\begingroup$ Nope, because knowing that, Black will play 26 above the two added white squares making the path go northwest ;) $\endgroup$
– Alix Eisenhardt
Commented Jan 11, 2018 at 12:20
$\begingroup$ @Bass added one more square to tackle the problem $\endgroup$
– paper1111
Commented Jan 11, 2018 at 12:22
1

$\begingroup$ @AlixEisenhardt, Funnily enough, black cannot play 26 there for exactly the same reason :-) $\endgroup$
– Bass
Commented Jan 11, 2018 at 12:23
$\begingroup$ Yup, looks like that would work, and six squares is a really good score! It's not quite the absolute minimum though. $\endgroup$
– Bass
Commented Jan 11, 2018 at 12:27

| Show 2 more comments

Alix Eisenhardt · Accepted Answer · 2018-01-14 11:52:45Z

1

Well, if 6 is a really good score, what about 4 ?

Here's the path:

edited Jan 14, 2018 at 11:52

answered Jan 14, 2018 at 11:44

Alix Eisenhardt

1,2577 silver badges15 bronze badges

$\begingroup$ I’ll repeat the comment from the other version of this problem: This variation was exactly the reason why I made the mistake with the targets. I of course checked the solution here, too, and everything seemed to work just as intended. 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 12:50

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Stepladder Puzzle 2: Edge Surfing (small target version)