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Nurikabe Strategies

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Posted 22nd Feb 2020 at 09:33
Last edited by JoergWausW 22nd Feb 2020 at 09:42
JoergWausW Daily subscriber
I don't know anymore whether I really promised it, but today I took some time to do it.

Here is a possible way to solve today's Nurikabe puzzle: Link to puzzle

Maybe it helps someone and introduces some ideas.


Step 1:

Fill in all black squares where a white square would connect two numbers

Pic 1

It always works with two diagonal adjacent numbers.
The green square is an example for the other possible case.


Step 2:

Squares with a "1" have to have black adjacent cells:

Pic 2


Step 3:

Some white numbers remain with only one "exit":

Pic 3

The 5 in the middle (light red square)

The 3 has to spread out down.
-> light yellow (white) square below
-> dark yellow (black) square left of it because of the adjacent 4
-> light green (white) square to the left, finishing the 3-area
-> dark green below, because a white one would make the area too big.

The light blue square now follows.

(I missed one easy square that has to be white! You may want to find it)


Step 4:

Black areas have to be connected.

Pic 4

-> the dark green squares have to be black
-> the dark red squares and the dark pink ones build create the only possible way out for already given black squares.


Step 5:

I know you could continue with the two bottom rows now, but I want to make another point first.

Rule: You cannot have four black squares building a square.

Pic 5

-> The yellow squares are needed to be white
-> the light red one has to be white - if it was black, the one above it would be black, too.

Filling in some obious stuff:

Pic 6

purple: finish the 2-area and add black (here still dark purple) around it (left top because of the needed exit for the black area)

yellow: finish the 4-area

blue: connect the 6 to the white square (only option), dark blue because of the adjacent 5-area, that now has to expand north.

green:
-> the green square in the 2nd from the bottom row connects
-> the two sqares in the bottom row follow, because there have to be 6 white squares in total (no exit north, no surrounded black one)

red:
the 6th white square now could be in one of the two red squares.

2 Reasons why it has to be the bottom one:
1) the black area at in the lower half needs an exit to the upper half
2) after finishing the 4-area there would be a black square of 4 cells left to the 6.

Reapplying all the so far mentioned strategies your puzzle should look like this:

Pic 7

Step 6:

"out of reach"

Some squares are too far away to be reached by any white area, so they have to be black:

Pic 8

Step 7:

Continue...

Pic 9

-> light red is white because of the "black square"-rule
-> light green is the only(!) way to connect the red square to a white area
-> the left red square has to be connected to the 5, but there are several ways.
-> still, the dark blue square has to be black

-> the dark yellow squares have to be black to connect the left black area with the rest.


Step 8:

Do the rest.

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