# Nurikabe: An Inconvenient Twelve

This puzzle is a Nurikabe. I've been busy and haven't made my trademark puzzle in a couple of months, so consider this my comeback puzzle and my apology! Hopefully you enjoy.

Rules of a Nurikabe (copied from my previous puzzle):

This is a Nurikabe puzzle. The goal is to paint some cells black so that the resulting grid satisfies the rules of Nurikabe:

• Numbered cells are white. (Think of them as "islands.")
• White cells are divided into regions, all of which contain exactly one number. The number indicates how many white cells there are in that region.
• Regions of white cells cannot be adjacent to one another, but they can touch at a corner.
• Black cells must all be orthogonally connected. (Think of them as "oceans.")
• There are no groups of black "ocean" cells that form a 2×2 square anywhere in the grid.

Now, here is the puzzle:

(Test-solved by the marvelous crown, @bobble.)

• Welcome back! Fun solve... Commented Aug 6, 2021 at 19:54
• Fun solve on the 8 part! Commented Aug 7, 2021 at 8:01

## Solved grid:

Starting with some basic deductions:

All of these are simple nurikabe logic, so shouldn't need any explanation.

Now looking at the middle of the grid:

There are 2 cells towards the middle which are unreachable, and hence must be filled. They connect to another cell in an L, hence a cell must be part of an island to avoid a 2x2. The only island that can reach it is the 5, which therefore must extend straight downwards.

The 2s and 12 are now key:

The 2s at the top can all be deduced, and the 12 must also extend outwards around the top. The black cells cant be isolated, meaning they must also extend outwards the right.

Focusing on the 12:

There is now a cell towards the middle right, which must be part of an island to prevent a 2x2. The only island that can reach is the 12, and it would be the 12th cell, meaning the 12 is complete. A few more 2s can also be at the least partially solved further down.

Nearly finished:

The 4 can only be solved one way to prevent a 2x2 forming. There are now some unreachable cells on the right which are filled, and the black cell next to the 8 must extend to the right

Finishing up:

The 8 must extend to the right and the 2 bottom left as well, to prevent any 2x2s or isolated regions

• Ah, seems you were just a minute faster! Well done! Commented Aug 6, 2021 at 19:54
• @Reinier wow close one! Good answer too with some nice explanation though! Commented Aug 6, 2021 at 19:55
• Very well done and a close call, both of you had awesome answers :) Commented Aug 6, 2021 at 20:29

# Step by step solution

## Step 1

As a start, we get the following shadings:

## Step 2

Consider the four 2x2-squares marked in the following image:

The yellow square can only be reached by the 5 clue at the top of the grid. The cyan square can only be reached by the 12. Now that we know that the 12 needs to go to the cyan square, both the red squares should contain some part of the 8-island. This gives the following progress:

## Step 3

There are a couple of 2x2-squares which are almost completely filled. By completing these squares with island cells, and furthermore using some connectivity logic, we get to the following state:

## Step 4

We shade some cells which are not reachable by any island:

Next we prevent some filled 2x2-squares from occuring, which completes all the 2-islands.

## Step 5

There is only one way to complete the 4- and 8-islands without forming any 2x2-ocean blocks:

And this completes the puzzle!