Nurikabe: Forties

The good news: It’s my birthday! The bad news: I’m 40 now. It’s not a great update. Just weaker stats with no cool new abilities. Anyway, here’s a Nurikabe to celebrate. Don’t worry, it should be good – I made it when I was still 39.

Rules of Nurikabe: Shade some cells in the grid. Each area of unshaded cells must contain exactly one number, which indicates the size of that area. Two unshaded areas may not share an edge, but they can touch at a corner. Shaded cells must form one orthogonally connected area, and no 2x2 square may be fully shaded.

Solve on Penpa+

• Still waiting for the Slitherlink-Nurikabe fusion... Commented Aug 18, 2023 at 15:35
• Happy birthday! For he's a Jafe good fellow...
– Stiv
Commented Aug 18, 2023 at 16:36
• Exciting. The rightmost "40" is very interesting. My first Nurikabe puzzle attempt. Commented Aug 18, 2023 at 17:18

The solution is here. I really enjoyed it for my first-ever time completing a Nurikabe. Happy 40th birthday!

First we need to notice something funny about the bottom right.

There are cells that have to be unshaded, but are unreachable by nearby numbers. So we have to use the first 40. At first I tried to have only one bend for the blue line in the bottom-right, but this still leaves unreachable cells. Hence there are two bends in the blue line in the bottom-right.

Then we notice that similar problems happen in the bottom left.

Because the grid itself is 20x20, and it takes a long time for the other 40 to reach the bottom left, the following is forced:

The rest is then not too difficult.

• The yellow 8 seems to have a 2x2 square that is fully shaded, though I might be missing something. Commented Aug 19, 2023 at 11:00
• @pigrammer The rules state that "no 2x2 square may be fully shaded". In my solution, shaded cells are represented by the colour grey, while unshaded cells are represented by any other colour. The yellow 8 is therefore unshaded, which is not restricted from having a 2x2 square. Hope that clears it up. I used different colours for unshaded regions to separate cells that belong to different shaded regions, which helps solving. Commented Aug 19, 2023 at 11:57
• I just misunderstood the puzzle; sorry for the confusion. Commented Aug 20, 2023 at 1:17