# Can you solve this nurikabe puzzle?

Here's a nurikabe for you. Let's see who can solve it first.

• It would help if you can give some description on what nurikabe is, or at least a link to a description. This way the puzzle will be more self-contained. Jan 24, 2017 at 15:30

This appears to be a valid solution. (I did about 3/4 of it by proving that cells had to be of one sort or another, and the rest by educated guesswork and backtracking.)

• Are you an AI or something? :) +1 Jan 24, 2017 at 15:49
• This is what I got also from certain deduction =). The key one was that the square at row 3 col 2 cannot be black, as it will cause the blacks at row 1 col 2 to be isolated. From there it's quite a breeze as it can only be connected to the 16. Jan 24, 2017 at 16:09
• That was one of the bits I deduced rigorously. The right-hand side was trickier, or at least looked sufficiently trickier that it seemed like it would be quicker to try to construct a solution. Jan 24, 2017 at 16:13
• You got the answer. Kudos! Jan 24, 2017 at 23:58

A late, but step-by-step solution. Click on any picture for a full-size version

1. Trivial oceans from filling in the cells around size-1 islands. Then, if R2C2 is an island, connectivity arguments force oceans to be in R2C3 and R3C2, which would in turn isolate R2C2 as a numberless island. Thus R2C2 is an ocean; since we can't have 2x2 squares of ocean R3C2 must be an island. Also, some simple connectivity of oceans/islands.

2. To avoid a 2x2 in R1-2C2-3, and a collision with the size-4 island in R1C7, there is only one possible shape for the island from R1C4. Some trivial surrounding oceans for the new island. Then, some simple connectivity of oceans/islands.

3. If R5C2 is an island, connectivity arguments force R4C3 to be so too, which would in turn isolate R4C2 as a lonely ocean. Thus R5C2 is an ocean, and by 2x2 R6C2 is a non-ocean. Simple connectivity of islands allows the size-3 island from R6C4 to be completely determined. Also, some trivial surrounding oceans for the new island. Then, some simple connectivity of oceans/islands.

4. The shape of the size-2 islands in the top right and bottom left corners can both be determined in the same fashion: if they go horizontal, 2x2 forces a certain cell to be an island, which can only then connect to the size-16 island, but this would isolate the oceans on one section of the board from the other side. Then, some simple connectivity of oceans/islands.

5. By 2x2, R8C3 must be an island. Its position means it can only connect to the size-16 island, so it must escape to the right to avoid collision with the island from R10C4. Said island's shape can be completely determined by 2x2 and collision avoidance. Also, some trivial surrounding oceans for the new island. Then, some simple connectivity of oceans/islands.

6. The island cells from R8C3 must connect to the size-16 island, which forces oceans to connect along the left (using R7C5) and then bottom (using R9C7) edges.

7. To avoid trapping oceans or collision with the island from R10C10, the island from R10C7 may be only one shape. Then, some simple connectivity of oceans/islands.

8. The size-2 and size-3 islands on the right side are forced to snake up, in turn forcing some oceans for surrounding them/connectivity to the top-edge oceans. Then, trivial 2x2 islands.

9. There is only one way to connect to the top-left corner oceans while still leaving enough space for the size-4 island from R1C7. Then, simple connectivity (R4C7) and counting finishes off the size-16 island.