# Another Nutakapa

This puzzle is another Nurikabe-Tapa hybrid puzzle, similar to one of the poster's previous puzzles. In this grid, your task is to create a single fully-connected shaded path with no 2-by-2 blocks respecting all of the clues. Some clues are Nurikabe clues, indicating the number of unshaded squares connected (horizontally and vertically) in the region, and every unshaded region must contain a single Nurikabe clue. Some are Tapa clues, giving the pattern of shaded squares around the clue. It is part of your task to determine which is which. As is standard, squares containing clues of either type cannot be shaded. I hope you enjoy!

UPDATE: A previous version of this puzzle had the same grid as the above, but the "1 1 1" clue in the middle had highlighting around it. This was simply an artifact of my stupidly leaving the cursor in that cell when I took a screenshot of the spreadsheet, and had no bearing at all on the puzzle.

Text Version:

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| 3 |   |   | 5 |   | 2 |   |   |   |   | 2 |   |
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|   |   |   |   |   |   |   |   | 5 |   |   |   |
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|   |   |   |   |   |   |   |   |   |   |   |   |
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|   |   | 6 |   |   |   |   |2 3|   | 6 |   | 4 |
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|   |   |   |   | 1 |   | 6 |   |   |   |   |   |
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|   | 4 |   |   |   |   |111|   |   |   |   | 5 |
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|   |   |   |   |   | 6 |   |   |   |   |   |   |
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|1 2|   | 6 |   |   |   |   |   |   | 7 |   |   |
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|   |   |   |122|   | 7 |   |   |   |   |   | 3 |
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|   |3 3|   |   |   |   |   | 4 |   |3 3|   |   |
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|   |   |   |   | 6 |   |   |   |   |   |   |   |
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|   |   |   |   |   |   |   |   |1 1|   |   |   |
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• Can there be zero nurikabe clues in a white region, or two or more nurikabe clues? Oct 12, 2020 at 14:19
• Ah shoot, accidentally removed that from the instructions. Will fix. Every blank region needs exactly one Nurikabe clue. Oct 12, 2020 at 14:20

Solution: (orange=nurikabe, green=tapa)

Explanation:

First, identify the multi-digit clues as Tapa. The 6 right above 111 cannot have a shaded run of 6 cells, so it is Nurikabe. Also, 122 with one cell blocked forces the two adjacent cells to be shaded, and that 6 cannot be Tapa. The 33 makes the opposite side shaded.

Now look at the lower right section. 11 forces the NW, W, E, SE sides of 33 to be shaded. If S of 33 is shaded, both SW and NE are blank, disconnecting the shaded strip at the corner. So N and S are blank and the rest is shaded.

Back to the lower left. Due to 12, the shaded strip at the lower left corner cannot escape through the hole between 12 and 6. Some case analysis gives the only possibility around the 33.

Close off the Nurikabe 6 region. The shaded strip at the bottom cannot escape through between 122 and 7, so it should go between 4 and 7 (which makes the 4 a Nurikabe).

Now to the center. If the center 1 is a Tapa, the six dots around 1 are forced, and it is a too large blank region, so it must be separated from the Nurikabe 6. But then it is a contradiction with the Tapa 1's.

Therefore the single 1 is a Nurikabe.

Since a white region can contain only one Nurikabe clue, the connected 6 is a Tapa, giving off a lot of information. The cell two steps on the left of the Tapa 6 is blank (due to 2x2 rule), which is naturally connected to the 4.

Now I realize that all clues on the border that close off itself when interpreted as Tapa are actually Nurikabe clues, so mark as such. The orange circle cannot be reached with existing Nurikabe clues, so the adjacent 6 is also a Nurikabe.

Back to center again. The 6 at the center cannot be joined with 23 (otherwise the Tapa clue 23 is not satisfied), so it is closed off as the following. Finish off the bottom middle section too.

EDIT: I found that the 23 is satisfiable, but then it either contradicts with 111 (if N of 6 is blank) or an island with no Nurikabe clue is formed (if E of 6 is blank).

The 23 forces 4 shaded cells and a blank as follows, revealing many shaded cells due to connectivity. The 2 at the corner is a Nurikabe; no other clues can reach the cell with the 2.

The 2 at the top middle is forced to be a Tapa. I did a lot of trial and error here, but I finally realized that the 2 forces the shape of 5 region, and the rest logically follows.

Finish off the rest, identifying Nurikabe clues from top to bottom.

• Looks good! I await your reasoning! Oct 12, 2020 at 16:34
• @JeremyDover Explanation added. Oct 13, 2020 at 1:00
• Excellent answer! Thanks for putting in the work to explain the path...it makes a great read. Oct 13, 2020 at 1:26