4
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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!

Grid

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:

-------------------------------------------------
| 3 |   |   | 5 |   | 2 |   |   |   |   | 2 |   |
-------------------------------------------------
|   |   |   |   |   |   |   |   | 5 |   |   |   |
-------------------------------------------------
|   |   |   |   |   |   |   |   |   |   |   |   |
-------------------------------------------------
|   |   | 6 |   |   |   |   |2 3|   | 6 |   | 4 |
-------------------------------------------------
|   |   |   |   | 1 |   | 6 |   |   |   |   |   |
-------------------------------------------------
|   | 4 |   |   |   |   |111|   |   |   |   | 5 |
-------------------------------------------------
|   |   |   |   |   | 6 |   |   |   |   |   |   |
-------------------------------------------------
|1 2|   | 6 |   |   |   |   |   |   | 7 |   |   |
-------------------------------------------------
|   |   |   |122|   | 7 |   |   |   |   |   | 3 |
-------------------------------------------------
|   |3 3|   |   |   |   |   | 4 |   |3 3|   |   |
-------------------------------------------------
|   |   |   |   | 6 |   |   |   |   |   |   |   |
-------------------------------------------------
|   |   |   |   |   |   |   |   |1 1|   |   |   |
-------------------------------------------------
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  • $\begingroup$ Can there be zero nurikabe clues in a white region, or two or more nurikabe clues? $\endgroup$
    – Bubbler
    Oct 12 '20 at 14:19
  • $\begingroup$ Ah shoot, accidentally removed that from the instructions. Will fix. Every blank region needs exactly one Nurikabe clue. $\endgroup$ Oct 12 '20 at 14:20
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Solution: (orange=nurikabe, green=tapa)

enter image description here

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.

enter image description here

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.

enter image description here

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.

enter image description here

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).

enter image description here

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.

enter image description here

Therefore the single 1 is a Nurikabe.

enter image description here

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.

enter image description here

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.

enter image description here

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).

enter image description here

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.

enter image description here

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.

enter image description here

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

enter image description here

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3
  • $\begingroup$ Looks good! I await your reasoning! $\endgroup$ Oct 12 '20 at 16:34
  • $\begingroup$ @JeremyDover Explanation added. $\endgroup$
    – Bubbler
    Oct 13 '20 at 1:00
  • $\begingroup$ Excellent answer! Thanks for putting in the work to explain the path...it makes a great read. $\endgroup$ Oct 13 '20 at 1:26

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