Logic Masters Deutschland e.V.

To Christmas 2023 some eager puzzlefriends have again arranged a group in which everybody had to make anonymously a puzzle for someone else. These puzzles are now presented one after the other here in the portal.

Claudia was deep in thought as she wandered across campus. It was pretty uncommon for the professor to call her into his private study. Even more intriguing was the message he had left behind: "Please meet me as soon as possible in my office. We are dealing with a fascinating phenomenon which we had observed together many years ago."
The professor greeted her warmly: "Claudia! So nice to see you again! I hope your puzzling adventures have been less boring than mine." Despite this greeting Claudia could immediately see that the professor was tired. A large puzzle grid was projected on the wall behind him. When the professor noticed her wandering gaze, he grinned mildly and said: "You're probably wondering what this thing is. I've been trying to figure it out for two days now, and I finally believe I've understood what we're dealing with. I hope you brought a pen!"
As Claudia sat down and pulled out her pencil case, the professor sat up a bit straighter. She was amused that the professor always explained things in the same manner, regardless of whether his audience was a single person or a full lecture hall. "Now then, do you recall the case that we worked on about 4 years ago? The one with the infested coral and the mutated seven?" Claudia remembered it very well. It was one of the hardest and most fascinating cases she'd ever worked on. "It appears that this case has returned. We already know that the mutation likes moist environments, those using Japanese Sums with the digits 1-9 in every row and column without repeats, and cryptified clues. However, this time there is no infested coral. Instead, the mutation has reached into a series of islands. All of the islands are marked in the grid, and the value in the marked cell indicates the size of the island. On any island, no digit may be repeat, and the waters surrounding the islands are all connected. Also, there is no 2x2 area entirely consisting of water."
Claudia interrupted the professor: "So it's simply a nurikabe?" — "Largely, yes," he replied. "But here's where it gets interesting. The mutation of the seven has no effect on the islands themselves, for indeed no seven appears in any island. Instead, each seven acts as a bridge, by touching two cells from different islands orthogonally and linking them in a straight line. The mutation has presented in such a way that, in the larger scheme, all of the islands are connected to all others by this bridge network. Because the bridges have water flowing under them, the sevens still act as water cells separating the islands. The fascinating thing, though, is that the bridges also count toward their Japanese Sums. Any other questions before we begin?"
Claudia did have one: "What's going on with the cryptification? It looks like half of the clues are missing!" The professor stood still for just a moment and then laughed briefly. "Oh yes, a good eye as ever, Claudia! The cryptification really drove me up the wall for a while. In the end I was able to see what was going on. Look, we have Japanese Sum clues outside and Nurikabe clues inside. I assume that the inner and outer clues use different cryptification systems, so that each letter represents two digits, one for the Japanese Sums and the other for the Nurikabe. All digits from 0 to 9 were used in this manner, and all digits that appear in one set of clues but are represented by letters in the other set, have been replaced by a '?'. And one more detail: you may have noticed that some letters don't appear in the clues. But even in such cases, the digit associated with that letter needs to be a valid clue value for its clue type. Thus, for example, the Nurikabe-P cannot stand for the value 7! That should cover everything. Shall we begin?"
Claudia nodded. The professor had not been lying in his message — it was indeed pretty fascinating.