Special Puzzle 8: It’s Erased

Domino Nurikabe. Follow regular Nurikabe rules (color some cells black so black cells form a single polyomino and white cells form separate polyominoes (islands) so each island contains exactly one number which represents its size). In addition, the black cells must be able to be partitioned into non-overlapping dominoes. Question mark represents an unknown number.

Sky woke up. “Darn, I shouldn’t make puzzles that late. What, I think it was 1 AM or something when I fell asleep…”
He reviewed his puzzle, and noticed something was smudged. “Err, what’s the number in this cell supposed to be?”
“Hey Sky! Has the puzzle been made?” someone shouted from outside, shocking him.
“Oh ya right! Just a little fix!” Sky rushed to find the number in the erased cell, but he couldn’t get the actual number. Hesitantly, he erased the smudge, put a question mark in it, and gave it to his senior that leads The Daily Puzzle, otherwise known as Chaos at the Sky.
“Domino Nurikabe, with an unknown number. Seems legit. Let’s see,” and the boss, chaotic_iak, left. Sky returned to his home sadly.

Special Puzzle 8: It’s Erased
Domino Nurikabe

To be continued…

…after I get someone that either verifies that this has only one solution or proves that this doesn’t have a unique solution (either zero or multiple).

After a usual day of working as the leader of Flygrass Town (which mainly comprises of hanging around and switching to his part-time job of making puzzles pretty often), Sky was greeted again by chaotic_iak. Sky felt saddened again.
“That puzzle I gave you in the morning… I think it’s flawed, right?” Sky started to sob.
“What? Not at all. In fact the readers enjoyed it.”
Sky’s face was brightened. “Really?!”
“…I guess that question mark was unintentional?”
“Kind of.”
“Yeah, it still has a unique solution. You haven’t tried testsolving it again?”
“I think no.”
“Haha. You should. Anyway, thanks for the puzzle, even though it’s rather easy.” chaotic_iak left, and Sky felt a surge of happiness inside himself. He went back to his puzzle table.
“Oh hey, this can be generalized!”

New puzzles! You now know why it’s a Special Puzzle instead of a regular puzzle.
– For what $n$ does the solution for an $n \times n$ grid like above (1s in R1C2, R2C3, R3C4, …, except the last two cells in the diagonal where it has an empty cell and a question mark instead) unique?
– What is the value of the question mark in terms of $n$ for those working $n$ values?

Also, let’s begin with the puzzle test’s teaser 😀
– 9 genres

2 thoughts on “Special Puzzle 8: It’s Erased”

1. Giovanni P. says:

By just solving it logically, there appears to be only one way to lay the wall that satisfies all the rules. My wall fills 30 cells, and can’t fill any more. The logic is fairly simple (ROT-13);

n ybg bs gur fdhnerf, fgnegvat jvgu E1P3 naq E1P1, pna bayl tb va bar qverpgvba gb sbez n qbzvab, naq nf n erfhyg, zbfg bs gur qbzvabrf jvyy rkgraq rvgure qbjajneq be gb gur evtug va n punva ernpgvba. Gur rkprcgvba vf E7P9, juvpu pnaabg rkgraq gb gur evtug be vg jvyy phg bss gur ragver gbc evtug pbeare sebz gur ovt haxabja vfynaq. E8P8 zhfg rkgraq qbjajneq sbe n fvzvyne ernfba.

So, basically it can only be done one way, and Sky should thank his lucky stars it turned out unique and he can keep his job :).