## Puzzle 328 (Fillomino) [Skyscrapers]

This is a Fillomino puzzle, with a twist. There are some clues on the outside edges of the puzzle. If one views the numbers in the completed grid as building heights, then a clue on the outside tells how many of the buildings are visible when looking into that row/column from that location. A clue is visible if and only if it is strictly greater than all clues before it. For instance, if a row reads “13235” from left to right, the clue on the left (if given) would be a 3 (13235) and the clue on the right would be a 1 (13235).

Puzzle 328

(Click for larger size)

This was made early before we had any idea which variations would actually be used. Neither of us ended up making any more Skyscrapers, and later we had enough good puzzles in other variations, so the variation never really entered serious consideration. It is likely a bit easier than what I usually put up on Friday, but that’s probably the case for any of the rejects I’m posting.

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### 8 Responses to “Puzzle 328 (Fillomino) [Skyscrapers]”

1. rob Says:

Thanks for this puzzle. I spent enough time staring at the second half that I think it fits Friday well.

The puzzle felt a little less beautiful than a lot of your other work, but it made that up for me with the interesting solve.

Cheers
Rob

2. Scott Says:

Strangely shaped skyscrapers, but fun puzzle :).

3. mathgrant Says:

Out of your Fillomino-Fillia rejects, this one might have humbled me the most, just because I had no idea that such an elegant and challenging Skyscraper Fillomino could be composed without any givens in the grid.

4. Marcin Says:

Just wow. The initial setup is not as esthetically appealing as most of your puzzles, but it is such a wonderful and rich solve. A true masterpiece!

5. Georgi Says:

When I solve a puzzle I usually try to only make 100% logical steps, but with this one, I gave it a good dose of instinct and half-assed deductions and it pretty much solved itself.

• Andy Says:

Same for me.. I liked the initial setup, and the way the first region sizes were constrained. Then I made some educated guesses based on the left-side clues, and kind of massaged the regions until it worked out. Not to say this reduced my enjoyment, I have come to appreciate some ‘feel’ in solving since I got the hang of Numberlinks. (Wish Bob on nikoli.com could either figure them out or stop solving them altogether)

6. David Scherzinger Says:

Holy balls, this was amazing. It’s a shame the variant is so tough to work with

The left half is actually solvable without any radical assumptions. Once you get the initial setup from the right and determine the absolute maximum area you have left to work with, and the minimum covered area, you have two choices for the leftovers. A combination of geometry and the clues on the left only allows one option, and the rest falls into place nicely.

7. chaotic_iak Says:

Hard. And we’ll have Fillomino-Fillia 2 with two Skyscrapers, one of which worth 18 points. I guess something like this will make a return…uh oh.

Also you should totally give a link to this puzzle when you post a Skyscrapers preview.