## Puzzle 334 (Fillomino) [Potpourri]

This is a Fillomino Potpourri puzzle. Almost all of your favorite Fillomino variations that made an appearance in Fillomino-Fillia have been rolled into one. Detailed rules follow below the image.

Puzzle 334

(Click for larger size)

Rules: Standard Fillomino rules apply. In addition, the following variations take effect:

• Star: Not all squares contain numbers. Each square without a number contains a star. Every row and column has exactly two stars. Squares with stars may not touch, even at a corner.
• Shape: The shapes shown beside the puzzle must appear as polyominoes in the grid. Shapes may be rotated, but not reflected.
• Sum: The grid contains some cages. The number at the top left of each cage gives the sum of all numbers that appear inside of it. Numbers may be repeated in cages. Stars count as 0 in sums.
• Greater-Than: The grid contains inequality signs. Each sign must point from a larger polyomino to a smaller one. Stars are less than any number; that is, they function as a 0 in inequalities.
• Even-Odd: The odd numbers must form a single polyomino, and the even numbers must similarly form a single polyomino. Stars are neither even nor odd.

(Shikaku and Cipher do not make an appearance in this puzzle.)

I came up with the idea for this while looking over our Fillomino variations, both ones we used and ones we didn’t. It occurred to me it almost looked like a list of Sudoku variations, what with there being Even-Odd, Nonconsecutive, Greater-Than…. Somehow this eventually got me to thinking about the chimeras at the end of Mutant Sudoku by Thomas Snyder and Wei-Hwa Huang. Could we do such a thing for Fillomino too?

Yes, it turns out we can. Enjoy.

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### 14 Responses to “Puzzle 334 (Fillomino) [Potpourri]”

1. mathgrant Says:

I haven’t begun to solve this puzzle yet, and I already like it. X3

2. xevs Says:

Cool design! Symmetorical, consecutive, no useless clues! And this difficulty. I really want to make puzzle like this!!
Now, I will go back to puzzle 23 and go on crawling 🙂

3. rob Says:

This one took me quite a while. I made quite a few wrong deductions along the way, but eventually I got through. Thanks!

4. David Scherzinger Says:

That break-in didn’t just blow my mind. It blew my soul.
I hope you’re happy.

5. Thomas Snyder Says:

Very nice.

6. Nikola Says:

This is one of the best puzzles which I ever solved. Great finishing of wonderful competition. Thanks for this.

Nikola

7. araya Says:

Melon, I’ve been solving your puzzles for just a few weeks with no comment, but after this one I feel compelled to post – this is one of the best puzzles I’ve ever had the pleasure of working on. What a beauty. Really high quality stuff. Thanks for all your hard work!!!

8. Giovanni P. Says:

Let me pretty much add to the “awesome puzzle” comments. I solved this a a little while back and never commented.

I have to say, I loved how all of the different rules interacted with each other for this puzzle, and how different rules were emphasized as the puzzle progressed. From the break in, to the star placement, to the filling in of the even-odd polyminoes. In one word, excellent.

And now you listed it as one of the hardest puzzles on your blog. I’m 2 for 5! 😀

A hint for anyone who is having trouble getting started: The maximum number of stars in a 2×2 area is 1. That, and read the rules carefully.

9. pestofruit Says:

Like araya, I’ve been solving your puzzles for a few weeks, but this one forces me out of lurkerdom to say “wow.” Amazing.

10. Parmenion Says:

I guess I’ll chime in as a lurker as well. It wasn’t anywhere near the hardest for me to do (I guess I didn’t have a broken logic chain while in slitherlinks I often make a mistake somewhere), but the tricks were nice all the way along. Great puzzle (and, in general, great puzzles).

11. Bryce Herdt Says:

Solved. And it only took me six months and two days!

12. Did I ever say my computer broke like a month or two ago? | Chaos at the Sky Says:

[…] that in terms of presentation (although I think I made a couple of insane variants, trying to match other works). Sooo… We’ll see if I have time to squeeze out something. Hey, I’m busy […]