### Fillomino (Symmetry) by John Bulten

PDF

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a number entry mode.)

Theme: Hungry Hearts

Author/Opus: This is the 7th puzzle from our contributing puzzlemaster John Bulten.

Rules: Standard Fillomino rules. For artistic reasons, clues have been replaced with letters using the standard code A=1, B=2, etc. Also, all polyominoes should have rotational symmetry as in this example:

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Use both digits for any two-digit number. Start with the 6th row, followed by a comma, followed by the 4th column.

Time Standards (highlight to view): Grandmaster = 6:00, Master = 8:00, Expert = 16:00

Solution: PDF; a solution video is available here.

Note: Follow this link for other classic Fillomino and this link for more variations on Fillomino puzzles. If you are new to this puzzle type, here are our easiest Fillomino puzzles to get started on.

• Neelix says:

This one has me stumped so far… I can’t find a symmetrical configuration for the O piece which doesn’t either overlap the E or M at the top, or block either the C or the D on the right from having a symmetrical solution…

– Neelix

• Neelix says:

Never mind, I solved it… 🙂
It’s amazing how much the symmetry aspect affects the approach you need to take to solve the puzzle.

– Neelix

• egrieg says:

I was very close to giving up on this one. After staring at it for about an hour with almost no success i was completely frustrated and felt like i had wasted my time. Then after a break i went back to it and managed to guess my way through. Still felt like work for me, and i think this is the first puzzle i encountered here where i have absolutely no clue how the logical solving path might look like. All in all a very unsatisfying solve for me…

• Neelix says:

Gur xrl vf va gur ebgngvbany flzzrgel erdhverzrag, nf gung frireryl yvzvgf gur cbylbzvab funcrf lbh pna hfr. Q’f pna bayl or V, F be B funcrf, R’f pna bayl or V K be M funcrf. Bapr lbh xabj fbzr bs gur rqtrf bs n cbylbzvab lbh pna fgneg ybbxvat ng jurer vg vf cbffvoyr gb cynpr gur zngpuvat bccbfvgr rqtrf. Creuncf gur zbfg pbhagre vaghvgvir guvat nobhg guvf cnegvphyne chmmyr, vf gung vg cynlf zber yvxr n fgnghr cnex guna n svyybzvab, naq lbh arrq gb cynpr gur ynetre cvrprf eryngviryl rneyl, nf gurl gura qrsvar jurer gur fznyyre cvrprf pna tb.

– Neelix

• skynet says:

Thanks for your post.I had the nudge in the proper direction and could complete after close to 2 days of torture.I had a hard time comprehending what rotational symmetry meant and ‘googling’ did not help me much but somehow your post touched the right area in my brain .

Thanks a lot !

• Neelix says:

You’re welcome. 🙂 I’m glad it was useful.

– Neelix

• drsudoku says:

Definitely challenging. As I covered in my walkthrough video, I solved this much more like a Spiral Galaxies using the symmetry constraints than a Fillomino.

• John B says:

Absolutely, this makes repeated use of an important lemma about odd-sized regions that I learned from Spiral Galaxies.

• Carl W says:

Thanks for the amazing puzzle, John! I loved this one.

It was one of those puzzles that just sat me down and said, “Here, you’re going to need to learn some things first before you start making any progress here.” So, I learned something new about spiral galaxies with even vs. odd cell counts that I had never realized before.

As others said, this was more Spiral Galaxies than Fillomino, but the Spiral Galaxies portion was so much more satisfying than straight Spiral Galaxies. Having to construct symmetrical shapes from the endpoints without knowing where the center might be was a really fun aspect here that I’d love to see in more puzzles somehow. And dealing with galaxies of known sizes (but unknown layout) was also a fun aspect not in regular Spiral Galaxies.

Then, aside from the fun words, I like how the theme hid the big numbers behind single “digit” letters. It was a fun surprise at the beginning to see A, B, C… OK…. D, E, F… Sure… Wait, M?!, O!?

And then I really enjoyed thinking through symmetrical possibilities for the several pentominos to try to fit them in (and similarly for the 6 and 7). For the big regions, I constructed those much more one cell at a time, (or at least eliminating possible center points one at a time), whereas with the 5, 6, and 7s I felt like I was placing them as whole “puzzle pieces” as it were.

Anyway, I could go on and on. But I just want to say that the logical path is here every step of the way and it was fun to find.

Thanks again.

• edderiofer says:

Those first few minutes when you first mistake this for a Cipher Fillomino. Then that next minute before you see that the regions all have to be symmetrical…

It still took me ages to solve this even after I noticed these two facts.

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