Fillomino (Symmetry) by John Bulten

Fillomino by John Bulten


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: Salt and Pepper (alphanumerically, 19 = S, 16 = P)

Author/Opus: This is the 18th puzzle from our contributing puzzlemaster John Bulten.

Rules: Standard Fillomino rules. Also, all polyominoes should have rotational symmetry as in this example:

Fillomino by Serkan Yürekli

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Enter just the last digit for any two-digit number. Start with the 1st row, followed by a comma, followed by the 10th column.

Time Standards (highlight to view): Grandmaster = 10:00, Master = 22:30, Expert = 45:00

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.

  • Cadavaca says:

    While this particular puzzle wasn’t my favorite, I really appreciate John Bulten’s approach to puzzlemaking. Thanks!

  • skynet says:

    Worst puzzle ever posted in GMP.Not clear how to put even a single digit.

    • Avatar photo drsudoku says:

      I believe you mean “hardest” and not “worst”. I grade the difficulty separate from the quality and I rated both high here. This does require some novel thinking / an aha before you can put in even a single digit.

      • Avatar photo drsudoku says:

        In terms of difficulty this does rank in the top few. Fun fact: Three of our test solvers were unable to finish the puzzle.

        I can confirm, as with all of our other puzzles, that there is just one answer.

      • skynet says:

        I equate worst to “harderst AND unsolveable”.This is one of those rare puzzles which I am not able to solve of all puzzles ever posted in GMP despite investing more than enough time that it deserves .

        • Loren says:

          skynet, this may or may not make you feel better: if you did a number of spiral galaxy puzzles which were made available via GMP (maybe only to patrons), you would note that this puzzle, although named Fillomino (Symmetry), is really very similar with different clue markings in terms of how to make progress. There were some patterns learned by doing that sequence that make this puzzle a lot easier to understand (in my memory/mind). That said, I can see why some people are stuck on this puzzle. -Loren

        • Avatar photo drsudoku says:

          I agree with your general points Loren on Spiral Galaxies experience helping (some others over email raised the same background from other places helping). When we do post Spiral Galaxies regularly — they are a subsection of The Art of Puzzles 2 and I will introduce as a puzzle style here soon — that may be a good time to revisit for some to revisit this puzzle and see if their techniques have gotten stronger.

  • Carl W says:

    This was an extremely unique puzzle! It doesn’t allow anything like an incremental “place one digit at a time” solution, (that I could find), so it’s not much like a typical Fillomino in that regard.

    I found I had most of the structure of the solution in place before I was placing any digits down.

    John, I’m very impressed that you pulled off a puzzle like this while preserving so much symmetry in the presentation. Well done!

    And I’m delighted to hear that this stumped some test solvers too. It’s great to have puzzles that require some very novel approaches.

    Thanks again, John and Thomas!

  • egrieg says:

    After my disastrous experience with the earlier fillomino from John’s debut week, I gave this one a chance, got absolutely nowhere, and happily went right to the walkthrough video. After watching that, i was very happy that i didn’t waste more time on this puzzle, because it would only have frustrated me to no end. Even the intended solving path seemed to me like there was very little logic involved. Definitely not a fair challenge in my opinion, i feel like this should have a disclaimer saying something like “warning: not solvable in a rigorous way” there may be people out there who enjoyed this, for me it was yet another fillomino from john that left me feeling annoyed.

    • Carl W says:

      It’s interesting to see the reactions to this puzzle. The puzzle definitely has something atypical about it because I don’t recall seeing similar reactions to any previous puzzle here.

      I haven’t watched the walkthrough video yet, but I disagree that the puzzle requires any disclaimer. The puzzle definitely does allow a rigorous solution.

      On my first time solving it, after the big breakthrough, I drew in several regions by intuition, (without proving uniqueness, though things felt very constrained so I was willing to believe the solution is unique). I went back now and solved it a second time more rigorously and convinced myself that the solution is definitely unique.

      I’m really curious to watch the video now and see if my approach is quite different than what Thomas came up with.

      • Avatar photo drsudoku says:

        My first reaction to the puzzle was quite similar to what I had when testing John’s Hidden Shape Sudoku which we posted last December. That seems by web comments to have ended up more liked than disliked, but perhaps it had a higher solving success rate than this one.

        It is worth pointing out in both cases that we had atypical test-solving results. I had 4 testers on that sudoku of which 2 did not finish; here I had 8 testers and 3 did not finish. Both puzzles are quite unusual and would fail if my editorial goal was 100% success across all our solvers. The only absolute editorial goals on Friday/Saturday are (A) me knowing there is one solution that I can demonstrate with 100% confidence by human means (I never ever rely on code to confirm this, but code is part of most of our regular publishing as back-up confirmation when generating the art) and (B) that there are sufficient rewards for enough solvers that it is worth risking being “too hard”.

        I do recognize in posting an unusual puzzle like this that I am necessarily dividing my solvers into these three groups:

        1) Those who never reach a solution/give up.

        2) Those who reach a solution but aren’t satisfied by the steps they took to get there (perhaps because they only reached the solution by trial and error; perhaps because they followed the intended path but the steps do not seem solid so the solver is left thinking they have an answer but not necessary THE answer).

        3) Those who reach a solution by seeing all the Ahas and/or persisting past state (2) to know they have THE answer.

        Group 1 will hate the puzzle. Group 2 will be, at best, indifferent and will want to know more, and in some cases may lose trust in me. Group 3 will be satisfied far beyond normal puzzle posts for having conquered the challenge. I weigh the expected joy of group 3 against the expected response of group 1/2 but not all decisions are easy.

        Rereading the Hidden Shape Sudoku comments, you can identifying members from each of these groups, including the natural group 2 desire to know more and the natural group 3 hesitancy to not hint too much to the other group because they don’t want to diminish the reward of seeing through the Ahas by oneself. Perhaps over time this comment thread will grow the same way.

        For many people, including myself, the greatest joys in puzzles come from conquering seemingly impossible challenges (e.g., MIT Mystery Hunt, Palmer’s toughest, …). I can’t hold back every challenge that will come from an unfamiliar place if it is an Everest some people can climb.

        Maybe we should do disclaimers; at the very least I think I should not try to release any timing info on a puzzle like this because this is not a fair competition puzzle. But we don’t only publish competition puzzles here that use well-explored heuristics. My greatest puzzling moment is still solving the toroidal sudoku at WSC1, where all other solvers in 15 minutes placed 1 digit. Is that a broken competition puzzle? Yes. Would I deny that level of challenge to my audience uniformly? No. But it will be a rare thing to post as only few solvers will be able to look at things a little differently and find THE answer.

        So thanks everyone for the feedback — it is taken seriously — and also thanks for your patience on posts like this where I push the boundaries. John made an amazing puzzle based on my quality rating, and I’m quite happy to receive such creative constructions that are rare to find. But I know you can’t all share my tastes or always be satisfied by the puzzles that surprise me.

        • Loren says:

          This puzzle is the exact reason I patronize GMP (and I suspect that I am not alone). I want the best/hardest/novel/diverse/interesting/curated logic puzzles to fill my limited time to engage my brain with pure logic puzzles. I don’t care if a puzzle sits in the back of my head for days waiting for the ahas. They almost always come with time and background thinking. That said, I do recall having to ask for spoilers for a few puzzles over the years in this forum; so I don’t want to discount anyone else’s frustration with a/this puzzle. But the rot13 help which almost always appears when someone gets stuck and asks for a community hint, is what makes this forum special IMHO.

          Regarding the need for special disclaimers. I think you already have it. Any puzzle listed as 45 minutes for the expert time (and if I recall correctly, there was once a 2 hour+ expert time) would seem to already be properly disclaimed…

          This is Grandmaster Puzzles not Slightly-Interesting Puzzles.

  • JuffoWup says:

    This is a beautiful puzzle, one of my favorites. I’m impressed by the way it manages to shoehorn itself into a unique and satisfying solution.

  • Rob says:

    A beautiful puzzle, count me in group 3! And I’m glad I didn’t have to solve this in competition.

    I would say I was quite close to a rigorous solve. I haven’t seen the walkthrough, but as far as I can tell nyy ohg gur pbeerpg zveebe bs gur obggbz evtug gevcyrg pna or ehyrq bhg dhvgr rnfvyl. (Vg urycf gb xabj gung gur 19f jvyy or ebgngvbanyyl flzzrgevp nebhaq n pryy pragre, gung qbrfa’g yrnir znal bcgvbaf.)

    Vg qvqa’g uryc gung V jnf pbaivaprq sbe n tbbq juvyr gung sbhe gvzrf avargrra cyhf gjb gvzrf fvkgrra cyhf gjb vf n uhaqerq…

  • Francis says:

    If I could triple-fave this, I would. John Bulten’s puzzles are always very challenging — sometimes in a way I find frustrating, and sometimes in a way I find exhilarating. This was the latter by a lot. One of the best puzzles ever published here, in my opinion anyway. (Granted, I already love both of the puzzle types being combined here.)

  • FoxFireX says:

    Late to the game, but count me in group three. This puzzle sat with no digits filled for several days as I stared at it each evening. After a few fruitless days, I finally reached one epiphany, but by itself that wasn’t enough to even let me get started. It was the following day when the companion realization finally dawned on me, and the moment that hit, the puzzle fell in a completely logical and solvable path.

    The difficulty was high. The pleasure in finally discovering the solution path even more so.

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