### Fillomino by Grant Fikes

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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: Clue Symmetry and Logic

Author/Opus: This is the 99th puzzle from our contributing puzzlemaster Grant Fikes.

Rules: Standard Fillomino rules.

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 4th column, followed by a comma, followed by the 7th column.

Time Standards (highlight to view): Grandmaster = 2:30, Master = 3:30, Expert = 7:00

Solution: PDF

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

• juffowup says:

I love it! Makes me wonder: if clues range from 1 through N, for what values of N is it possible to create an arbitrarily large unclued region ?

• juffowup says:

Thinking about it further, arbitrarily large is overly ambitious. If clues range from 1 through N, how large of an unclued region can one create?

• chaotic_iak says:

I believe you can only create an unclued region of size at most 4N+1, with a proof that is unchecked. (I haven’t solved the above though, so can’t tell if this hypothesis still holds.).

• chaotic_iak says:

…of course I failed myself. Proved that 4N+2 is possible.

Note that this assumes at least one given on the grid, because otherwise we get FAST: a 1×2 Fillomino without givens, where N can’t be determined (what’s the maximum of nothingness?).

• drsudoku says:

I also see the 4N+2 construction, but I don’t quickly see a route to anything larger.

• chaotic_iak says:

02:33.

Oh hey, that’s what it meant for large unclued region. Nice construction, with plenty of hidden polyominoes.

• Nathan says:

Is there a trick to entering 2 digit numbers in solution? I’ve solved this, but keeps telling me my entry is incorrect. Went and solved it from scratch a second time to verify no mistakes, but got identical answer but it won’t accept it as correct.

• furudo.erika says:

As the answer string section of the instructions says: “Enter just the last digit for any two-digit number”

• drsudoku says:

Because of the large number of Fillomino puzzles this week, and not wanting to spoil when two-digit numbers appear, we added the instruction “Enter just the last digit for any two-digit number” and will keep this for Fillomino puzzles in the future.

So if you had a 10 cell, please enter just a 0 for that, and so on. If you are still having problems, feel free to send us email.

• Nathan says:

Ah thanks for clarifying, was driving me mad, and there it was explained the whole time.

I was checking the generic fillomino rules for answer string (as it had example), didn’t think to re-read the original problem statement answer string in detail.

• drsudoku says:

You’ve made a good observation that there is nothing about the two-digit thing either way on the main rules page; I’ll make an edit there to improve the clarity of the entry process.

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