### Fillomino by Grant Fikes

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.

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 ?

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?

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.).

…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?).

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

02:33.

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

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.

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

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.

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.

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.