Tenth in a series with puzzle solving tips. This time with advice on Fillomino puzzles and hidden polyominoes.

Fillomino is one of my favorite puzzle styles, in part because it is one of the few where I think the author’s touch can come across in the puzzle in so many different ways. In the set of Fillominoes I’ve gotten from different authors, I think I can pick out some authors from others just based on how much they use visual patterns, one-option polyomino growth, crowding, counting, how well they conceal hidden pentominoes, and so on. While having a variety of puzzle constructors will improve most sections of The Art of Puzzles, Fillomino is hands-down in my mind the one where having many authors will have the greatest effect on quality.

I wanted to talk about one of my own constructing trends which I learned this week after writing 7 Fillomino puzzles (only a few that went online; some are going to GAMES and others are being saved). That is what I’ll call the “known unknowns”. The picture you should have in your head when considering a choice based on the hidden polyominoes you’ll leave behind. The contradictions in the “known unknowns” are the basis for the Saturday Fillomino.

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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: Squeeze Play

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 7th row, followed by a comma, followed by the 9th column.

Time Standards (highlight to view): Grandmaster = 4:30, Master = 9:00, Expert = 18:00

Note: Advice on solving this puzzle has now been posted in “Ask Dr. Sudoku #10”

Solution: PDF

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.

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: Rough Diamond, or Diamond in the Rough?

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 9th row, followed by a comma, followed by the 6th column.

Time Standards (highlight to view): Grandmaster = 2:45, Master = 4:00, Expert = 8:00

Solution: PDF

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.

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: Two by Fours

Rules: Standard Fillomino rules.

Answer String: For each cell in the marked rows/columns, enter the area of the polyomino it belongs to. Start with the 9th row, followed by a comma, followed by the 10th column.

Time Standards (highlight to view): Grandmaster = 1:15, Master = 1:45, Expert = 3:30

Solution: PDF

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.