Fillomino (Checkered) by Jonas Gleim
or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing, a number entry mode, and shading for this variation.)
Theme: 2020
Author/Opus: This is the 3rd puzzle from guest contributor Jonas Gleim.
Rules: Standard Fillomino rules. Also, it must be possible to shade some polyominoes black so that no bordering polyominoes are the same color (in other words, the grid must allow a two-color shading).
See also this example:
Difficulty: 4 stars
Time Standards (highlight to view): Grandmaster = 8:30, Master = 15:00, Expert = 30:00
Solution: PDF; a solution video is also available here.
Note: Follow this link for classic Fillomino and this link for Fillomino variations. If you are new to this puzzle type, here are our easiest Fillomino puzzles to get started on. More Fillomino puzzles can be found in The Art of Puzzles, in Fill o’ Fillomino and Fill o’ Fillomino 2 by Grant Fikes, and in our beginner-friendly books Logic Puzzles 101 and Starter Pack 1: Fillomino.
Difficult but great puzzle! The checkerboard logic works surprisingly well with the fillomino logic, and the ways in which certain potentially-ambiguous parts of the grid get resolved are really clever.
Took me a bit to get started, but only because I was trying to solve it with my usual fillomino notation and keep track of the shading in my head. Once I actually started marking it, it all suddenly fell together and went very smoothly with some very nice logical steps. Might be my favorite puzzle of the year, in fact. Would very much like to see more of these.
Solved it without actually doing any shading; my thinking was that gurer arrqf gb or na rira ahzore bs jnyyf ng rnpu vagrefrpgvba, rkprcg ng gur obeqref. That was enough for me to get there, but it was a struggle.
Having now seen your solving video, I’ll actually do the shading next time (if there is a next time). Should’ve known that it would be quite helpful.