This is a Fillomino Potpourri puzzle. Almost all of your favorite Fillomino variations that made an appearance in Fillomino-Fillia have been rolled into one. Detailed rules follow below the image.
(Click for larger size)
Rules: Standard Fillomino rules apply. In addition, the following variations take effect:
- Star: Not all squares contain numbers. Each square without a number contains a star. Every row and column has exactly two stars. Squares with stars may not touch, even at a corner.
- Shape: The shapes shown beside the puzzle must appear as polyominoes in the grid. Shapes may be rotated, but not reflected.
- Sum: The grid contains some cages. The number at the top left of each cage gives the sum of all numbers that appear inside of it. Numbers may be repeated in cages. Stars count as 0 in sums.
- Greater-Than: The grid contains inequality signs. Each sign must point from a larger polyomino to a smaller one. Stars are less than any number; that is, they function as a 0 in inequalities.
- Even-Odd: The odd numbers must form a single polyomino, and the even numbers must similarly form a single polyomino. Stars are neither even nor odd.
(Shikaku and Cipher do not make an appearance in this puzzle.)
I came up with the idea for this while looking over our Fillomino variations, both ones we used and ones we didn’t. It occurred to me it almost looked like a list of Sudoku variations, what with there being Even-Odd, Nonconsecutive, Greater-Than…. Somehow this eventually got me to thinking about the chimeras at the end of Mutant Sudoku by Thomas Snyder and Wei-Hwa Huang. Could we do such a thing for Fillomino too?
Yes, it turns out we can. Enjoy.