Boulder (Fillomino/Heyawake)
(Published on 29. April 2023, 16:15 by mathpesto)
This puzzle is inspired by zetamath’s “Denver”, so please be sure to check that out too!
Rules:
Fillomino: Divide the grid into polyominoes so that no two polyominoes of the same size share an edge. Each cell contains a number equal to the size of its polyomino.
Heyawake: Shade some cells so that shaded cells are not orthogonally adjacent. The remaining unshaded cells form one orthogonally connected area. A line of consecutive unshaded cells may not cross more than one polyomino region border.
Arrows: The number in a cell containing an arrow gives the number of shaded cells in the polyomino that the arrow is directly pointing to.
Solve:
Solution code: Numbers in Column 1 (top to bottom, no spaces)
Comments
on 24. May 2024, 17:22 by mdjvz
Very nice puzzle
on 7. May 2023, 23:07 by Christounet
I had to restart once because of a miscount that made me take a wrong decision at a specific crossroad. Heyawake messes with my brain, but it was very nicely embroidered with the fillomino here ! Thanks !
on 4. May 2023, 15:45 by mathpesto
Removed unnecessary arrow (doesn't affect solve path)
on 4. May 2023, 06:50 by TJReds
Not a big fan of Heyawake so this puzzle was a bit tougher for me, but it was beautifully constructed!
on 30. April 2023, 15:48 by Bootenks
What a piece of art. Simply a must-have solve puzzle.
on 30. April 2023, 10:23 by twobear
Very fun and smooth. Thank you!
on 30. April 2023, 07:05 by Chefofdeath
That was a beautiful puzzle! Thank you for sharing!
on 30. April 2023, 06:20 by KNT
@twobear: the line may not be diagonal
on 30. April 2023, 05:49 by twobear
Clarification question: in the Heyawake rule, “ A line of consecutive unshaded cells may not cross more than one polyomino region border”; here, is the line horizontal/vertical, or can it be diagonal?
on 29. April 2023, 21:44 by Jesper
Very nice combo, thanks
on 29. April 2023, 18:23 by KNT
Super fun and flowy after that hiccup with the rules :)
thanks for this one!
on 29. April 2023, 17:52 by KNT
@mathpesto @h5663454. Thanks! Totally understand now. I misinterpreted the rule as
"A number in a cell with an arrow indicates the number of shaded cells in the direction of that arrow contained within the same region as that arrow."
on 29. April 2023, 17:38 by h5663454
@KNT
Let me think about it, maybe what he meant to express is this:
Also take R2C2 as an example, the arrow in this cell points to a polyomino of unknown size, and this polyomino contains several shaded cells. And the number in R2C2 is the number of shaded cells in this polyomino.
on 29. April 2023, 17:04 by KNT
I do not understand the rule for the arrows at all, nor can I even figure out a sensible way to interpret them.
Take R2C2: this arrow may only point to at most one cell (R1C1), or two if directly pointing can include itself, which doesn't make sense, so R2C2 is a 1 or 2. But these shaded cells must be "in" the polyomino per the rules, and in neither case 1 or 2, the shaded cells that the arrow is referencing would be in the region containing the arrow. What am i missing?
—————-
The arrow in R2C2 is pointing directly to R1C1, so if R2C2 is part of a four-cell polyomino, for example, then R1C1 is part of a polyomino containing 4 shaded cells. Hope that clarifies! -Math Pesto
