Pentominous Haisu Permaculture
(Published on 1. April 2026, 23:39 by Andrewsarchus)
Rules:
- Permaculture:
Divide the grid into two orthogonally connected regions.
(One Pentominous region and one Haisu region). - Pentominous:
Divide the Pentominous Region fully into pentominoes (orthogonally-connected regions of five cells each).
Cells with a Letter clue (excluding S and G) belong to the Pentominous Region, and indicate which type of pentomino contains that cell (using the standard pentominous nomenclature: F,I,L,P,N,T,U,V,W,X,Y,Z).
Within the Pentominous Region, pentominoes of the same type cannot share an edge. - Haisu:
Divide the Haisu region into subregions, and draw a non-intersecting path which connects the cell centers of orthogonally adjacent cells.
Cells with a Number clue as well as the given one-cell "S" and "G" regions belong to the Haisu Region.
The path starts at "S" and ends at "G" and must visit every cell in the Haisu Region.
The path may only enter a cell containing a digit N on its Nth visit to that subregion.
In this puzzle:
Henceforth, the term "subregion" will exclude the one-cell "S" and "G" regions.
The Haisu subregions must each contain at least one cell with a given digit, and may not contain repeated digits.
The given digits included in the Haisu subregion must include the digit equal to the total number of visits to that region. - Interaction:
Every Haisu subregion on the boundary of the Pentominous Region must share at least one edge with a Pentominous subregion (pentomino) which is the same shape as itself (allowing for rotation and reflection).
...and likewise...
Every Pentomino in the Pentominous Region on the boundary of the Haisu Region must share at least one edge with a Haisu subregion of the same shape as itself (allowing for rotation and reflection).
Additionally...
Any pair of Haisu subregions which share a border must include at least one subregion which also shares a border with the Pentominous Region. - Answer Check:
Red Edges for region borders.
Green Lines for the path.
If solution check does not trigger, try removing any surface coloring. There appears to be a penpa glitch causing it to affect the solution check.
Play Online:
penpa+: Pentominous Haisu Permaculture
Solution code: Number of turns in each row from top to bottom
Comments
on 13. April 2026, 05:10 by SamuPiano
Really impressive construction! Finding a grid that satisfied all these restrictions must have been pretty tough :)
on 9. April 2026, 09:36 by tnop62830
An excellent puzzle, with an excellent solve path!
It's perhaps implied, but not expicitly stated:
**The path remains entirely within the Haisu region.**
...that tripped me up for a little while trying to find a "canonical" solution when multiple exist without the constraint
on 5. April 2026, 12:42 by Agent
Epic puzzle, the variety of logic is impressive!
on 2. April 2026, 01:03 by Justalilguy
Incredibly intricate puzzle with amazing interaction between two permacultures. Loved it.
on 2. April 2026, 01:02 by Andrewsarchus
fixed solution code
