Aqres of Shikaku Country (9x9)
(Published on 29. October 2022, 22:57 by mathpesto)
A collaboration by Nordy and Math Pesto.
Rules:
Each digit or "?" in a circle is a clue referring to Shikaku, Country Road, and/or Aqre rules. Each region contains at most one of each clue type. A region may contain zero, one, or more than one circle. A ? represents a nonnegative integer, and ?’s within the same circle have the same value. Region borders and the country road loop may not go through any circles.
Shikaku: Divide the grid into rectangular regions. A Shikaku clue is the amount of cells in that region. (Note: Unlike standard Shikaku, not every region necessarily has a Shikaku clue.)
Country Road: Draw a non-intersecting loop through the centers of some cells which passes through each region exactly once. For any pair of orthogonally adjacent cells on either side of a region border, at least one of those cells must be visited by the loop. A Country Road clue is the amount of cells visited by the loop in that region.
Aqre: Shade some cells so that all shaded cells form one orthogonally connected area. There may not exist a run of more than three consecutive shaded or unshaded cells horizontally or vertically in the grid. An Aqre clue is the amount of shaded cells in that region.
Solution code: The number of regions in Row 1, then Row 3, then Row 9. The number of cells visited by the loop in Row 1, then Row 3, then Row 9. The number of shaded cells in Row 1, then Row 3, then Row 9. (9 digits, no spaces)
Comments
on 1. January 2024, 15:01 by Jasura
This was delicious. Thank you
on 21. May 2023, 06:08 by Agent
Great puzzle, took a while to get accustomed to the rules but once I did it flowed very nicely.
on 10. January 2023, 02:55 by Myxo
Incredible puzzle!
on 7. January 2023, 00:27 by filuta
I really liked how all the rules are used all the time - as a side effect it makes the individual rules harder to forget.
The puzzle is really well set and so much fun till the end.
on 4. November 2022, 11:09 by MagnusJosefsson
Fantastic! Very nice solution path that really requires switching back and forth between the different rulesets continuously throughout the solve. Really important to choose good notation and coloring to keep track of everything.
on 2. November 2022, 18:03 by ONeill
Great puzzle, even though I broke it several times. Thanks :)
on 1. November 2022, 17:24 by mathpesto
Updated links and images to include dashed grid.
on 31. October 2022, 07:23 by 85392
Nice puzzle, although there are parts where I had to bifurcate because I didn’t get the logic. I also had to do the 5x5 example and the 6x6 version to get a grasp of the logic required here. Although the aqre part of the 6x6 also required some bifurcation…
on 30. October 2022, 10:08 by Jesper
Awesome puzzle, thanks!
on 30. October 2022, 07:36 by wooferzfg
Excellent! The logic was really satisfying after getting a good grasp on the ruleset.
