Thursday 5 July 2012

Puzzle #121: Heyawake; Symmetry

I had first seen this variant on Mathgrant's blog. I thought it worked nicely. So I figured I'd give it a go too. It wasn't the easiest to start as Symmetry is always a weakness for me when solving. It doesn't really register with me too well, usually. But then I got the idea to bring back the Antisymmetry label, which I had added to Puzzle #1, but hadn't used since. I always like to build in some kind of antisymmetry in the givens of my puzzles, except it somehow had never come back in any of my puzzles for my blog. So for this puzzle rotationally symmetrical cages with clues have the opposite clues given. This doesn't hold for cages without givens. It would have been cool if it did, but I think that would be awfully difficult to accomplish.
I think the puzzle worked out in the end. The one cell pairs were to fix uniqueness issues, which didn't really bother the solving path. Enjoy.

Rules for Heyawake

Follow normal Heyawake rules. Additionally, this puzzle has no numbers as clues. Instead the clues indicate if a room has 180 degree rotational symmetry or not. An S indicates that the room has 180 degree rotational symmetry. An A indicates that the room does not have 180 degree rotational symmetry.


  1. the Symmetric boxes nicely set the puzzle up. It was pleasing until the first 18 cells were painted.But after that I had to do t-n-e to determine that R10C4 shouldbe painted.Its a pity that the 2x2 box in the bottom left had to be labelled to allow painting R10C1. I think it could be labelled S , and still be unique.

    1. There's no need for trial and error to solve it.

      Also, I was happy that the bottom left cage was actually necessary. As I made the puzzle with antisymmetric clue distribution, I would have hated it if a clue would have been redundant.

  2. The puzzle solved pretty smoothly for me. I like how the antisymmetry worked out. Always liked this variant.

  3. Solved this one too. Very ingenious design!

    I'm sure you know the ∀人∃HEYA variant where each room is 180 symmetric. This puzzle reminds me of that.