Elemental Balance
(Published on 20. November 2025, 03:46 by Xidak11)
Normal 8x8 Sudoku rules apply. The 4 circles in the grid represent pillars of the four elements of fire (red), earth (green), water (blue), and air (yellow). For the purposes of the remaining rules, these count as 1x1 regions.
The rest of the board consists of 12 regions that are uniquely shaped as the 12 pentominoes (5 orthogonally connected squares). Color each region with an elemental color so that they orthogonally touch as many other colors as possible. Each element has the same number of regions. Regions of the same color cannot touch orthogonally.
These 5 cell regions act as killer cages where the top row's leftmost cell is marked by the sum of the region. The number that appears on the elemental pillars does not appear in the opposite elements regions. For example, the number that appears on the fire (red) pillar does not appear in any water (blue) regions and vice versa. This is the same for air (yellow) and earth (green). All pillars have a unique number.
This is the first puzzle I've set, so all comments and feedback are welcome!
Solution code: Enter the digits from rows 3 and 6 without spaces
Comments
on 22. November 2025, 11:19 by vollbesonderbar
What a gorgeous pleasure!
Long way i followed a rule, that wasn`t demanded ... but still al long beautiful path to go!
Thanks a lot!
on 20. November 2025, 18:59 by Xidak11
Clarification of rules.
on 20. November 2025, 18:08 by jmw
Really nice puzzle. Seemed like 3.5 to 4 stars to me, but maybe I missed a trick.
I found the instructions slightly confusing to begin with, so possibly worth clarifying for other solvers: "The number that appears on the elemental pillars does not appear in the opposite elements regions" means diagonally opposite, i.e. the number in the red circle can't appear in any blue region and vice versa, while the number in the yellow circle can't appear in any green region and vice versa.
