Unique Yet Equal
(Published on 27. November 2025, 18:34 by fnin)
Unique Yet Equal
Rules:
Standard placement: The digits from 1 to 8 are placed so that each appears exactly once in every row and every column.
Division into Teams: The digits 1 to 8 are divided into two Teams, with each digit assigned to exactly one Team.
Unique Regions: The final grid is fully partitioned into Regions of orthogonally connected cells (a Region may consist of a single cell). Each Region is built from digits belonging to a single Team, and orthogonally adjacent Regions belong to opposite Teams. Digits do not repeat within a Region. All Regions are unique in their composition of digits.
Connectors: If two adjacent Regions have an equal sum of digits, they are linked by exactly one Connector. In addition, digits separated by a Circular Connector are consecutive, while digits separated by a Square Connector are not required to be.
see also: Battle for territory
Solution code: Enter Row 4 digits.
Comments
on 30. November 2025, 17:12 by ymhsbmbesitwf
@erml digits with an equal sum - adjacent regions 234 and 18 would both sum to 9 and they would necessarily have exactly one connector between them, even if they share borders in two places.
i enjoyed it a lot, i feel it's not for everyone though. there are cool deductions to find within the ruleset and how regions are allowed to connect in this grid, but unless i missed some massive shortcut - eliminating options requires too much lookahead to be universally pleasing
on 28. November 2025, 21:20 by erml
Im in doubt about the equal sum of digits: Equal number of digits or digits with an equal sum?
on 27. November 2025, 21:30 by fnin
Note: Connectors are placed exclusively on Region borders, never on corners.
on 27. November 2025, 20:27 by lmdemasi
Does a connector always lie on a region border?
