Duelling Regions Intro
(Published on 3. August 2026, 13:30 by Mad-Tyas)
Sudoku on:
SudokuPad
Rules:
Chaos Construction: The grid has to be devided into six regions of orthogonally connected cells. Each row, column and region has to contain the digits 1-6 once each.
Duels: At each region border, a duel takes place between the adjacent regions. To determine the outcome, for both sides the contiguous sequences of cells extending perpenticular from the region border to the next region border or the edge of the grid are compared. The region whose sequence of cells has the higher sum of digits wins the duel. An award of X points for the winning region and a penalty of -X points for the defeated region are taken by the cells touching the region border where the duel takes place. X equals the number of cells in the sequence of the defeated region. If the sum in both sequences is equal it's a tie and no points are awarded.
Clues:
- An arrow between cells marks a region border and points to the defeated region in the duel at that border.
- A diamond marks a region border where the outcome of the duel is a tie.
- A small number in the bottom-right corner of a cell gives the total points this cell wins/loses in the duels at it's up to 3 region borders.
Have fun solving!
Example: This is the solution to a 5x5 example puzzle. For the arrows shown, the points gained or lost are indicated to illustrate how duels work. For example, the central cell loses the duel at its left-hand region border (sum of 5 [4+1] is less than sum of 8 [5+3]) and receives 2 minus points, as the sequence of cells in the losing region (blue) consists of 2 cells. The cell wins the duel at its upper region border (4 against 2) and gains 1 positive point for this, as the losing region (green) contributes only one cell to the duel. At the lower region border, the result is a tie (4 = 3 + 1). This results in a total score of -2 + 1 + 0 = -1 for the cell in question.
Solution code: The 6 digits from column 4 (top-to-bottom) separated by (+) for borders between regions
Comments
on 3. September 2026, 10:12 by PrimeWeasel
Lovely ruleset and great execution of an introduction to it!
on 18. August 2026, 16:59 by War
Very cool Ruleset! Can't wait to catch up on your puzzles :D
on 4. August 2026, 03:46 by Big Tiger
Well, I see the two stars and people solving it with enthusiasm ... I can't get my first digit, ha ha. I'll come back and try again with a fresh brain another time.
on 3. August 2026, 19:48 by wuc
What a nice flowing approachable cc puzzle. What a great fun to play. Looking forward to me using this ruleset.
-Reply: Thank you for your comment! Another setter who wants to create puzzles with a ruleset I invented is probably the best compliment as a setter I can get. And I always enjoy to solve these puzzles so I'm looking forward to whatever you come up with if you have a go on the ruleset.
on 3. August 2026, 19:15 by Clipper
This was an extremely satisfying solve once I understood the scoring constraint. The example was very useful for that.
I loved the novelty of some of the early deductions and anticipate where this will go when extended to larger grids.
-Reply: Thank you for your comment! It's nice to read you found the solve satisfying. I enjoy exploring the constraint so there will very likely be a lot more puzzles based on this concept.
on 3. August 2026, 16:50 by Sinuit
Very cool ruleset and puzzle! It almost took me longer to read and understand the rules than solving the puzzle. :-)
But once I got my head around it, everything flowed very nicely.
Looking forward to the 9x9 puzzle hoping it will still be approachable.
-Reply: Thank you for your comment! I'm glad you liked the puzzle. The 9x9 I already finished can not be called "approachable" and is quite a challenge. But I'll definitely construct more puzzles and also more approachable ones. If I manage to finish an approachable 9x9 during the next few days I'll probably publish it before the difficult one.
