Fortress Fillomino - Greatest Lines (7×7)
(Published on 25. September 2026, 16:45 by aqjhs)
So Dorlir kindly asked for more puzzles using the Greatest Line constraint, and I found Fortress Fillomino was the way to deliver.
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Fortress Fillomino:
- Divide the grid into orthogonally connected regions and fill each cell with a number (not necessarily single-digit) showing the number of cells in the region to which it belongs;
- Each region must be either strictly larger than all of its orthogonal neighbours or strictly smaller than all of its orthogonal neighbours.
- Greatest Lines: On each line, there is exactly one cell whose value is greater than the sum of any other two cells on that line.
See also:
Solution code: Column 6, top to bottom.
Comments
on 29. September 2026, 16:37 by Piatato
Neat!
on 27. September 2026, 17:31 by kasperd
It was easy to find a solution (1-2 stars of difficulty), but I don't see any straightforward way to show that this solution is unique.
on 27. September 2026, 09:12 by richcard
Is there an ambiguity in the rules? I'm not sure whether a line could be 1135, for example.
Allowed: The 5 is the only cell whose value is greater than all pairs of two other cells
Not allowed: The 3 and 5 are both "greater than the sum of any other two cells" because they are greater than 1 + 1
It's my first time seeing these lines, so I may be being thick...
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the example 1135 is a valid line since it has one digit (5) that is greater than any possible sum of two of the other digits.
a non example is 1235, because 5 itself is not greater than 2+3.
on 25. September 2026, 22:47 by Flinty
Very swish setting! :)
on 25. September 2026, 19:56 by ThePedallingPianist
Thank you for this excellent debut in the series! Lots of very fresh-feeling logic in this, loved it!
