Numbered Regions X-Sums (9x9 Chaos Construction)
(Published on 24. November 2022, 22:58 by ONeill)
Divide the grid into nine orthogonally connected regions, each containing nine cells. Each row, column and region must contain the digits 1 to 9.
Each region has a unique region number, equal to the digit in the top left cell of that region. That is, the cell in the region furthest to the left of the highest row the region occupies.
Clues outside the grid are equal to the sum of the first X cells in that row/column from that direction (where X is first digit from that direction), multiplied by the region number of the region the summands belong to. The first X cells from that direction belong to the same region, and the (X+1)th cell belongs to a different region.
A question mark represents any positive integer.
Cells separated by a white dot are consecutive. Cells separated by a black dot have a ratio of 2:1. Not all dots are given.
The puzzle:
Answer check is enabled with digits and green edges.
Solution code: Row 8 with dashes for region borders. For example 231-4-56-987
Comments
on 25. November 2023, 15:42 by Piatato
Lovely!
on 30. November 2022, 20:10 by wildbush7
Loved this rule set - thanks for the puzzle!
on 28. November 2022, 22:08 by KNT
that beginning made me question my sanity for a little bit
awesome CC and not overly difficult at all
on 27. November 2022, 11:27 by Christounet
Excellent puzzle !
Loved the interplay between the clues. The white dot in r6c6-7 was a very subtle addition !
Thanks !
on 27. November 2022, 09:26 by cmb
Brilliant puzzle.
Smooth but narrow solution path.
Thank you.
on 26. November 2022, 20:31 by filuta
fun puzzle, thanks!
on 25. November 2022, 15:22 by Jesper
Lovely puzzle, flows really well!
on 25. November 2022, 12:47 by Vebby
Excellent!
on 25. November 2022, 12:23 by marcmees
very nice. thanks.
on 25. November 2022, 12:12 by Niverio
Enjoyable!
on 25. November 2022, 11:34 by cdwg2000
Very nice!
on 25. November 2022, 11:29 by MagnusJosefsson
Fantastic puzzle with a tight but very clear solution path!
on 25. November 2022, 09:45 by Statistica
"unique region number" means all nine region numbers are different?
—- Yes, essentially each number between 1 and 9 is some region’s region number.
on 25. November 2022, 06:43 by Elliott810
Absolutely brilliant puzzle! Very nice use of the constraints, esp. the region numbers. Take a bow and thanks:)
on 25. November 2022, 00:03 by ONeill
Clarified rules
on 24. November 2022, 23:56 by kjholt
Do the question marks represent single digits or any integer? Also on the link it says every possible clue is given, how is that possible?
--- A question mark represents any positive integer. That rule isn't supposed to be there, I'll remove it now.
on 24. November 2022, 23:03 by lerroyy
Great puzzle with a smooth solve, thanks!
