Double+Negative X-Sums
(Eingestellt am 4. Juli 2025, 18:21 Uhr von qoala)
Chaos Construction messing with double-chaos-X-Sums and a pair of negative constraints.
- Normal Chaos Construction: Fill each row, column, & region with the digits 1-9 once each. Regions consist of 9 orthogonally-connected cells and must be determined by the solver.
- Chaos X-Sums: Black and red clues outside the grid give the sum of the first N cells in that row/column, where N is the first digit seen from the clue. These N cells all belong to the same region, and if the N+1th cell is inside the grid, it must be a different region.
- Double Chaos X-Sums: Red clues outside the grid apply again starting from the N+1th cell. (The same clue indicates the sum of the M cells starting from cell N+1, where M is the value in the N+1th cell. Those M cells all belong to the same region, and the subsequent N+M+1th cell belongs to a different region, if present.)
- A '?' clue can indicate a series of cells with any sum. The red '?' clue may have different sums for the first and second seen regions.
- Squares: A digit in a square indicates the number of cells in the same region seen orthogonally, including itself. Region borders block vision.
- Negative Constraint: All outside edge positions that could have a valid Chaos X-Sum clue have one.
- Negative Constraint: All valid squares are given.
- Two region borders are given between r3c1:r4c1 and between r4c2:r4c3.
Example for Double Chaos X clues and the negative constraint:
- In row 4 with a red clue, the 3 and 2 give the extents of those first two regions in the row. As the clue is a question mark, 3+4+5=12 and 2+7=9 may have different sums.
- In row 5 with a black clue, the 4 gives the extent of the first region of its row.
- Similarly for row 2 and the 2. This could have been a red question mark, because the 1 in r2c3 correctly describes the extent of that second region, but a black clue is sufficient to satisfy the negative constraint. A black clue gives no indication about digits and regions beyond the first.
- In column 4, the 3 in r2c4 correctly describes the extent of that second region in the column, but because r1c4 contains a 6, no Chaos X clue is possible.
- The corner-marked 1 in r1c1 cannot actually be a 1, because it would correctly describe the extent of the first region in its row and no Chaos X clue is present for the row.
SudokuPad: https://sudokupad.app/zd3sn059zf
Chaos Constructions:
- Impostor Chaos
- HeX-Sums
- Double+Negative X-Sums
Lösungscode: Row 5 (9 digits), with '-' for region borders.
Gelöst von Eespi, Joyofrandomness, jkuo7, marcmees, wenchang, zeniko, Vodakhan , Voidslime, halakani, wildbush7, BeeBoi, MaizeGator, Kavman15, sehringdipity, steeto, mellowrobinson, Asphodel, AAAAAAAAAAAAAAAAAAA, peacherwu2, dogfarts, dustpan, jsalomon, bansalsaab
Kommentare
am 6. Juli 2025, 16:20 Uhr von Voidslime
Very fun and satisfying!
am 5. Juli 2025, 23:39 Uhr von zeniko
This felt a bit easier than HeX-Sums, but was still quite hard due to the two negative constraints. Thanks for sharing.
am 5. Juli 2025, 18:52 Uhr von marcmees
enjoyable solve. Thanks