Off by Sum
(Published on 8. November 2025, 04:28 by Quillslash)
click on image to play
Normal sudoku rules apply.
Killer cages: Digits in a cage sum to the small number (value)* in the top left of the cage
Region sum lines: A line crossing a border between two boxes splits it into two regions, which sum to the same value*
*Offset numbers: Digits outside the 5x5 offset the values in their row/column** by that amount. Each row and column has a unique offset from the digits 0-4 (there are 0-4 in both the column and row outside the 5x5)
** For a region sum line/killer cage to be in the row/column it must be in 2 cells of that row/column
example
Solution code: The offset numbers read top to bottom (column), then left to right (row) - should be 10 characters long.
Comments
on 12. November 2025, 20:38 by dzamie
The hardest part of the puzzle by far is understanding the rules. They seem to be:
* Each row has a unique Offset value 0-4, as does each column. If at least two cells in a cage or on a line are in a row or column, that cage's or line's Offset is equal to the Offset value of the row or column. If a cage or line has 2+ cells in both a row and a column, then the row's, column's, and cage/line's Offset values are all the same number.
* Offsets do not affect the digits in the grid in any way; they only affect how cages and lines work.
* The sum of digits in a killer cage differs from the small number in the top left by exactly the cage's Offset.
* For digits on a region sum line, the sums of numbers on either side of a box border differ from each other by exactly the line's Offset.
(I explicitly stated the "affected by row AND column" thing, because a similar ruleset could well have it be that the offsets get added and/or subtracted)
on 9. November 2025, 16:12 by MartinR
Interesting idea, but think the offset rule could be better worded, maybe each rule in a row/column is off by x, or wrong by exactly x"
Otherwise, as the rules say the *values* in a row are offset by x, this causes a problem in the example 2-4 region sum (where region sums to same value) you can't offset both values as written as it would still be wrong.
