Doubles, Halves and the Lines
(Published on 19. November 2022, 19:13 by Nai Night)
I believe that is a hard puzzle and it must be resolved with caution because it is easy to make a false conclusion.
Rules:
- Normal Sudoku rules apply.
- Digits in a cage cannot repeat and must sum to the small clue in the top left corner of the cage.
- Blue lines are '2-union equal sum lines', and for each line has a cell that acts as a pivot(to be discovered by the solver), that will split the line in 2 'equal sum lines' and the value of the pivot will count for both lines, each 'equal sum lines' will pass for at least 2 boxes and can have different sum than the other line. A 'equal sum lines' is a line that, the digits along these line must have the same sum in each 3x3 box entered by the line. The sum applies to each individual visit a line makes to a box.
- The grid contains nine 'multipliers', one in each row, column and 3x3 box, each digit from 1-9 is a 'multiplier' exactly once. Odd digits will be multiplied by two and the even digits will be multiplied by half for the purposes of the lines.
A small exemple of grid with this rules:
The red circles are the multipliers and the blue square is the pivot of the line.
Solve online:
Solution code: Column 7, followed by Column 8 (18 digits, no spaces).
Solved by gfoot, WedgeOfCheese, Bootenks
Comments
Last changed on 3. December 2022, 13:02on 3. December 2022, 13:02 by Bootenks
Intrigued puzzle searches for enthusastic solvers who want to be challenged.
Chapeau!
on 20. November 2022, 23:12 by gfoot
Nice puzzle, very tricky and hard to spot how to proceed but there was always a way - it's one of those that I want to solve again afterwards to optimise the solution path in retrospect