Logic Masters Deutschland e.V.

A tougher, foggier version of Double-wrapped X-sums


You can attempt this puzzle at this sudokupad link

Important things to note: Guessing is not required at any point, there are logical deductions to be found in order to clear the fog. No two s-cells can have the same pair of digits, and every digit is doubled exactly once. The other rules are all standard and listed below.

Good Luck!

Questions, comments, feedback are always welcome, either here or on the CTC community discord.

Thanks to Bootenks and Darth Paradox for testing and feedback.



The rules:

The grid is covered in fog. Placing correct digits will clear the fog from surrounding cells, possibly revealing more clues. (S-cells are not able to clear fog.)

Normal Schrodinger Sudoku rules apply: Fill the grid with the digits 0-9 such that no digit repeats in a row, column, or box.

S-cells: In each row, column, and box there is exactly one S-cell, S-cells contain two digits instead of one, and their value for the purpose of other clues is the sum of those digits. No two s-cells can have the same pair of digits.

Doublers: One cell in each row, column and box is a doubler. For the purpose of other clues, the cell's value is double the digit (or digits) in the box. Each digit from 0-9 appears exactly once in a doubler cell.

Kropki: Values in cells separated by a white dot are consecutive. Values in cells separated by a black dot are in a 1:2 ratio. Not all dots are necessarily given.

German Whispers: On green lines, adjacent cells have values that differ by at least 5.

Renban: Each purple line contains a set of consecutive values with no repeats. (Digits may repeat if they are in cells with different values)

Killer cages: Digits do not repeat in cages (though values may repeat) and values sum to the total in the top left corner of each cage.

X-sums: Numbers outside the grid give the sum of the first X values in the corresponding row or column, where X is the value closest to the clue.

If the closest value is larger than 9, then the X-sum wraps back to the first value again.
e.g. If the row reads 63291508(47), with a doubled 6 to start and a (47) s-cell to finish, then the X-sum starting from the left would use 12 cells. The first nine cells sum to 51, then the clue wraps, the next three cells are 12+3+2=17, so the X-sum from the left would be 68. If starting from the right, the first value is 11. The first nine cells sum to 51, then the clue wraps, the next two cells are 11+8=19, so the X-sum from the right would be 70.

My three most recent puzzles:
Pacman in the big city
Double-wrapped X-sums
DoubleX-somedoku
If you enjoy this one, please try them too.