Logic Masters Deutschland e.V.

Title: XV Schrödinger VX
Type: Sudoku
Link: CTC App link to XV Schrödinger VX Sudoku
Link: F-puzzles link to XV Schrödinger VX Sudoku
Variants: XV, Modified VX, Schrödinger Cells, Oddruples, Quadruples

1) Sudoku

• 1.1) Place the digits 0 through 9 once each in every row, column, and box. Two of the digits will have to share a Schrödinger Cell.
• 1.2) When using f-puzzle, I recommend leaving a cell empty but with a certain color to represent 0.
• 1.3) When using the CTC App, to enable answer check, only enter the lowest digit of the Schrödinger Cell.

• 2.1) An X either sums or multiplies two adjacent cells (being simultaneously a sum and a multiplication is permitted).
• a) When X acts as a sum, the two cells sum to 10.
• b) When X acts as a multiplication sign, the two cells are multiplied together with their product immediately following to the right for rows or downward for columns. Multiplications cannot have a leading zero. e.g. 4 X 8 0 3 2 is not permitted, but 4 X 5 2 0 is permitted.
• i) Not all sums of 10 are given.
• ii) Not all multiplications are given.
• 2.2) A V either sums or represents an inequality between two adjacent cells (being simultaneously a sum and an inequality is permitted).
• a) When V acts as a sum, the two cells sum to 5.
• b) When V acts as an inequality, the one cell is greater than the other in the direction of the V. Note two V's in Box 8 have been rotated to preserve symmetry.
• i) Not all sums of 5 are given.
• ii) Not all inequalities are given.

3) Schrödinger Cells

• 3.1) There is one Schrödinger Cell for every row, column and box for a total of nine cells. They cannot see each other.
• 3.2) A Schrödinger Cell contains two different digits of 1 to 9 (no 0's).
• a) For the nine Schrödinger Cells, the set of 1 to 9 will be used twice (18 total). e.g. [13] [14] [17] is not permitted as the digit 1 is used three times.
• b) The value of the two digits are added together for constraint calculations. e.g. A Schrödinger Cell containing [13] has a value of 4 and counts as two odd. [49] a value of 13, counts as one odd. [03] would not be permitted as it contains a 0.

4) Oddruple

• The digit in a grey circle indicates how many odd digits occur in the 4 surrounding cells. Note: if there are surrounding Schrödinger Cells, the Oddruple could be as high as 6!

5) Quadruple

• Digits in a white circle must appear somewhere in the 4 surrounding cells and may repeat if allowed by Sudoku. Note: two of the digits may be in Schrödinger Cells.

Examples (0 for CTC/Penpa+, 9 for f-puzzles):

ROW 2--Six multiplied by five equals thirty (6 X 5 3 0).
ROW 3--Five summed with zero equals five (5 V 0).
ROW 4--Three summed with two equals five, also two multiplied by four equals eight (3 V 2 X 4 8).
COLUMN 1--Six is greater than five, also five is greater than three (6 V 5 V 3).
COLUMN 2--Five is greater than zero but also five summed with zero equals zero (5 V 0).
COLUMN 3--Two multiplied by three equals six, also six summed with four equals ten (2 X 3 6 X 4).
COLUMN 4--Seven is greater zero, also two summed with eight equals ten (7 V 0 2 X 8)