Logic Masters Deutschland e.V.

Title: XV Kropki VX
Type: Sudoku
Link: Penpa+ link to XV Kropki VX Sudoku You may use Normal/Large/Medium/Small Blue, Green, or Red numbers in any combination.
Link: F-puzzles link to XV Kropki VX Sudoku
Variants: XV, Modified VX, Kropki pairs

1) Normal Sudoku

• 1.1) Place the digits 0 through 8 once each in every row, column, and box.
• 1.2) When using f-puzzle, the 9 digit represents a zero. Treat the 9 as if the value is zero in all aspects of the puzzle (including mathematical operations and inequalities).
• 1.3) 36 is the secret number.

• 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.
• i) Not all sums of 5 are given.
• ii) Not all inequalities are given.

3) Kropki pairs

• 3.1) Two adjacent cells that share a white dot have digits that are consecutive.
• a) White dots can also contain an X or a V.
• b) Not all white dots have been given.
• 3.2) Two adjacent cells that share a black dot have digits that are in a ratio of 1 to 2.
• a) Black dots can also contain an X or a V.
• b) Not all black dots have been given.

Examples of Modified VX (0 for Penpa+, 9 for f-puzzles):
ROW 2--Six multiplied by five equals thirty (6 X 5 3 0/9).
ROW 3--Five summed with zero equals five (5 V 0/9).
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 0/9).
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)