Logic Masters Deutschland e.V.

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

1) Irregular Toroidal Sudoku

• 1.1) Place the digits 0 through 8 once each in every row, column, and shape.
• 1.2) The grid is a Torus. Regions can continue from one side of the grid to the opposite side. I have shaded some regions for you.
• 1.3) 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).
• 1.4) 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.
• iii) The products of multiplication follow toroidal rules.
• 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) Equal Sums

• 3.1) Digits along a blue line have an equal sum in all the regions they cross, including re-entry into a region previously departed, i.e., multiple occurrences will have equal sums and not a total sum.
• 3.2) The Equal Sum lines in R1C1 and R9C9 do not connect in the torus.

Examples (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)