Logic Masters Deutschland e.V.

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

1) Irregular Sudoku

• 1.1) Place the digits 0 through 8 once each in every row, column, and shape.
• 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) Star Battle

• Two of the digits 0 through 8 act like stars and both will appear once in every row, column and shape.
• a) The stars cannot touch another star; orthogonally or diagonally.
• b) Which two numbers act like stars needs to be deduced.
• c) The green marked square in Row 4 Column 7 indicates the position of a star.

4) Even/Odd Cell

• 4.1) A Cell with a grey square in it must contain an even digit.
• 4.2) A Cell with a grey circle in it must contain an odd digit.

5) Notes

• 5.1) There is only one possible StarBattle solution, but a couple ways to attack it; a long tedious way, and a fast way.
• 5.2) Bifurcation is not required, but if you get stuck, a tiny look ahead may be helpful.

6) Hints and Spoilers--highlight row to see.

• Can a 1 or a 0 ever be adjacent to an X?

• Is the X in Column 6 a multiplication or sum? If a multiplication with a two digit product, how does this effect the stars in R5, R6, and R7?

• What impact does R6C6 have on R5C7?

• If you have narrowed down the candidates for X in column 6, what are the candidates for R4C7 and R5C5?

• Did you forget about R1C1?

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)