Logic Masters Deutschland e.V.

Special thanks to @Sktx for the idea behind XV Life VX Sudoku. The original creator of the Game of Life is famed British mathematician John Conway. You can read about him and the game here.

The goal of the puzzle, besides Classic Sudoku, is to color cells as Dead or Alive and have them remain that way if there were to be an iteration. This is called a Stable Configuration. The rules are simple. Dead cells cannot have exactly 3 cells touching them (orthogonally or diagonally) that are alive. Alive cells must have exactly 2 or 3 other alive cells touch them (orthogonally or diagonally). Cells in Killer Cages or on Killer Diagonals are dead. A digit in a circle tells you how many touching cells have the same state. A digit in a diamond tells you how many touching cells have a different state. A digit that has the properties of a circle and a diamond will contain both shapes (or a star in Penpa+). XV and Modified VX rules also apply. Detailed rules are below if you need clarification, as well as an example puzzle already filled out.

If you would like to try a mini 5X5 version first, you can do so here. XV Little Life VX Sudoku. Digits are 1 through 5.

Here is a Game of Life simulator Game of Life.

Title: XV Life VX
Type: Sudoku
Link: Penpa+ link to XV Life VX Sudoku You may use Normal/Large/Medium/Small Blue, Green, or Red numbers in any combination. You must shade dead cells in black or dark grey for the answer check to function.
Link: F-puzzles link to XV Life VX Sudoku
Variants: XV, Modified VX, Killer, Little Killer, Life

The XV Easy Life VX: If you found the puzzle too difficult, I added more approachable initial conditions to the puzzle below.
Link: Penpa+ link to XV The Easy Life VX Sudoku You may use Normal/Large/Medium/Small Blue, Green, or Red numbers in any combination. You must shade dead cells in black or dark grey for the answer check to function.
Link: F-puzzles link to XV The Easy Life VX Sudoku

1) 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) Killer Cages

• 3.1) Digits inside a cage must sum to the total in the top left.
• 3.2) Digits may not repeat in a cage.

4) Little Killer

• 4.1) Digits along an indicated diagonal must sum to the total.
• 4.2) Digits may repeat along the diagonal.

5) Life

• 5.1) There are two types of cells in this world; dead or alive.
• 5.2) A neighbor of a cell is any cell that is orthogonal or diagonal to that cell.
• a) The four corner squares have 3 neighbors.
• b) All other squares in Row 1, Row 9, Column 1, and Column 9 have 5 neighbors.
• c) All other squares have 8 neighbors.
• 5.3) Shade all of the DEAD cells dark grey so that the grid is stable. That is to say, the grid would not change during the next generation (the grid only contains still lives).
• a) Any live cell with fewer than two live neighbors dies during the next generation, as if by underpopulation.
• b) Any live cell with more than three live neighbors dies during the next generation, as if by overpopulation.
• c) Any live cell with two or three live neighbors lives on to the next generation.
• d) Any dead cell with exactly three live neighbors becomes a live cell during the next generation, as if by reproduction.
• e) Any cell in a Killer Cage or on a Killer Diagonal is dead, as if by murder.
• f) IN SUMMATION: A live cell must have and only have 2 or 3 live neighbors. A dead cell cannot have exactly 3 live neighbors.
• 5.4) If a cell has a diamond in it, the digit in the cell represents how many neighbors are in a different state from that cell.
• 5.5) If a cell has a circle in it, the digit in the cell represents how many neighbors are in the same state as that cell.
• 5.6 All circles and diamonds have been given and negative constraints apply.

Example of a valid Life puzzle. All circles and diamonds are given.

Modified VX 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)