Extreme Sudoku XV Puzzles

About Sudoku XV

Sudoku XV is a variation of standard Sudoku with 'V' and 'X' Roman numeral markers. All pairs of touching squares which add up to a total of 5 or 10 are marked with a 'V' or 'X' respectively.

If there is no 'V' or 'X' between two touching squares then they do not add up to 5 or 10.

Basic Rules / How to Play

• Grid Size: The puzzle is played on a 9x9 grid, which is divided into nine 3x3 subgrids.
• Numbers: Each row, column, and 3x3 box must contain the digits 1 through 9 with no repetition.
• No Repeats: Numbers in each row, columns and diagonals should appear only once without repetition.
• X Marker: If two adjacent cells (horizontally or vertically) are marked with an "X," the sum of the numbers in those cells must equal 10.
• V Marker: If two adjacent cells are marked with a "V," the sum of the numbers in those cells must equal 5.
• XV Constraint: The two cells connected by an "X" (diagonally) must sum up to 15 and, the two cells connected by a "V" (in the shape of the letter "V") must also sum to 15.

Solving Tips and Techniques:

The XV rule makes Sudoku XV harder than the regular puzzle, and it usually needs different strategies to solve. Here are some helpful methods to solve it:

• Elimination: Use the XV markers to eliminate possible numbers from cells based on the adjacent cell's potential values. For example, if a cell with an "X" marker has a 2, the adjacent cell cannot be an 8.
• Naked Singles: Identify a number that can only appear in one cell within a row, column, or subgrid.
• Look for XV Relationships: If an "X" marker is present, the possible pairs of numbers are (1, 9), (2, 8), (3, 7), and (4, 6). Further, if a "V" marker is present, the possible pairs of numbers are (1, 4) and (2, 3).
• No X or V Marking: If two adjacent cells do not have an "X" or a "V" between them, their values cannot sum to 10 or 5.
• Use Pencil Marks: Lightly pencil in possible numbers in each cell to help track your progress and eliminate options.