# Sudoku XV – Hard

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"Sudoku XV" is a variant of the classic Sudoku puzzle, which introduces an additional arithmetic element to the traditional number-placing logic game. In addition to adhering to the standard Sudoku rules, players must also consider the sum of certain neighboring cells, which are marked with specific symbols to indicate their arithmetic relationship.
##### Basic Rules
1. Grid Structure: The puzzle is played on a 9x9 grid, divided into 3x3 subgrids (also known as regions or boxes).
2. Number Placement: Each row, column, and 3x3 subgrid must contain all of the digits from 1 to 9, without repetition.
##### Additional Rules for Sudoku XV
1. X Marks: If two neighboring cells (horizontally or vertically) are marked with an "X", their digits must add up to 10.
2. V Marks: If two neighboring cells are marked with a "V", their digits must add up to 5.
##### Basic Solving Tips
• Single Possibility: If a cell has only one possible number, write it in.
• Single Candidate: For each box, row, or column, if a number can only go in one cell, write it in.
• Elimination: Exclude numbers from cells using the basic Sudoku rules and the additional XV rules.
• XV Consideration: Use the X and V marks to guide number placement and elimination. For example, if there's an X between two cells, consider numbers that add up to 10 (1 and 9, 2 and 8, etc.) and see how they fit with the existing numbers in the row, column, and box.
##### Tips Specific to Sudoku XV
• Avoiding Repetition: Ensure that the numbers adhering to the X and V rules do not violate the basic Sudoku rule of non-repetition in rows, columns, and boxes.
• XV Interaction: Pay attention to how X and V clues interact with each other and use them to eliminate possibilities.
• Logical Deduction: Sometimes, deducing the number in a cell due to its relationship (X or V) with its neighbor can help in placing numbers in other related cells.