Vudoku – Hard

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Vudoku is a variant of the classic Sudoku puzzle, which incorporates arithmetic into the traditional number-placing logic game. In addition to adhering to the standard Sudoku rules, players must also consider the mathematical relationship between certain numbers in the grid, specifically those positioned in a "V" shape.

Basic Rules

1. Standard Sudoku Rules:
   • Each row, column, and specified region must contain all of the numbers from 1 to 9, without repetition.
   • A number cannot appear more than once in a row, column, or specified region.
2. Vudoku-Specific Rule:
   • The number at the vertex of each marked "V" must be either the sum or the difference of the other two numbers of the "V".

Additional Rules (if needed)

• The "V" shapes may overlap with each other, and in such cases, the vertex number must satisfy the Vudoku condition for all overlapping Vs.
• The Vs can be located anywhere on the board and can be of any orientation (upward, downward, leftward, or rightward).

Basic Solving Tips

1. Identify Constraints:
   • Begin by identifying the numbers that are already provided in the grid and use them to determine the possible values for other cells, considering both Sudoku and Vudoku rules.
2. Focus on the Vs:
   • Pay special attention to the Vs, as they provide additional constraints and can often help you deduce the values of other cells more quickly.
3. Use Elimination:
   • Use the process of elimination to identify where numbers cannot go, thereby narrowing down the possibilities for each cell.
4. Look for Certainties:
   • Always place a number if you are certain of its position, and use it to further deduce the positions of other numbers.
5. Consider All Possibilities:
   • For the Vudoku-specific rule, always consider both the sum and difference possibilities and check which one adheres to the existing grid without violating any rules.