Calcudoku – Hard

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Calcudoku (also known as "Minuplu", "KenDoku", "MathDoku", "Yukendo", "Square Wisdom") is a mathematical and logical puzzle loosely similar to Sudoku. It was invented by Japanese mathematics teacher Tetsuya Miyamoto. The objective is to fill the grid with the digits 1 through N (where N is the number of rows or columns in the grid) such that:

Basic Rules

• Each row contains exactly one of each digit.
• Each column contains exactly one of each digit.
• Each bold-outlined group of cells (block) contains digits that achieve the specified result using the specified mathematical operation: addition (+), subtraction (-), multiplication (×), and division (÷).
• Unlike Killer Sudoku, digits may repeat within a block.

Additional Rules for Calcudoku

• The mathematical operation in each block must be applied to all the digits within that block to achieve the specified result.
• Each block's result and operation are given, and the digits must be arranged to satisfy these conditions.

Basic Solving Tips

• Start with blocks that have only one cell since they directly provide the digit.
• Use the row and column rules to eliminate possibilities for digits in each cell.
• For larger blocks, consider the mathematical operation and the result to determine possible combinations of digits.
• Look for intersections where certain digits must appear to satisfy both row/column rules and block rules.
• Remember that digits can repeat within a block but must be unique within rows and columns.