Girandola Sudoku – Hard

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Girandola Sudoku is a variant of the classic Sudoku, a number-placement puzzle that is widely recognized and enjoyed by many puzzle enthusiasts. The classic Sudoku is typically a 9x9 grid, divided into 3x3 subgrids, also known as "regions". Some of the cells in the grid are pre-filled with numbers, which are referred to as "givens". The objective is to fill the empty cells in such a way that each row, column, and region contains the numbers 1 through 9, without repetition. Girandola Sudoku introduces an additional twist with an extra group of cells that also need to adhere to the rule of containing digits 1 through 9 without repetition.

Basic Rules

1. Grid Structure: The puzzle consists of a 9x9 grid, and this grid is further divided into nine 3x3 subgrids or regions.
2. Givens: Some cells are pre-filled with numbers, known as "givens", which provide solvers with starting points.
3. Number Placement: The solver must fill in the empty cells with numbers 1 through 9.

Additional Rules for Girandola Sudoku

1. Extra Group: In addition to the standard rules, Girandola Sudoku features an extra group of cells, often arranged in a pattern (commonly a circle or a star), which must also contain the digits 1 through 9 without repetition.

Basic Solving Tips

1. Single Possibility: If a cell is the only one in its row, column, or region that can contain a particular number, that number goes in the cell.
2. Elimination: Exclude numbers from consideration for a particular cell based on the numbers already present in the cell’s row, column, and region.
3. Double Pairs: If two cells in a row, column, or region can only be two numbers (a pair), then those two numbers can be excluded from consideration for other cells in that row, column, or region.
4. Look for Grid Symmetry: Often, the givens and the extra group in Girandola Sudoku are arranged in a symmetrical pattern, which may help in deducing the logical placement of numbers.