Skyscraper Sudoku – Hard

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"Skyscraper Sudoku" is a variant of the classic Sudoku puzzle, which incorporates additional clues located outside the grid. Each digit placed within a cell represents the height of a skyscraper in that particular cell. The clues provided outside the grid indicate the number of skyscrapers visible when looking from that direction. A skyscraper obscures all others behind it that are of equal or lesser height.

Basic Rules

1. Grid Fill: Fill the grid with digits so that each row, column, and specified region contains the numbers 1 through to the grid size (e.g., 1-9 for a 9x9 grid).
2. Unique Numbers: Each number must be unique in every row, column, and specified region.
3. Skyscraper Clues: Adhere to the skyscraper clues outside the grid, which indicate how many skyscrapers can be seen from that point, considering taller ones hide shorter ones behind them.

Additional Rules

• Visibility: A taller skyscraper hides all shorter or equally tall skyscrapers behind it from view.
• Clue Adherence: All provided clues must be satisfied by the final grid solution.

Basic Solving Tips

• Start with Definite Clues: Begin solving from the clues that are definite (e.g., if in a 5x5 grid a clue is 5, the row or column must be 1-2-3-4-5).
• Use Elimination: Use regular Sudoku elimination methods for numbers within rows, columns, and regions.
• Consider Visibility: Keep the visibility rule in mind and consider how placing a number may affect the visibility of other skyscrapers.
• Check Clues Regularly: Regularly check that the current grid adheres to all the provided clues.