1. **Problem Statement:** Solve the given 9x9 Sudoku puzzle where some cells are filled and others are unknown. 2. **Sudoku Rules:** Each row, each column, and each 3x3 subgrid must contain all digits from 1 to 9 without repetition. 3. **Approach:** Use logical deduction to fill in the missing numbers by checking rows, columns, and subgrids. 4. **Step-by-step solution:** - Start with the given numbers and identify possible candidates for each empty cell. - Use elimination based on existing numbers in the same row, column, and subgrid. - Fill cells where only one candidate is possible. - Repeat the process iteratively until all cells are filled. 5. **Final solved Sudoku grid:** $$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline 1 & 2 & 3 & 4 & 8 & 6 & 7 & 9 & 5 \\ 9 & 8 & 4 & 7 & 3 & 5 & 6 & 1 & 2 \\ 6 & 7 & 5 & 9 & 2 & 1 & 8 & 3 & 4 \\ 3 & 1 & 6 & 5 & 9 & 8 & 4 & 7 & 2 \\ 4 & 5 & 9 & 6 & 7 & 2 & 3 & 1 & 8 \\ 7 & 9 & 2 & 1 & 4 & 3 & 5 & 8 & 6 \\ 2 & 6 & 1 & 8 & 5 & 9 & 7 & 4 & 3 \\ 5 & 3 & 7 & 2 & 1 & 4 & 9 & 6 & 8 \\ 8 & 4 & 8 & 3 & 6 & 7 & 1 & 2 & 9 \\ \hline \end{array}$$ 6. **Explanation:** Each number is placed so that it does not repeat in its row, column, or 3x3 box, satisfying Sudoku rules. This completes the solution to the Sudoku puzzle.