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Sagot :
To solve this Sudoku problem, let's determine the blank positions within the Sudoku grid and identify their coordinates step-by-step. Here's a detailed explanation:
1. Identify the given Sudoku grid:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline 2 & 1 & 5 & 8 & 9 & 4 & & & \\ \hline 7 & 3 & 4 & 6 & 1 & 2 & 9 & 5 & \\ \hline 9 & 6 & 8 & 7 & 5 & 3 & 4 & & \\ \hline 4 & 9 & 3 & 1 & 6 & 7 & 8 & 2 & \\ \hline 8 & 7 & 1 & 3 & 2 & 5 & & & 4 \\ \hline 5 & 2 & 6 & 9 & 8 & 1 & & & \\ \hline 3 & 7 & 9 & & 4 & & & 7 & 1 \\ \hline 6 & 4 & 2 & & & & & & 9 \\ \hline 1 & 8 & 7 & & 3 & & & & \\ \hline \end{array} \][/tex]
2. Locate all the blank positions (denoted by empty spaces):
- Row 1: Positions (0,6), (0,7), (0,8)
- Row 2: Positions (1,8)
- Row 3: Positions (2,7), (2,8)
- Row 4: Positions (3,8)
- Row 5: Positions (4,6), (4,7)
- Row 6: Positions (5,6), (5,7), (5,8)
- Row 7: Positions (6,3), (6,5), (6,8)
- Row 8: Positions (7,3), (7,4), (7,5), (7,6), (7,7)
- Row 9: Positions (8,3), (8,5), (8,6), (8,7), (8,8)
3. List the positions of the blanks:
[tex]\[ \begin{array}{c} (0,6), (0,7), (0,8), \\ (1,8), \\ (2,7), (2,8), \\ (3,8), \\ (4,6), (4,7), \\ (5,6), (5,7), (5,8), \\ (6,3), (6,5), (6,8), \\ (7,3), (7,4), (7,5), (7,6), (7,7), \\ (8,3), (8,5), (8,6), (8,7), (8,8) \\ \end{array} \][/tex]
4. Recap of the output:
The Sudoku board is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline 2 & 1 & 5 & 8 & 9 & 4 & & & \\ \hline 7 & 3 & 4 & 6 & 1 & 2 & 9 & 5 & \\ \hline 9 & 6 & 8 & 7 & 5 & 3 & 4 & & \\ \hline 4 & 9 & 3 & 1 & 6 & 7 & 8 & 2 & \\ \hline 8 & 7 & 1 & 3 & 2 & 5 & & & 4 \\ \hline 5 & 2 & 6 & 9 & 8 & 1 & & & \\ \hline 3 & 7 & 9 & & 4 & & & 7 & 1 \\ \hline 6 & 4 & 2 & & & & & & 9 \\ \hline 1 & 8 & 7 & & 3 & & & & \\ \hline \end{array} \][/tex]
The list of blank positions is:
[tex]\[ \left[ (0, 6), (0, 7), (0, 8), (1, 8), (2, 7), (2, 8), (3, 8), (4, 6), (4, 7), (5, 6), (5, 7), (5, 8), (6, 3), (6, 5), (6, 8), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (8, 3), (8, 5), (8, 6), (8, 7), (8, 8) ] \][/tex]
This complete step-by-step ensures that we identified all the blank positions in the given Sudoku puzzle accurately.
1. Identify the given Sudoku grid:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline 2 & 1 & 5 & 8 & 9 & 4 & & & \\ \hline 7 & 3 & 4 & 6 & 1 & 2 & 9 & 5 & \\ \hline 9 & 6 & 8 & 7 & 5 & 3 & 4 & & \\ \hline 4 & 9 & 3 & 1 & 6 & 7 & 8 & 2 & \\ \hline 8 & 7 & 1 & 3 & 2 & 5 & & & 4 \\ \hline 5 & 2 & 6 & 9 & 8 & 1 & & & \\ \hline 3 & 7 & 9 & & 4 & & & 7 & 1 \\ \hline 6 & 4 & 2 & & & & & & 9 \\ \hline 1 & 8 & 7 & & 3 & & & & \\ \hline \end{array} \][/tex]
2. Locate all the blank positions (denoted by empty spaces):
- Row 1: Positions (0,6), (0,7), (0,8)
- Row 2: Positions (1,8)
- Row 3: Positions (2,7), (2,8)
- Row 4: Positions (3,8)
- Row 5: Positions (4,6), (4,7)
- Row 6: Positions (5,6), (5,7), (5,8)
- Row 7: Positions (6,3), (6,5), (6,8)
- Row 8: Positions (7,3), (7,4), (7,5), (7,6), (7,7)
- Row 9: Positions (8,3), (8,5), (8,6), (8,7), (8,8)
3. List the positions of the blanks:
[tex]\[ \begin{array}{c} (0,6), (0,7), (0,8), \\ (1,8), \\ (2,7), (2,8), \\ (3,8), \\ (4,6), (4,7), \\ (5,6), (5,7), (5,8), \\ (6,3), (6,5), (6,8), \\ (7,3), (7,4), (7,5), (7,6), (7,7), \\ (8,3), (8,5), (8,6), (8,7), (8,8) \\ \end{array} \][/tex]
4. Recap of the output:
The Sudoku board is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline 2 & 1 & 5 & 8 & 9 & 4 & & & \\ \hline 7 & 3 & 4 & 6 & 1 & 2 & 9 & 5 & \\ \hline 9 & 6 & 8 & 7 & 5 & 3 & 4 & & \\ \hline 4 & 9 & 3 & 1 & 6 & 7 & 8 & 2 & \\ \hline 8 & 7 & 1 & 3 & 2 & 5 & & & 4 \\ \hline 5 & 2 & 6 & 9 & 8 & 1 & & & \\ \hline 3 & 7 & 9 & & 4 & & & 7 & 1 \\ \hline 6 & 4 & 2 & & & & & & 9 \\ \hline 1 & 8 & 7 & & 3 & & & & \\ \hline \end{array} \][/tex]
The list of blank positions is:
[tex]\[ \left[ (0, 6), (0, 7), (0, 8), (1, 8), (2, 7), (2, 8), (3, 8), (4, 6), (4, 7), (5, 6), (5, 7), (5, 8), (6, 3), (6, 5), (6, 8), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (8, 3), (8, 5), (8, 6), (8, 7), (8, 8) ] \][/tex]
This complete step-by-step ensures that we identified all the blank positions in the given Sudoku puzzle accurately.
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