To solve the given Sudoku puzzle, we need to fill in the blank cells such that every row and column contains all the digits from 1 to 6 exactly once.
Here is the grid with empty cells:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
& 2 & & 3 & 6 & \\ \hline
& & & 5 & & 2 \\ \hline
1 & 5 & & & & 4 \\ \hline
2 & & 3 & 1 & 5 & 6 \\ \hline
4 & 3 & & 6 & 1 & \\ \hline
6 & 1 & & 4 & 2 & \\ \hline
\end{array}
\][/tex]
Let's fill in the empty cells step-by-step.
Step 1: Fill in the first row.
In the first row:
[tex]\[
\_ \quad 2 \quad \_ \quad 3 \quad 6 \quad \_
\][/tex]
The missing numbers are 1, 4, and 5. To find where these can go:
1. 1 cannot go in the second or fifth column (No repetitions).
2. 4 cannot go in the second or fourth column.
3. 5 cannot go in the fifth column.
So, fill these in accordingly:
[tex]\[
1 \quad 2 \quad 5 \quad 3 \quad 6 \quad 4
\][/tex]
Step 2: Fill in the second row.
In the second row:
[tex]\[
\_ \quad \_ \quad \_ \quad 5 \quad \_ \quad 2
\][/tex]
The missing numbers are 1, 3, 4, and 6. Place them considering restrictions.
1. 1 cannot go in the fifth or sixth column.
2. 3 cannot go in the second or fourth column.
3. 4 cannot go in the fourth column.
4. 6 cannot go in the sixth column.
So, the second row now becomes:
[tex]\[
3 \quad 4 \quad 6 \quad 5 \quad 1 \quad 2
\][/tex]
Step 3: Fill in the third row.
In the third row:
[tex]\[
1 \quad 5 \quad \_ \quad \_ \quad \_ \quad 4
\][/tex]
The missing numbers are 2, 3, and 6.
1. 2 cannot go in the first or second columns.
2. 3 cannot go in the first or second columns.
3. 6 cannot go in the sixth column.
Thus, the third row becomes:
[tex]\[
1 \quad 5 \quad 2 \quad 6 \quad 3 \quad 4
\][/tex]
Step 4: The fourth row is already complete.
[tex]\[
2 \quad \_ \quad 3 \quad 1 \quad 5 \quad 6
\][/tex]
Missing number: 4.
Thus the fourth row becomes:
[tex]\[
2 \quad 4 \quad 3 \quad 1 \quad 5 \quad 6
\][/tex]
Step 5: Fill in the fifth row.
In the fifth row:
[tex]\[
4 \quad 3 \quad \_ \quad 6 \quad 1 \quad \_
\][/tex]
The missing numbers are 2 and 5.
1. 2 cannot go in the first, second, or fourth column.
2. 5 cannot go in the fourth column.
So, the fifth row becomes:
[tex]\[
4 \quad 3 \quad 2 \quad 6 \quad 1 \quad 5
\][/tex]
Step 6: Fill in the sixth row.
In the sixth row:
[tex]\[
6 \quad 1 \quad \_ \quad 4 \quad 2 \quad \_
\][/tex]
The missing numbers are 3 and 5.
Thus the sixth row becomes:
[tex]\[
6 \quad 1 \quad 5 \quad 4 \quad 2 \quad 3
\][/tex]
Now the complete sudoku puzzle is:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
1 & 2 & 5 & 3 & 6 & 4 \\ \hline
3 & 4 & 6 & 5 & 1 & 2 \\ \hline
1 & 5 & 2 & 6 & 3 & 4 \\ \hline
2 & 4 & 3 & 1 & 5 & 6 \\ \hline
4 & 3 & 2 & 6 & 1 & 5 \\ \hline
6 & 1 & 5 & 4 & 2 & 3 \\ \hline
\end{array}
\][/tex]
