Problem Description:
The task is to identify and mark all occurrences of the number
9 in a grid, regardless of its orientation. The instruction specifies that even if the number appears in a different orientation (e.g., rotated or flipped), it should still be marked.
Solution Approach:
1.
Identify the Target Number: The target number is
9.
2.
Understand Orientation Variations: The number
9 can appear in various orientations:
- Standard upright
9
- Rotated versions (e.g., 90°, 180°, 270° rotations)
- Flipped versions (e.g., horizontal or vertical flips)
3.
Search the Grid: Carefully examine each cell in the grid to identify all instances of
9, including those with different orientations.
4.
Mark the Identified Numbers: Once identified, mark them as instructed.
Step-by-Step Analysis:
#### Key Observations:
- The standard
9 is easily recognizable.
- Rotated or flipped versions of
9 may look different but still represent the same number. For example:
- A
9 rotated 180° looks like a backward
6.
- A
9 flipped horizontally may look like a
P-like shape.
- A
9 flipped vertically may look like a
q-like shape.
#### Grid Examination:
We will scan the grid row by row and column by column, identifying all instances of
9 in any orientation.
---
#### Row-by-Row Analysis:
1.
First Row:
```
3 8 ∞ 3 2 3 8 8 3 2
```
- No
9 found.
2.
Second Row:
```
3 6 8 3 2 6 8 3 2 9
```
- One
9 found at the end.
3.
Third Row:
```
9 9 3 2 8 9 2 8 8 9
```
- Four
9s found: first, second, sixth, and tenth columns.
4.
Fourth Row:
```
9 3 2 6 8 9 8 2 6 9
```
- Three
9s found: first, sixth, and tenth columns.
5.
Fifth Row:
```
8 8 ∞ 2 3 2 8 9 2 8
```
- One
9 found in the eighth column.
6.
Sixth Row:
```
2 2 8 3 2 2 8 3 8 8
```
- No
9 found.
7.
Seventh Row:
```
9 6 8 2 9 2 9 8 8 8
```
- Three
9s found: first, fifth, and seventh columns.
8.
Eighth Row:
```
9 6 8 2 3 2 9 6 2 3
```
- Three
9s found: first, fifth, and seventh columns.
9.
Ninth Row:
```
9 6 8 2 3 2 9 6 ∞ 2
```
- Three
9s found: first, fifth, and seventh columns.
10.
Tenth Row:
```
3 8 9 2 2 9 8 3 2
```
- Two
9s found: third and sixth columns.
---
Final Marked Numbers:
After carefully examining the grid, the following cells contain the number
9 (in any orientation):
- Row 2, Column 10
- Row 3: Columns 1, 2, 6, 10
- Row 4: Columns 1, 6, 10
- Row 5: Column 8
- Row 7: Columns 1, 5, 7
- Row 8: Columns 1, 5, 7
- Row 9: Columns 1, 5, 7
- Row 10: Columns 3, 6
---
Final Answer:
Mark all the identified cells containing
9 in the grid. The positions are:
\[
\boxed{
(2, 10), (3, 1), (3, 2), (3, 6), (3, 10), (4, 1), (4, 6), (4, 10), (5, 8), (7, 1), (7, 5), (7, 7), (8, 1), (8, 5), (8, 7), (9, 1), (9, 5), (9, 7), (10, 3), (10, 6)
}
\]
Where the notation \((row, column)\) indicates the position in the grid.
Parent Tip: Review the logic above to help your child master the concept of cognitive worksheet.