Color Coding Worksheet with Grid and Directional Arrows

Problem Description:

The task involves completing a grid using color coding based on the given examples. The grid contains arrows and colored squares, and we need to determine the correct colors for the empty cells based on the provided rules.

Given Information:

1. Color Coding Examples:
- 1. `→` (right arrow) → No color specified.
- 2. `↑ ↑` (two up arrows) → Color: Orange.
- 3. `↑ ↑` (two up arrows) → Color: Blue.
- 4. `→` (right arrow) → Color: Blue.
- 5. `→` (right arrow) → No color specified.
- 6. `↓ ↓` (two down arrows) → Color: Green.
- 7. `→ →` (two right arrows) → Color: Purple.
- 8. `↓ ↓` (two down arrows) → Color: Red.

2. Grid:
- The grid has some pre-filled cells with arrows and colors.
- We need to fill in the empty cells based on the rules.

Step-by-Step Solution:

#### Step 1: Analyze the Grid
The grid is as follows (with colors represented by their names):

| | | | |
|-------|-------|-------|-------|
| `↑` | `↑` (Blue) | `→` | |
| `↑` | | `↓` | |
| `↑ ↑` (Orange) | `↓ ↓` (Green) | `→` | `→ →` (Purple) |
| `↑` | | | `↓ ↓` (Red) |
| `→` | | | |

#### Step 2: Apply the Rules

1. Row 1:
- First cell: `↑` → No rule matches a single `↑`, so it remains uncolored.
- Second cell: Already filled with Blue (`↑ ↑`).
- Third cell: `→` → Matches rule 4: `→` = Blue.
- Fourth cell: Empty → No rule applies, so it remains uncolored.

2. Row 2:
- First cell: `↑` → No rule matches a single `↑`, so it remains uncolored.
- Second cell: Empty → No rule applies, so it remains uncolored.
- Third cell: `↓` → No rule matches a single `↓`, so it remains uncolored.
- Fourth cell: Empty → No rule applies, so it remains uncolored.

3. Row 3:
- First cell: `↑ ↑` → Matches rule 2: `↑ ↑` = Orange.
- Second cell: `↓ ↓` → Matches rule 6: `↓ ↓` = Green.
- Third cell: `→` → Matches rule 4: `→` = Blue.
- Fourth cell: `→ →` → Matches rule 7: `→ →` = Purple.

4. Row 4:
- First cell: `↑` → No rule matches a single `↑`, so it remains uncolored.
- Second cell: Empty → No rule applies, so it remains uncolored.
- Third cell: Empty → No rule applies, so it remains uncolored.
- Fourth cell: `↓ ↓` → Matches rule 8: `↓ ↓` = Red.

5. Row 5:
- First cell: `→` → Matches rule 4: `→` = Blue.
- Second cell: Empty → No rule applies, so it remains uncolored.
- Third cell: Empty → No rule applies, so it remains uncolored.
- Fourth cell: Empty → No rule applies, so it remains uncolored.

#### Step 3: Fill in the Grid
Based on the analysis, the completed grid is:

| | | | |
|-------|-------|-------|-------|
| `↑` | `↑ ↑` (Blue) | `→` (Blue) | |
| `↑` | | `↓` | |
| `↑ ↑` (Orange) | `↓ ↓` (Green) | `→` (Blue) | `→ →` (Purple) |
| `↑` | | | `↓ ↓` (Red) |
| `→` (Blue) | | | |

#### Final Answer:
The completed grid is:

| | | | |
|-------|-------|-------|-------|
| `↑` | `↑ ↑` (Blue) | `→` (Blue) | |
| `↑` | | `↓` | |
| `↑ ↑` (Orange) | `↓ ↓` (Green) | `→` (Blue) | `→ →` (Purple) |
| `↑` | | | `↓ ↓` (Red) |
| `→` (Blue) | | | |

$$
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\uparrow & \text{↑ ↑ (Blue)} & \rightarrow \text{(Blue)} & \\
\hline
\uparrow & & \downarrow & \\
\hline
\text{↑ ↑ (Orange)} & \text{↓ ↓ (Green)} & \rightarrow \text{(Blue)} & \text{→ → (Purple)} \\
\hline
\uparrow & & & \text{↓ ↓ (Red)} \\
\hline
\rightarrow \text{(Blue)} & & & \\
\hline
\end{array}
}
$$