Prompt:
You are an expert at solving Zebra logic puzzles. Your task is to write a Python program that algorithmically solves the given logic puzzle by implementing all constraints and rules. The program must actually compute the solution using the given parameters, not just print a pre-determined answer.
Input puzzle:
There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`
 - Each person has an occupation: `engineer`, `doctor`
 - Each person has a unique birthday month: `april`, `sept`
 - Each person lives in a unique style of house: `victorian`, `colonial`
 - People have unique heights: `very short`, `short`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`

## Clues:
1. The person who is an engineer is in the first house.
2. The person whose birthday is in April and the person who is a doctor are next to each other.
3. The person living in a colonial-style house is the person who is an engineer.
4. The person who is very short is the person who is an engineer.
5. The person who is short is the person partial to Pall Mall.
6. The person who is an engineer is Eric.


Generate a complete, self-contained Python program that:
1. Takes the above puzzle constraints as input variables
2. Computes the solution using logical rules and constraints
3. Outputs the solution as a JSON-formatted dictionary with the following EXACT structure:
{
  "solution": {
    "header": ["House", "Name", "Occupation", "Birthday", "HouseStyle", "Height", "Cigar"],
    "rows": [
      ["1", VALUE_FOR_HEADER1, VALUE_FOR_HEADER2, ...],
      ["2", VALUE_FOR_HEADER1, VALUE_FOR_HEADER2, ...]
    ]
  }
}

Important Requirements:
- The 'header' field MUST use exactly these attribute names: ["House", "Name", "Occupation", "Birthday", "HouseStyle", "Height", "Cigar"]
- Maintain the exact order of houses (1, 2, 3, ...)
- Include all attributes in each row
- The output must be valid JSON that can be parsed by Python's json module

Output only the complete Python code with no additional text or explanation.
The code must run independently and output valid JSON when executed.The script should be clean, well-formatted, and enclosed within ```python and ```. 

Response:
```python
import json
from itertools import permutations

def solve_puzzle():
    # Define all possible values for each attribute
    names = ["Arnold", "Eric"]
    occupations = ["engineer", "doctor"]
    birthdays = ["april", "sept"]
    house_styles = ["victorian", "colonial"]
    heights = ["very short", "short"]
    cigars = ["pall mall", "prince"]
    
    # Generate all possible permutations for each attribute
    for name_perm in permutations(names):
        for occ_perm in permutations(occupations):
            for bday_perm in permutations(birthdays):
                for style_perm in permutations(house_styles):
                    for height_perm in permutations(heights):
                        for cigar_perm in permutations(cigars):
                            # Create assignment for house 1 and 2
                            assignment = {
                                1: {
                                    "Name": name_perm[0],
                                    "Occupation": occ_perm[0],
                                    "Birthday": bday_perm[0],
                                    "HouseStyle": style_perm[0],
                                    "Height": height_perm[0],
                                    "Cigar": cigar_perm[0]
                                },
                                2: {
                                    "Name": name_perm[1],
                                    "Occupation": occ_perm[1],
                                    "Birthday": bday_perm[1],
                                    "HouseStyle": style_perm[1],
                                    "Height": height_perm[1],
                                    "Cigar": cigar_perm[1]
                                }
                            }
                            
                            # Check all constraints
                            # Clue 1: The person who is an engineer is in the first house.
                            if assignment[1]["Occupation"] != "engineer":
                                continue
                            
                            # Clue 2: The person whose birthday is in April and the person who is a doctor are next to each other.
                            april_house = None
                            doctor_house = None
                            for house in [1, 2]:
                                if assignment[house]["Birthday"] == "april":
                                    april_house = house
                                if assignment[house]["Occupation"] == "doctor":
                                    doctor_house = house
                            
                            if april_house is None or doctor_house is None or abs(april_house - doctor_house) != 1:
                                continue
                            
                            # Clue 3: The person living in a colonial-style house is the person who is an engineer.
                            colonial_engineer = False
                            for house in [1, 2]:
                                if assignment[house]["HouseStyle"] == "colonial" and assignment[house]["Occupation"] == "engineer":
                                    colonial_engineer = True
                                    break
                            if not colonial_engineer:
                                continue
                            
                            # Clue 4: The person who is very short is the person who is an engineer.
                            very_short_engineer = False
                            for house in [1, 2]:
                                if assignment[house]["Height"] == "very short" and assignment[house]["Occupation"] == "engineer":
                                    very_short_engineer = True
                                    break
                            if not very_short_engineer:
                                continue
                            
                            # Clue 5: The person who is short is the person partial to Pall Mall.
                            short_pallmall = False
                            for house in [1, 2]:
                                if assignment[house]["Height"] == "short" and assignment[house]["Cigar"] == "pall mall":
                                    short_pallmall = True
                                    break
                            if not short_pallmall:
                                continue
                            
                            # Clue 6: The person who is an engineer is Eric.
                            engineer_eric = False
                            for house in [1, 2]:
                                if assignment[house]["Occupation"] == "engineer" and assignment[house]["Name"] == "Eric":
                                    engineer_eric = True
                                    break
                            if not engineer_eric:
                                continue
                            
                            # If we reach here, all constraints are satisfied
                            return assignment
    
    return None

def main():
    solution = solve_puzzle()
    
    if solution is None:
        print('{"solution": null}')
        return
    
    # Format the solution as required
    header = ["House", "Name", "Occupation", "Birthday", "HouseStyle", "Height", "Cigar"]
    rows = []
    
    for house in sorted(solution.keys()):
        row = [str(house)]
        row.append(solution[house]["Name"])
        row.append(solution[house]["Occupation"])
        row.append(solution[house]["Birthday"])
        row.append(solution[house]["HouseStyle"])
        row.append(solution[house]["Height"])
        row.append(solution[house]["Cigar"])
        rows.append(row)
    
    result = {
        "solution": {
            "header": header,
            "rows": rows
        }
    }
    
    print(json.dumps(result, indent=2))

if __name__ == "__main__":
    main()
```

Reasoning extracted:
