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 house
    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
                            house1 = {
                                'House': '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]
                            }
                            
                            # Create assignment for house 2
                            house2 = {
                                'House': '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 clue 1: The person who is an engineer is in the first house.
                            if house1['Occupation'] != 'engineer':
                                continue
                            
                            # Check clue 2: The person whose birthday is in April and the person who is a doctor are next to each other.
                            # Since there are only 2 houses, they are always adjacent
                            april_found = False
                            doctor_found = False
                            for house in [house1, house2]:
                                if house['Birthday'] == 'april':
                                    april_found = True
                                if house['Occupation'] == 'doctor':
                                    doctor_found = True
                            if not (april_found and doctor_found):
                                continue
                            
                            # Check clue 3: The person living in a colonial-style house is the person who is an engineer.
                            colonial_engineer = None
                            for house in [house1, house2]:
                                if house['HouseStyle'] == 'colonial':
                                    colonial_engineer = house
                            if colonial_engineer is None or colonial_engineer['Occupation'] != 'engineer':
                                continue
                            
                            # Check clue 4: The person who is very short is the person who is an engineer.
                            very_short_engineer = None
                            for house in [house1, house2]:
                                if house['Height'] == 'very short':
                                    very_short_engineer = house
                            if very_short_engineer is None or very_short_engineer['Occupation'] != 'engineer':
                                continue
                            
                            # Check clue 5: The person who is short is the person partial to Pall Mall.
                            short_pallmall = None
                            for house in [house1, house2]:
                                if house['Height'] == 'short':
                                    short_pallmall = house
                            if short_pallmall is None or short_pallmall['Cigar'] != 'pall mall':
                                continue
                            
                            # Check clue 6: The person who is an engineer is Eric.
                            engineer_eric = None
                            for house in [house1, house2]:
                                if house['Occupation'] == 'engineer':
                                    engineer_eric = house
                            if engineer_eric is None or engineer_eric['Name'] != 'Eric':
                                continue
                            
                            # All clues satisfied, return the solution
                            return [house1, house2]
    
    return None

def main():
    solution = solve_puzzle()
    
    if solution:
        # Prepare the output in the required JSON format
        header = ["House", "Name", "Occupation", "Birthday", "HouseStyle", "Height", "Cigar"]
        rows = []
        
        for house in solution:
            rows.append([
                house['House'],
                house['Name'],
                house['Occupation'],
                house['Birthday'],
                house['HouseStyle'],
                house['Height'],
                house['Cigar']
            ])
        
        # Sort rows by house number
        rows.sort(key=lambda x: int(x[0]))
        
        output = {
            "solution": {
                "header": header,
                "rows": rows
            }
        }
        
        print(json.dumps(output, indent=2))
    else:
        print(json.dumps({"solution": None}))

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

Reasoning extracted:
