#!/usr/bin/env python3
"""
Puzzle Solver: 2-digit × 3-digit = 5-digit
All digits 0-9 used exactly once, first digit of result is 1
"""

def has_unique_digits(numbers):
    """Check if all digits across the numbers are unique (0-9 used exactly once)"""
    all_digits = []
    for num in numbers:
        all_digits.extend(str(num))
    
    # Check if we have exactly 10 digits (0-9) and all are unique
    return len(all_digits) == 10 and len(set(all_digits)) == 10

def solve_puzzle():
    """Find all solutions to the puzzle"""
    solutions = []
    
    # Iterate through all 2-digit numbers (10-99)
    for two_digit in range(10, 100):
        # Iterate through all 3-digit numbers (100-999)
        for three_digit in range(100, 1000):
            product = two_digit * three_digit
            
            # Check if product is 5-digit and starts with 1
            if 10000 <= product <= 19999:
                # Check if all digits are unique across all three numbers
                if has_unique_digits([two_digit, three_digit, product]):
                    solutions.append((two_digit, three_digit, product))
    
    return solutions

def main():
    print("Solving the puzzle:")
    print("2-digit × 3-digit = 5-digit")
    print("All digits 0-9 used exactly once")
    print("First digit of result is 1")
    print("-" * 50)
    
    solutions = solve_puzzle()
    
    if solutions:
        print(f"Found {len(solutions)} solution(s):")
        for i, (a, b, c) in enumerate(solutions, 1):
            print(f"Solution {i}: {a} × {b} = {c}")
            
            # Verify the solution
            print(f"  Verification: {a} × {b} = {a * b}")
            
            # Show digit usage
            all_digits = str(a) + str(b) + str(c)
            used_digits = sorted(set(all_digits))
            print(f"  Digits used: {used_digits}")
            print(f"  All digits 0-9: {sorted([str(i) for i in range(10)])}")
            print()
    else:
        print("No solutions found!")
    
    return solutions

if __name__ == "__main__":
    main()