various correct solutions with different local models

triplets.py

# see - https://news.ycombinator.com/item?id=41890158
deepseekcoder2.5.py
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def find_combinations(target_product):
    combinations = []
    for i in range(1, target_product):
        for j in range(i + 1, target_product):
            k = target_product // (i * j)
            if k > j and i * j * k == target_product:
                combinations.append((i, j, k))
    return combinations

target_product = 108
combinations = find_combinations(target_product)

print(f"All combinations of three distinct positive integers that multiply to {target_product}:")
for combo in combinations:
    print(combo)
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gemma27b.py
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from itertools import permutations

def find_factors(target):
  """Finds all unique combinations of three distinct positive integers that multiply to the target."""
  factors = []
  for i in range(1, int(target**0.33) + 1): # Optimize by checking up to cube root
    for j in range(i + 1, int(target**(0.5)) + 1): # Optimize by checking up to square root
      k = target // (i * j)
      if i * j * k == target and i < j < k:  # Ensure distinct and ordered
        factors.append((i, j, k))
  return factors

target = 108
result = find_factors(target)

print(f"The ways to express {target} as a product of three distinct positive integers are:")
for factor_set in result:
  print(factor_set)
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llama405b.py
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def find_triplets(product):
    """
    Find all distinct triplets of positive integers that multiply to the given product.

    Args:
        product (int): The target product.

    Returns:
        list[tuple[int, int, int]]: A list of distinct triplets.
    """
    triplets = set()  # Use a set to avoid duplicates
    factors = [i for i in range(1, product + 1) if product % i == 0]

    for a in factors:
        for b in factors:
            if a != b:  # Ensure a and b are distinct
                c = product // (a * b)
                if a != c and b != c and a * b * c == product:  # Ensure c is distinct and product matches
                    triplet = tuple(sorted((a, b, c)))  # Sort to ensure uniqueness
                    triplets.add(triplet)

    return list(triplets)


# Example usage
product = 108
triplets = find_triplets(product)
print(f"Distinct triplets with a product of {product}:")
for triplet in triplets:
    print(triplet)
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llama70b.py
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import itertools

def find_triplets():
    # Define the target product
    target_product = 108
    
    # Generate all possible triplets of distinct positive integers
    triplets = list(itertools.combinations(range(1, target_product + 1), 3))
    
    # Filter the triplets that have a product of 108
    valid_triplets = [triplet for triplet in triplets if triplet[0] * triplet[1] * triplet[2] == target_product]
    
    return valid_triplets

# Find and print all valid triplets
triplets = find_triplets()
for i, triplet in enumerate(triplets):
    print(f"Triplet {i+1}: {triplet}")
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mistral.py
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def find_triplets(product):
    solutions = []

    # Loop through all possible values for the first number
    for i in range(1, int(product**(1/3)) + 1):
        if product % i == 0:
            # Loop through all possible values for the second number
            for j in range(i + 1, int((product / i)**(1/2)) + 1):
                if product % j == 0:
                    # Calculate the third number
                    k = product // (i * j)
                    # Check if the third number is distinct from the first two numbers
                    if k > j:
                        solutions.append((i, j, k))

    return solutions

# Define the product
product = 108

# Find and print all the solutions
solutions = find_triplets(product)
for solution in solutions:
    print(solution)
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qwen2.5-72b.py
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def find_triplets(product):
    triplets = []
    # Iterate through possible values for the first integer
    for i in range(1, product + 1):
        if product % i == 0:
            # Iterate through possible values for the second integer
            for j in range(i + 1, product // i + 1):
                if (product // i) % j == 0:
                    k = product // (i * j)
                    if j < k:
                        triplets.append((i, j, k))
    return triplets

# Define the product
product = 108

# Find all triplets
triplets = find_triplets(product)

# Print the results
print("The triplets of distinct positive integers whose product is 108 are:")
for triplet in triplets:
    print(triplet)
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