import itertools

length = 5
digits = set(range(10))
numbers = set(itertools.product(digits, repeat=length))

print(f"|Z| = {len(digits)}")
print(f"|N| = {len(numbers)}")

counter = 0
for n in numbers:
    if len(set(n)) == 1:
        counter += 1
print(f"|A| = {counter}")
# Ausgabe: |A| = 10

counter = 0
for n in numbers:
    if sum(n.count(x) == 4 for x in set(n)) > 0:
        counter += 1
print(f"|B| = {counter}")
# Ausgabe: |B| = 450

counter = 0
for n in numbers:
    if len(set(n)) == 3 and any(n.count(x) == 3 for x in set(n)):
        counter += 1
print(f"|C| = {counter}")
# Ausgabe: |C| = 7200

counter = 0
for n in numbers:
    if len(set(n)) == 2 and any(n.count(x) == 3 for x in set(n)):
        counter += 1
print(f"|D| = {counter}")
# Ausgabe: |D| = 900

counter = 0
for n in numbers:
    if len(set(n)) == 3 and any(x != y and n.count(y) == 2 and n.count(x) == 2 for x in set(n) for y in set(n)):
        counter += 1
print(f"|E| = {counter}")
# Ausgabe: |E| = 10800

counter = 0
for n in numbers:
    if len(set(n)) == 5:
        counter += 1
print(f"|F| = {counter}")
# Ausgabe: |F| = 30240

def contains_twin_pair(combo):
    """Check if the combination contains at least one twin pair."""
    for x in range(len(combo)):
        for y in range(len(combo)):
            if abs(combo[x] % 49 - combo[y] % 49) == 1:
                return True
    return False

# Generate all combinations of 6 numbers out of 49
numbers = list(range(1, 50))
all_combinations = list(itertools.combinations(numbers, 6))

# Filter combinations with and without twin pairs
combinations_with_twin = [combo for combo in all_combinations if contains_twin_pair(combo)]
combinations_without_twin = [combo for combo in all_combinations if not contains_twin_pair(combo)]

# Output the count of combinations
print(len(all_combinations))
print(f"Number of combinations with at least one twin pair: {len(combinations_with_twin)}")
print(f"Number of combinations without any twin pairs: {len(combinations_without_twin)}")
print(len(combinations_with_twin)/len(all_combinations))