def smallest_multiple(limit):
product_ = Basic.product(range(1, limit + 1))
primes = primes_under(limit)
primes_product = Basic.product(primes)
max_step = product_ // primes_product
for multiplier in range(1, max_step + 1):
num = primes_product * multiplier
for j in range(2, limit + 1):
if not is_factor_of(j, num):
break
else:
return num
return product_
def solve008(num, length):
digits = [int(i) for i in list(num)]
max_product = 1
for i in range(len(num) - length + 1):
product = Basic.product(digits[i:i + length])
if product > max_product:
max_product = product
return max_product
def solve004(digit_size):
check_size = digit_size // 10
checks = range(digit_size - check_size, digit_size)
mult_table = Basic.multiplication_table(checks, checks)
palindromes = list()
for row in mult_table:
for num in row:
if General.is_palindrome(num):
palindromes.append(num)
return max(palindromes)
def nth_permutation(n, list_):
permutation = list()
num_permutations = Basic.factorial(len(list_))
n %= num_permutations
while n > 0:
permutations_per_index = num_permutations // len(list_)
index = n // permutations_per_index
n %= permutations_per_index
num_permutations = permutations_per_index
permutation.append(list_.pop(index))
permutation += list_
return permutation
def num_factors_of(num):
primes = prime_factors_of(num)
count_values = General.count_list(primes).values()
return Basic.product([x + 1 for x in count_values])
def n_choose_k(n, k):
n_fact = Basic.factorial(n)
nk_fact = Basic.factorial(n - k)
k_fact = Basic.factorial(k)
return n_fact // (k_fact * nk_fact)
def solve006(size):
square_of_sum = Basic.square_of_sum_up_to(size)
sum_of_squares = Basic.sum_of_squares_up_to(size)
return square_of_sum - sum_of_squares
def solve020(num):
factorial = Basic.factorial(num)
return General.sum_of_digits(factorial)
def solve012(limit):
num = 2
while NumberTheory.num_factors_of(Basic.sum_up_to(num)) <= limit:
num += 1
return Basic.sum_up_to(num)