def eul33():
"""If the product of these four fractions is given in its lowest common terms, find the value of the denominator."""
fracs = []
for d in range(10, 100):
for n in range(10, d):
common = set(eul.get_digits(n)).intersection(eul.get_digits(d))
for digit in common:
if digit:
r_n = int(str(n).replace(str(digit), "", 1))
r_d = int(str(d).replace(str(digit), "", 1))
if r_d and r_n / r_d == n / d:
fracs.append((n, d))
n = d = 1
for frac in fracs:
n *= frac[0]
d *= frac[1]
return d / math.gcd(n, d)
def eul32():
""""Find the sum of all products whose multiplicand/multiplier/product identity can be written as a
1 through 9 pandigital."""
products = set()
for product in range(1000, 10000):
if len(set(eul.get_digits(product))) == len(str(product)):
for i in eul.get_proper_divisors(product):
j = int(product / i)
test = ''.join([str(i), str(j), str(i*j)])
if len(test) == 9 and eul.pandigital(test):
products.add(i*j)
return sum(products)
def eul34():
"""Find the sum of all numbers which are equal to the sum of the factorial of their digits."""
return sum([i for i in range(3, 100000) if sum([math.factorial(x) for x in eul.get_digits(i)]) == i])
def eul30():
"""Find the sum of all the numbers that can be written as the sum of fifth powers of their digits."""
return sum([x for x in range(2, 1000000) if sum([y ** 5 for y in eul.get_digits(x)]) == x])
def eul16():
"""What is the sum of the digits of the number 2^n = 1000?"""
return sum([x for x in eul.get_digits(2 ** 1000)])
