def euler():
# set of the digits to use for generating numbers: all the digits except
# '1', see related hack
digits = list(set(range(10)) - {1})
# number of matches found, only take the second one
matches_count = 0
# for each permutation of the digits
for digit_permutation in sequence.permutations(digits):
# for each truncation in that permutation
for base_digits in sequence.right_truncations(digit_permutation):
# add '1' at the beginning of the number, because the number
# must start with a '1' in order to have the same number of digits
# when multiplied by 6
base_digits = [1] + base_digits
# the base number which will be multiplied
base = int(''.join(str(digit) for digit in base_digits))
# found will stay True if all the multiplications by the FACTORS
# have the same digits
found = True
# for each factor, check if it yields the same digits
for factor in FACTORS:
found = found and set(str(base)) == set(str(base * factor))
# if it's a valid answer
if found:
# return the second valid answer found
matches_count += 1
if matches_count == 2:
return base
def euler():
products_cache = {}
accumulator = 0
for permutation in sequence.permutations('123456789'):
permutation = ''.join(permutation)
products = valid_products(permutation)
for product in products:
if not product in products_cache:
accumulator += product
products_cache [product] = True
return accumulator
def euler():
# list of digits
tokens = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
# current permutation counter
index = 0
# for each permutation of the digits
for permutation in sequence.permutations(tokens):
index += 1
# if the permutation is the one we want
if index == ANSWER_INDEX:
# return it, as a string
return ''.join(map(str, permutation))
def euler():
# highest pandigital prime found so far
highest_pandigital = 0
# for number of digits from 4 to 9
for length in range(4, 9):
# generate the list of digits from 1 to n
digits = list(range(1, length + 1))
# for each permutation of these digits
for permutation in sequence.permutations(digits):
number = int(''.join(str(digit) for digit in permutation))
# check if the number is prime
if prime.is_prime(number):
# set the new value of the highest pandigital prime if needed
highest_pandigital = max(number, highest_pandigital)
# return the highest pandigital prime found
return highest_pandigital