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 is_truncatable(number):
if number < 10:
return False
for truncation in sequence.left_truncations(str(number)):
if not primeutils.is_prime(int(truncation)):
return False
for truncation in sequence.right_truncations(str(number)):
if not primeutils.is_prime(int(truncation)):
return False
return True