def challenge041():
# loop through number of digits
highest = 0
for n in [4, 7]:
chars = string.join([str(c) for c in xrange(1, n + 1)], "")
for potential in [int(p) for p in permutate(chars) if isPrime(int(p))]:
if potential > highest: highest = potential
return highest
def challenge032():
source = "123456789"
products = []
for potential in [int(p) for p in permutate(source)]:
# * can be after 1, 2, 3, 4
# = can only be between 5 and 6
third = potential % 10**4
for i in xrange(1, 3):
first = potential // 10**(9 - i)
second = (potential // 10**(4)) % 10**(5 - i)
product = first * second
if product == third:
products.append(third)
return sum(set(products))
def challenge043():
source = "0123456789"
total = 0
for n in [int(n) for n in permutate(source) \
if int(n) >= 1000000000 and \
int(n[1:4]) % 2 == 0 and \
int(n[2:5]) % 3 == 0 and \
int(n[3:6]) % 5 == 0 and \
int(n[4:7]) % 7 == 0 and \
int(n[5:8]) % 11 == 0 and \
int(n[6:9]) % 13 == 0 and \
int(n[7:10]) % 17 == 0]:
total += n
return total
def challenge024():
number = "0123456789"
permutations = (s for s in permutate(number))
millionth = -1
millionth = [n for n, i in zip(permutations, xrange(1000000)) if i == 999999]
return int(millionth[0])
