def is_pandigital(n):
second = number.is_pandigital(str(n % 1000000000))
if not second:
return False
while n > 1000000000000000:
n = n // 1000000
while n > 1000000000:
n = n // 10
return number.is_pandigital(str(n))
def solve():
result = 0 #@UnusedVariable
pandigital_concatenated_products = []
# since n > 1, 5 digits are enough
for m in range (1,10**5):
for n in range(1,10):
p = concatenated_product(m, range(1, n+1))
if len(str(p)) > 9:
break
if is_pandigital(p, 9):
pandigital_concatenated_products.append(p)
result = sorted(pandigital_concatenated_products)[-1]
print("The largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n > 1 is %(result)d" % vars())
def solve():
# log_10(a) + log_10(b) + log_10(c) <= 9
# ==> 2*log_10(ab) <= 9
# ==> log_10(b) <= 4.5 - log_10(a)
pandigital_products = []
for a in range(1, int(4.5**10)+1):
for b in range(1, int((4.5**10)/a)+1):
c = a*b
pandigital_candidate = str(a)+str(b)+str(c)
if len(pandigital_candidate) == 9 and is_pandigital(pandigital_candidate):
pandigital_products.append((a, b, c))
print(pandigital_products)
result = sum(set([c for (a,b,c) in pandigital_products])) #@UnusedVariable
print("The sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital is %(result)d" % vars())
import number
largest = 0
for n in range(1, 100000):
for limit in range(1, 11):
triple = [i * n for i in range(1, limit)]
concat = "".join(str(i) for i in triple)
if number.is_pandigital(concat):
concat = int(concat)
if concat > largest:
largest = concat
print("Largest concatination: {}".format(largest))
import number
products = set()
for a in range(100):
if '0' in str(a):
continue
for b in range(9876):
if '0' in str(b):
continue
product = a * b
if number.is_pandigital(str(product) + str(a) + str(b)):
products.add(product)
print("Sum of products: {}".format(sum(products)))
