p038.py

#Take the number 192 and multiply it by each of 1, 2, and 3:
#
#    192 x 1 = 192
#    192 x 2 = 384
#    192 x 3 = 576
#
#By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3)
#
#The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1,2,3,4,5).
#
#What is 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?

import numpy as np
def check_pandigital(n):
   """ check if a string represents a pandigital number """
   if len(n) > 9:
      return False
   for i in range(1,10):
      if not str(i) in n:
         return False
   return True

for n in xrange(10000):
   if not str(n)[0] == '9': continue
   for i in xrange(2,10):
      pan = reduce(lambda a,b: a+str(b*n),range(1,i+1),"")
      if(check_pandigital(pan)):
            print pan,n,i