The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:
d2d3d4=406 is divisible by 2
d3d4d5=063 is divisible by 3
d4d5d6=635 is divisible by 5
d5d6d7=357 is divisible by 7
d6d7d8=572 is divisible by 11
d7d8d9=728 is divisible by 13
d8d9d10=289 is divisible by 17
Find the sum of all 0 to 9 pandigital numbers with this property.
Run this solution at repl.io
here.
from itertools import permutations
# Create a (sorted) list of 0 to 9 pandigital string numbers
pandigitals = []
table = list(permutations([0,1,2,3,4,5,6,7,8,9]))
for tpl in table:
num = [str(x) for x in tpl]
num = ''.join(num)
pandigitals.append(num)
print(len(pandigitals))
total = []
for pd in pandigitals:
if int(pd[1:4]) % 2 == 0 and int(pd[2:5]) % 3 == 0 \
and int(pd[3:6]) % 5 == 0 and int(pd[4:7])% 7 == 0 \
and int(pd[5:8]) % 11 == 0 and int(pd[6:9]) % 13 == 0 \
and int(pd[7:10]) % 17 == 0:
total.append(int(pd))
print(sum(total), total)