Problem 43 : Sub-string divisibility
Problem Statement
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.
Solution
from itertools import permutations
a='1234567890'
p=permutations(a[:10])
sum1=0
for i in p:
if i[0]!='0':
temp=''.join(list(i))
if int(temp[1:4])%2==0 and int(temp[2:5])%3==0 and int(temp[3:6])%5==0 and int(temp[4:7])%7==0 and int(temp[5:8])%11==0 and int(temp[6:9])%13==0 and int(temp[7:10])%17==0:
sum1=sum1+int(temp)
print(sum1)
Output
16695334890