Problem43.py

# Code by @AmirMotefaker

# projecteuler.net
# https://projecteuler.net/problem=43

# Sub-string divisibility
# Problem 43

# 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 1
# simple solution using direct if else statements.

import time
from itertools import permutations

start_time = time.time()   #Time at the start of program execution

p = permutations('0123456789')   # permutations of 0-9 pandigital

solution = 0  # store the value of sum

for i in p:
    if (int(''.join(i[7:10])) % 17 == 0 and
        int(''.join(i[6:9])) % 13 == 0 and
        int(''.join(i[5:8])) % 11 == 0 and
        int(''.join(i[4:7])) % 7 == 0 and
        int(''.join(i[3:6])) % 5 == 0 and
        int(''.join(i[2:5])) % 3 == 0 and
        int(''.join(i[1:4])) % 2 == 0):
        solution += int(''.join(i))

# printing the solution
print (solution)

end_time = time.time()   #Time at the end of execution
print ("Time of program execution:", (end_time - start_time))   # Time of program execution



### Answer:  16695334890