sol1.py

"""
Problem 43: https://projecteuler.net/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.
"""

fromitertoolsimportpermutations


defis_substring_divisible(num: tuple) ->bool:
"""
 Returns True if the pandigital number passes
 all the divisibility tests.
 >>> is_substring_divisible((0, 1, 2, 4, 6, 5, 7, 3, 8, 9))
 False
 >>> is_substring_divisible((5, 1, 2, 4, 6, 0, 7, 8, 3, 9))
 False
 >>> is_substring_divisible((1, 4, 0, 6, 3, 5, 7, 2, 8, 9))
 True
 """
ifnum[3] %2!=0:
returnFalse

if (num[2] +num[3] +num[4]) %3!=0:
returnFalse

ifnum[5] %5!=0:
returnFalse

tests= [7, 11, 13, 17]
fori, testinenumerate(tests):
if (num[i+4] *100+num[i+5] *10+num[i+6]) %test!=0:
returnFalse
returnTrue


defsolution(n: int=10) ->int:
"""
 Returns the sum of all pandigital numbers which pass the
 divisibility tests.
 >>> solution(10)
 16695334890
 """
returnsum(
int("".join(map(str, num)))
fornuminpermutations(range(n))
ifis_substring_divisible(num)
 )


if__name__=="__main__":
print(f"{solution() =}")