Python/project_euler/problem_043/sol1.py
Maxim Smolskiy 1a43c92c77
Improve Project Euler problem 043 solution 1 (#5772)
* updating DIRECTORY.md

* Fix typo

* Improve solution

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
2021-11-05 20:44:24 +01:00

68 lines
1.8 KiB
Python

"""
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.
"""
from itertools import permutations
def is_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
"""
if num[3] % 2 != 0:
return False
if (num[2] + num[3] + num[4]) % 3 != 0:
return False
if num[5] % 5 != 0:
return False
tests = [7, 11, 13, 17]
for i, test in enumerate(tests):
if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0:
return False
return True
def solution(n: int = 10) -> int:
"""
Returns the sum of all pandigital numbers which pass the
divisibility tests.
>>> solution(10)
16695334890
"""
return sum(
int("".join(map(str, num)))
for num in permutations(range(n))
if is_substring_divisible(num)
)
if __name__ == "__main__":
print(f"{solution() = }")