mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
67 lines
1.8 KiB
Python
67 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() = }")
|