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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
59 lines
1.5 KiB
Python
59 lines
1.5 KiB
Python
"""
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We shall say that an n-digit number is pandigital if it makes use of all the
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digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through
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5 pandigital.
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The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing
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multiplicand, multiplier, and product is 1 through 9 pandigital.
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Find the sum of all products whose multiplicand/multiplier/product identity can
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be written as a 1 through 9 pandigital.
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HINT: Some products can be obtained in more than one way so be sure to only
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include it once in your sum.
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"""
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import itertools
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def is_combination_valid(combination):
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"""
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Checks if a combination (a tuple of 9 digits)
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is a valid product equation.
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>>> is_combination_valid(('3', '9', '1', '8', '6', '7', '2', '5', '4'))
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True
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>>> is_combination_valid(('1', '2', '3', '4', '5', '6', '7', '8', '9'))
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False
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"""
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return (
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int("".join(combination[0:2])) * int("".join(combination[2:5]))
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== int("".join(combination[5:9]))
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) or (
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int("".join(combination[0])) * int("".join(combination[1:5]))
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== int("".join(combination[5:9]))
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)
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def solution():
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"""
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Finds the sum of all products whose multiplicand/multiplier/product identity
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can be written as a 1 through 9 pandigital
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>>> solution()
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45228
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"""
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return sum(
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{
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int("".join(pandigital[5:9]))
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for pandigital in itertools.permutations("123456789")
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if is_combination_valid(pandigital)
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}
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)
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if __name__ == "__main__":
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print(solution())
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