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45 lines
1.2 KiB
Python
45 lines
1.2 KiB
Python
"""Problem Statement (Digit Fifth Powers): https://projecteuler.net/problem=30
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Surprisingly there are only three numbers that can be written as the sum of fourth
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powers of their digits:
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1634 = 1^4 + 6^4 + 3^4 + 4^4
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8208 = 8^4 + 2^4 + 0^4 + 8^4
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9474 = 9^4 + 4^4 + 7^4 + 4^4
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As 1 = 1^4 is not a sum it is not included.
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The sum of these numbers is 1634 + 8208 + 9474 = 19316.
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Find the sum of all the numbers that can be written as the sum of fifth powers of their
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digits.
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9^5 = 59049
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59049 * 7 = 413343 (which is only 6 digit number)
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So, numbers greater than 999999 are rejected
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and also 59049 * 3 = 177147 (which exceeds the criteria of number being 3 digit)
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So, number > 999
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and hence a number between 1000 and 1000000
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"""
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DIGITS_FIFTH_POWER = {str(digit): digit**5 for digit in range(10)}
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def digits_fifth_powers_sum(number: int) -> int:
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"""
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>>> digits_fifth_powers_sum(1234)
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1300
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"""
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return sum(DIGITS_FIFTH_POWER[digit] for digit in str(number))
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def solution() -> int:
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return sum(
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number
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for number in range(1000, 1000000)
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if number == digits_fifth_powers_sum(number)
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)
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if __name__ == "__main__":
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print(solution())
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