46 lines
1.1 KiB
Python
46 lines
1.1 KiB
Python
#!/usr/bin/python3
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# Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
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#
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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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#
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# As 1 = 1^4 is not a sum it is not included.
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#
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# The sum of these numbers is 1634 + 8208 + 9474 = 19316.
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#
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# Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
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from timeit import default_timer
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def main():
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start = default_timer()
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tot = 0
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# Straightforward brute force approach. The limit is chosen considering that
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# 6*9^5=354294, so no number larger than that can be expressed as sum
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# of 5th power of its digits.
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for i in range(10, 354295):
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j = i
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sum_ = 0
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while j > 0:
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digit = j % 10
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sum_ = sum_ + digit ** 5
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j = j // 10
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if sum_ == i:
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tot = tot + i
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end = default_timer()
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print('Project Euler, Problem 30')
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print('Answer: {}'.format(tot))
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print('Elapsed time: {:.9f} seconds'.format(end - start))
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if __name__ == '__main__':
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main()
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