37 lines
1.1 KiB
Ruby
37 lines
1.1 KiB
Ruby
descr=%{
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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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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 digits.
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}
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thoughts=%{
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First, remark it is not so surprising:
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remark the greatest number done with 5 digits is: 99999 => 9^4 + ... + 9^4 < 33000
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and as number is an exponential function depending on the number of digits and power function is less (in the end) than this function. For each n there is always a maximal value.
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now using the same reasonment for the power 5 we see the maximal value will have at most 6 digits (9^5 * 6 < 999999)
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}
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pow=5
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list=[]
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(10..1000000).each do |n|
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sum=0
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n.to_s.each_byte do |b|
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sum+=( b - "0"[0] )**pow
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end
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if n == sum
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puts "#{n}"
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list<<=n
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end
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end
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puts "Sum=" + list.inject(0) { |sum,x| sum+x }.to_s
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