36 lines
1.3 KiB
Ruby
36 lines
1.3 KiB
Ruby
descr=%{
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The fraction ^(49)/_(98) is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that ^(49)/_(98) = ^(4)/_(8), which is correct, is obtained by cancelling the 9s.
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We shall consider fractions like, ^(30)/_(50) = ^(3)/_(5), to be trivial examples.
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There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.
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If the product of these four fractions is given in its lowest common terms, find the value of the denominator.
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}
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# n/m
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res=[]
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(10..99).each do |n|
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(n+1..99).each do |m|
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next if n%10 == 0 and m%10 == 0
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next if n%11 == 0 and m%11 == 0
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nb_first=0
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n.to_s.split('').each do |c|
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newn=c.to_i
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nb_first+=1
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nb_second=0
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m.to_s.split('').each do |d|
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nb_second += 1
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next if nb_first == nb_second
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newm=d.to_i
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if newm == 0
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next
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end
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if n.to_f/m == newn.to_f/newm
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res <<= [n,m,newn,newm]
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puts %{#{n}/#{m} = #{newn}/#{newm}}
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end
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end
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end
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end
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end
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