Problem 33

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.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

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.

If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

import Control.Arrow
p033 =product***product$unzip$[(a,c)|a<-[1..9],b<-[1..9],c<-[(10*a-9*b+1)..9],9*a*c+b*c==10*a*b]

最後の約分をサボったのは内緒だ。

なおした。

import Data.Ratio
p033 =product[a%c|a<-[1..9],b<-[1..9],c<-[(10*a-9*b+1)..9],9*a*c+b*c==10*a*b]

それにしても、有理数が扱えるなんて、Haskellは便利だな。

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