Editing Euler problems/31 to 40 (section)

== [http://projecteuler.net/index.php?section=problems&id=33 Problem 33] ==
Discover all the fractions with an unorthodox cancelling method.

Solution:
<haskell>
import Data.Ratio
problem_33 = denominator . product $ rs
{-
 xy/yz = x/z
(10x + y)/(10y+z) = x/z
9xz + yz = 10xy
 -}
rs = [(10*x+y)%(10*y+z) | x <- t, 
                          y <- t, 
                          z <- t,
                          x /= y ,
                          (9*x*z) + (y*z) == (10*x*y)]
  where t = [1..9]
</haskell>

That is okay, but why not let the computer do the ''thinking'' for you?  Isn't this a little more directly expressive of the problem?  -- HenryLaxen 2008-02-34
<haskell>
import Data.Ratio
problem_33 = denominator $ product 
             [ a%c | a<-[1..9], b<-[1..9], c<-[1..9],
                     isCurious a b c, a /= b && a/= c]
   where isCurious a b c = ((10*a+b)%(10*b+c)) == (a%c)
</haskell>