-- 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 Euler

main = print $ denominator $ product $
   [ n
   | a <- [1..9]
   , b <- [1..9]
   , c <- [1..9]
   , d <- [1..9]
   , let x = 10 * a + b
   , let y = 10 * c + d
   , let n = x % y
   , n < 1
   , (a == c && b % d == n) ||
     (a == d && b % c == n) ||
     (b == c && a % d == n) ||
     (b == d && a % c == n)
   ]