Euler problems/181 to 190
((183) If we must have a solution here, let's at least have a decent one.)
Revision as of 20:30, 24 February 2008
Investigating in how many ways objects of two different colours can be grouped.
Solution: This was my code, published here without my permission nor any attribution, shame on whoever put it here. Daniel.is.fischer
fun a1 b1 = sum [ e | e <- [2..a*b-1], gcd e (a*b) == 1, gcd (e-1) a == 2, gcd (e-1) b == 2 ] where a=a1-1 b=b1-1 problem_182=fun 1009 3643
Maximum product of parts.
-- Does the decimal expansion of p/q terminate? terminating p q = 1 == reduce [2,5] (q `div` gcd p q) where reduce  n = n reduce (x:xs) n | n `mod` x == 0 = reduce (x:xs) (n `div` x) | otherwise = reduce xs n -- The expression (round $ fromIntegral n / e) computes the integer k -- for which (n/k)^k is at a maximum. Also note that, given a rational number -- r and a natural number k, the decimal expansion of r^k terminates if -- and only if the decimal expansion of r does. answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n | n <- [5 .. 10^4]] where e = exp 1 main = print answer