Add Haskell solutions for Problem 29, 41, 52

Haskell/ProjectEuler.hs

@@ -3,6 +3,7 @@ module ProjectEuler
 , digitSum
 , sumProperDivisors
 , countDivisors
+, isPandigital
 ) where
 
 import Data.Char (digitToInt)
@@ -30,3 +31,8 @@ countDivisors :: (Integral a) => a -> Int
 countDivisors n = length $ nub $ concat [ [x, n `div` x] | x <- [1..limit], n `mod` x == 0 ]
     where limit = floor $ sqrt $ fromIntegral n
 
+isPandigital :: Integer -> Bool
+isPandigital n = n_length == length (nub n_char) && '0' `notElem` n_char && digitToInt (maximum n_char) == n_length
+    where n_char = show n
+          n_length = length n_char
+

Haskell/p029.hs

@@ -0,0 +1,21 @@
+-- Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
+--
+-- 2^2=4, 2^3=8, 2^4=16, 2^5=32
+-- 3^2=9, 3^3=27, 3^4=81, 3^5=243
+-- 4^2=16, 4^3=64, 4^4=256, 4^5=1024
+-- 5^2=25, 5^3=125, 5^4=625, 5^5=3125
+--
+-- If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
+--
+-- 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
+--
+-- How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
+import Data.List
+
+powerCombinations :: (Integral a) => a -> [a]
+powerCombinations n = nub [ x^y | x <- [2..n], y <- [2..n] ]
+
+main = do
+    let result = length $ powerCombinations 100
+    putStrLn $ "Project Euler, Problem 29\n"
+        ++ "Answer: " ++ show result

Haskell/p041.hs

@@ -0,0 +1,14 @@
+-- We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital
+-- and is also prime.
+--
+-- What is the largest n-digit pandigital prime that exists?
+
+import ProjectEuler (isPrime, isPandigital)
+
+maxPandigitalPrime :: Integer
+maxPandigitalPrime = head $ filter isPrime (filter isPandigital [7654321,7654319..])
+
+main = do
+    let result = maxPandigitalPrime
+    putStrLn $ "Project Euler, Problem 41\n"
+        ++ "Answer: " ++ show result

Haskell/p052.hs

@@ -0,0 +1,12 @@
+-- It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
+--
+-- Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
+import Data.List
+
+smallestPermutedMultiples :: Integer
+smallestPermutedMultiples = head  [ x | x <- [1..], sort (show x) == sort (show (2 * x)), sort (show x) == sort (show (3 * x)),  sort (show x) == sort (show (4 * x)),  sort (show x) == sort (show (5 * x)),  sort (show x) == sort (show (6 * x)) ]
+
+main = do
+    let result = smallestPermutedMultiples
+    putStrLn $ "Project Euler, Problem 52\n"
+        ++ "Answer: " ++ show result