More Haskell, more Project Euler . Again I thought I
would share my solutions to the next few problems. I should point out in
advance that, for the most part, these are naive solutions. I plan on taking a
second pass later to devise more clever approaches.

Problem 4
` `answer = maximum . filter isPalindrome $ products
where products = [ x * y | x <- [ 111 .. 999 ], y <- [ x .. 999 ] ]
isPalindrome n = n == reverse n 0
where reverse 0 r = r
reverse n r = reverse ( n ` div ` 10 ) ( r * 10 + n ` mod ` 10 )

Problem 5
` `answer = head . filter good $ [ 20 , 40 .. ]
where good n = not $ any ( \ t -> n ` rem ` t /= 0 ) [ 2 .. 19 ]

Problem 6
` `answer = squareSum - sumSquare
where squareSum = ( sum [ 1 .. 100 ]) ^ 2
sumSquare = sum $ map ( ^ 2 ) [ 1 .. 100 ]

Problem 7
` `primes :: [ Integer ]
primes = 2 : 3 : primes'
where 1 : p : candidates = [ 6 * k + r | k <- [ 0 .. ], r <- [ 1 , 5 ]]
primes' = p : filter isPrime candidates
isPrime n = all ( not . divides n ) $ takeWhile ( \ p -> p * p <= n ) primes'
divides n p = n ` mod ` p == 0
answer = primes !! 10001

####Problem 8####

` `import Char
largestDigitProduct d n = maximum products
where products = [ digitProduct x digits | x <- [ 0 .. 995 ]]
digitProduct t ds = product $ take d ( drop t ds )
digits = map digitToInt ( show n )
answer = largestDigitProduct 5 < number >