Solutions to the first eight Project Euler problems.

.gitignore

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+*.o
+*.hi
+Problem[0-9]
+Problem[0-9][0-9]
+Problem[0-9][0-9][0-9]
+!*.hs

Problem1.hs

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+-- Find the sum of all the multiples of 3 or 5 below 1000.
+main = print $ sum [ n | n <- [1..999], n `mod` 3 == 0 || n `mod` 5 == 0 ]

Problem2.hs

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+-- By considering the terms in the Fibonacci sequence whose values do not exceed 
+-- four million, find the sum of the even-valued terms.
+fibs = 1 : 2 : zipWith (+) fibs (tail fibs)
+main = print $ sum $ filter even $ takeWhile (<= 4000000) fibs

Problem3.hs

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+-- What is the largest prime factor of the number 600851475143 ?
+n `divides` m = m `mod` n == 0
+primes = go [2..] where go (p:ps) = p : go (filter (\n -> not (p `divides` n)) ps)
+
+factors n = go primes n
+   where go (p:ps) n | n < p         = []
+                     | p `divides` n = p : go (p:ps) (n `div` p)
+                     | otherwise     = go ps n
+
+main = print $ last $ factors 600851475143

Problem4.hs

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+-- Find the largest palindrome made from the product of two 3-digit numbers.
+import Data.List
+
+-- Shortcut: 924 * 962 = 888888, a palindrome, so at least one factor must be >= 924.
+products = sortBy (flip compare) [ n * m | n <- [999,998..924], m <- [999,998..100] ]
+palindrome n = show n == reverse (show n)
+main = print $ head $ filter palindrome products

Problem5.hs

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+-- What is the smallest positive number that is evenly
+-- divisible by all of the numbers from 1 to 20?
+import Data.List
+main = print $ foldl1' lcm [1..20]

Problem6.hs

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+-- Find the difference between the sum of the squares of the first
+-- one hundred natural numbers and the square of the sum.
+main = print $ (sum [1..100])^2 - sum (map (^2) [1..100])

Problem7.hs

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+-- What is the 10 001st prime number?
+primes :: [Int]
+primes = let go (p:ps) = p : go [ n | n <- ps, n `mod` p /= 0 ] in go [2..]
+main = print $ primes !! 10000

Problem8.hs

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+-- Find the thirteen adjacent digits in the 1000-digit number that
+-- have the greatest product. What is the value of this product?
+import Data.List
+
+number = "73167176531330624919225119674426574742355349194934" ++
+         "96983520312774506326239578318016984801869478851843" ++
+         "85861560789112949495459501737958331952853208805511" ++
+         "12540698747158523863050715693290963295227443043557" ++
+         "66896648950445244523161731856403098711121722383113" ++
+         "62229893423380308135336276614282806444486645238749" ++
+         "30358907296290491560440772390713810515859307960866" ++
+         "70172427121883998797908792274921901699720888093776" ++
+         "65727333001053367881220235421809751254540594752243" ++
+         "52584907711670556013604839586446706324415722155397" ++
+         "53697817977846174064955149290862569321978468622482" ++
+         "83972241375657056057490261407972968652414535100474" ++
+         "82166370484403199890008895243450658541227588666881" ++
+         "16427171479924442928230863465674813919123162824586" ++
+         "17866458359124566529476545682848912883142607690042" ++
+         "24219022671055626321111109370544217506941658960408" ++
+         "07198403850962455444362981230987879927244284909188" ++
+         "84580156166097919133875499200524063689912560717606" ++
+         "05886116467109405077541002256983155200055935729725" ++
+         "71636269561882670428252483600823257530420752963450"
+
+main = print $ maximum $ map (product . take 13) $ take 988 $
+       tails $ map (read . (:[])) number