1.hs

import System.IO

digits n | n < 10 = [n]
         | otherwise = let (d, m) = quotRem n 10 in (digits d) ++ [m]

r = sum . digits . fact

fact n | n < 2 = 1
       | otherwise = n * fact (n-1)

main = do
    hSetBuffering stdout NoBuffering
    print $ filter (\(x,y) -> y == 8001) $ map (\x -> (x, r x)) [1..]

2.hs

import Data.List

-- xmllint --format 2.html > 2a.html
-- then got the numbers:
-- cat 2a.html | grep '<p>'
-- cat 2a.html | grep '  <p>'
-- cat 2a.html | grep '    <p>'
-- etc. :P

list = replicate 19 1 ++ replicate 7 2 ++ replicate 4 3 ++ replicate 5 4 ++ replicate 4 5
mean = sum list / genericLength list

var = sum (map (\x -> (x - mean)^2) list) / genericLength list

stddev = sqrt var

3.hs

x = 2520
freqs =  map (\y -> round $ x / y) [1..900]
len = sum $ freqs

-- then tried to bisect:
--  sum $ take 40 freqs
--  sum $ take 20 freqs
--  etc :P.