-- Count number of digits in 100!
-- I think the answer is below 192 but above 92
-- One can use sterling's formula to estimate the number of digits

-- Expected output is 158

main = printDigitsInFactorialOf 100 where
       printDigitsInFactorialOf = putStr . show . countDigits . calculateFactorial

calculateFactorial 0 = 1
calculateFactorial n = n * calculateFactorial predn where
                       predn = pred n

countDigits 0 = 0
countDigits n = 1 + countDigits nDiv10 where
                nDiv10 = n `div` 10

158