second :: [Int] -> Int
-- testing 47 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
second xs  =  head (tail xs)

third :: [Int] -> Int
-- testing 34 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 5 candidates of size 4
third xs  =  head (tail (tail xs))

sum :: [Int] -> Int
-- testing 37 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 5 candidates of size 4
-- looking through 13 candidates of size 5
-- looking through 26 candidates of size 6
-- looking through 63 candidates of size 7
-- looking through 154 candidates of size 8
-- looking through 368 candidates of size 9
-- looking through 902 candidates of size 10
sum xs  =  if null xs then 0 else head xs + sum (tail xs)

product :: [Int] -> Int
-- testing 37 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 5 candidates of size 4
-- looking through 13 candidates of size 5
-- looking through 26 candidates of size 6
-- looking through 63 candidates of size 7
-- looking through 154 candidates of size 8
-- looking through 368 candidates of size 9
-- looking through 902 candidates of size 10
product xs  =  if null xs then 1 else head xs * product (tail xs)

sum :: [Int] -> Int
-- testing 37 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 8 candidates of size 4
sum xs  =  foldr (+) 0 xs

product :: [Int] -> Int
-- testing 37 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 2 candidates of size 2
-- looking through 3 candidates of size 3
-- looking through 8 candidates of size 4
product xs  =  foldr (*) 1 xs