count([], _, 0).
count([H|T], H, R) :- count(T, H, RT), R is RT + 1.
count([H|T], X, R) :- H \= X, count(T, X, R).

add_if_count_is_one(H, T, RT, R) :- count(T, H, 1), R is RT + 1.
add_if_count_is_one(H, T, R, R) :- count(T, H, X), X \= 1.

num_pairs([], 0).
num_pairs([H|T], R) :- delete(T, H, TT),
                       num_pairs(TT, RT),
                       add_if_count_is_one(H, T, RT, R).

:- num_pairs([4,1,1,1,4], N), write(N).