There are 20 unknown unique pairs of 16-bit sequences $(a_i, b_i)$: $$a_i = (a_{i,0}, a_{i,1}, ..., a_{i,15}), a_{i,k} \in \{0,1\}$$ $$b_i = (b_{i,0}, b_{i,1}, ..., b_{i,15}), b_{i,k} \in \{0,1\}$$ $i=1,2,3,..., 20$
I know two sets: $$A=\{a_1,a_2,...,a_{20}\}$$ $$B=\{b_1,b_2,...,b_{20}\}$$
How, using only questions
Is there a pair, such that...
where all given parameters are in total at last 20 bits long, find all pairings?
I was thinking about describing set $A$ and $B$ using 5 4-bit numbers, but in general it is not good way.