I see one of recent local informatics Olympiad question. i have a trouble to solve it. any idea? hint? or solutions? thanks to all creative man.
We have two function $P_1, P_2$ and input an array $n$ bit called $x$. $P_1$ calculate $y_1=A_1x$ and $P_2$ calculate $y_2=A_2x$. $A_1, A_2$ is $n*n$ bit matrix. the output of these two functions is $n$ bit array $y_1, y_2$. we nothing know about these matrix but know $A_1, A_2$ is the same except one slot $(I,J)$. we can call $P_1,P_2$ with different $x$'s and compare the output of these calls. with how many number of calls can find $I, J$ index?