In good conditions bacteria in a Petri cup spreads quite fast, it doubles every second. If, initially there was one bacteria, then in \(32\) seconds they will cover the whole surface of the cup. In what time the bacteria will cover the surface of the cup, if initially there were \(4\) bacteria?
The first player is thinking about a finite sequence of numbers \(a_1,a_2, ..., a_n\). The second player can try to find the sequence by naming his own sequence \(b_1, b_2, ...b_n\), after that the first player will tell the result \(a_1b_1 + a_2b_2 + ...a_nb_n\). In the next step the second player can say another sequence \(c_1, c_2, ...c_n\) to get another answer \(a_1c_1+ a_2c_2 + ... a_nc_n\). Find the smallest amount of steps the second player has to take to find out the sequence \(a_1,a_2,...a_n\).