Problem #WSP-5295

Problem

Two players are playing a game. The first player is thinking of a finite sequence of positive integers $a_{1}$ , $a_{2}$ , ..., $a_{n}$ . The second player can try to find the first player’s sequence by naming their own sequence $b_{1}$ , $b_{2}$ , ..., $b_{n}$ . After this, the first player will give the result $a_{1} b_{1} + a_{2} b_{2} + . . . + a_{n} b_{n}$ . Then the second player can say another sequence $c_{1}$ , $c_{2}$ , ..., $c_{n}$ to get another answer $a_{1} c_{1} + a_{2} c_{2} + . . . + a_{n} c_{n}$ from the first player. Find the smallest number of sequences the second player has to name to find out the sequence $a_{1}$ , $a_{2}$ , ..., $a_{n}$ .

To see the solution register and get verified.