Question 31
Fatima and Asma are playing the following game. First, Fatima chooses $2013$ pairwise different numbers, called $a_{1}, a_{2}, \ldots, a_{2013}$. Then, Asma tries to know the value of each number $a_{1}, a_{2}, \ldots, a_{2013}$. At each time, Asma chooses $1 \leq i \lt j \leq 2013$ and asks Fatima "What is the set $\{a_{i}, a_{j}\}$?" (For example, if Asma asks what is the set $\{a_{1}, a_{2}\}$, and $a_{1} = 17$ and $a_{2} = 13$, Fatima will answer $\{13, 17\}$). Find the least number of questions Asma needs to ask, to know the value of all the numbers $a_{1}, a_{2}, \ldots, a_{2013}$.