3. $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ are five different real numbers. The number of different values that the sum $a_{i}+a_{j}$ can take for all $i, j$ with $1 \leq i<j \leq 5$ we call $m$.

Determine the smallest possible value of $m$.
3. We order the five numbers from smallest to largest and call them $a, b, c, d$, and $e$, so $a<b<c<d<e$. Then it holds that: $a+b<a+c<a+d<a+e<b+e<c+e<d+e$. Therefore, the smallest value of $m$ satisfies: $m \geq 7$. With the example $a=1, b=2, c=3, d=4$ and $e=5$, we find the sums to be $3,4,5,6,7,8$ and 9. Thus, 7 is the smallest possible value of $m$.