A2. Triangle ABC has integer side lengths and perimeter 7. Determine all possible lengths of side $\mathrm{AB}$.
Solution: By the triangle inequality, the largest possible length of any side is 3 . Moreover, if all side lengths were less than 3 , the perimeter would be less than 7 . Thus, at least one side has length 3 . This leaves the other sides has $(2,2)$ or $(1,3)$. Thus, $\mathrm{AB}$ can be 1,2 , or 3 .
Answer: $1,2,3$.