Question 3
Let $S_1,S_2,\ldots,S_{2011}$ be nonempty sets of consecutive integers such that any $2$ of them have a common element. Prove that there is an integer that belongs to every $S_i$, $i=1,\ldots,2011$. (For example, $\{2,3,4,5\}$ is a set of consecutive integers while $\{2,3,5\}$ is not.)