3 $\text{Let} S_1,S_2,...S_{2011}$ $\text{be nonempty sets of consecutive integers such that any}$ $2$ $\text{of them have a common element. Prove that there is a positive integer that belongs to every}$ $S_i, i=1,...,2011$ (Por ejemplo, ${2,3,4,5}$ es un conjunto de enteros consecutivos mientras que ${2,3,5}$ no lo es.)