SMO 2012 Senior Round 1 Question 13

Let $S=\{1,2,\ldots,10\}$. A collection $\mathcal F$ of subsets of $S$ is intersecting if $A\cap B\ne\varnothing$ for every two subsets $A,B$ in $\mathcal F$. What is the maximum size of $\mathcal F$?