Consider the set L of binary strings of length less than or equal to 9, and for a string w define w^{+} to be the set \left\{w, w^{2}, w^{3}, \ldots\right\} where w^{k} represents w concatenated to itself k times. How many ways are there to pick an ordered pair of (not necessarily distinct) elements x, y \in L such that x^{+} \cap y^{+} \neq \varnothing?