Find the number of addition problems in which a two-digit number is added to a second two-digit number to give a two-digit answer, such as in the three examples: \[\begin{tabular}{@{\hspace{3pt}}c@{\hspace{3pt}}}23\\42\\\hline 65\end{tabular}\,, \begin{tabular}{@{\hspace{3pt}}c@{\hspace{3pt}}}36\\36\\\hline 72\end{tabular}\,, \begin{tabular}{@{\hspace{3pt}}c@{\hspace{3pt}}}42\\23\\\hline 65\end{tabular}\,.

Let's think step by step and output the final answer within \boxed{}.
user