2017 Cayley Problem 8

Each of three cards is labelled with three numbers. Which of the following groups of three cards has the properties that the first and second cards have exactly one number in common, the first and third cards have exactly one number in common, and the second and third cards have exactly one number in common?

\textbf{(A)}\ \boxed{135}\ \boxed{367}\ \boxed{246}\quad \textbf{(B)}\ \boxed{147}\ \boxed{234}\ \boxed{245}\quad \textbf{(C)}\ \boxed{234}\ \boxed{257}\ \boxed{124}\quad \textbf{(D)}\ \boxed{147}\ \boxed{234}\ \boxed{257}\quad \textbf{(E)}\ \boxed{135}\ \boxed{147}\ \boxed{235}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.