2001 Gauss 7 Problem 25

A triangle can be formed having side lengths 4, 5 and 8. It is impossible, however, to construct a triangle with side lengths 4, 5 and 9. Ron has eight sticks, each having an integer length. He observes that he cannot form a triangle using any three of these sticks as side lengths. The shortest possible length of the longest of the eight sticks is

\textbf{(A)}\ 20\quad \textbf{(B)}\ 21\quad \textbf{(C)}\ 22\quad \textbf{(D)}\ 23\quad \textbf{(E)}\ 24

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

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