# Problem #1849

 1849 A set $S$ consists of triangles whose sides have integer lengths less than 5, and no two elements of $S$ are congruent or similar. What is the largest number of elements that $S$ can have? $\textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12$ This problem is copyrighted by the American Mathematics Competitions.
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