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, 2006

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

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 10. Using the side lengths 2, 3, 5, 7 and 11, how many different triangles with exactly two equal sides can be formed?

(A) $8$ (B) $5$ (C) $20$ (D) $10$ (E) $14$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.