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Will is given 10 rods, whose lengths are all distinct integers. However, he finds that given any 3 rods, he is unable to construct a (non-degenerate) triangle with them. What is the shortest possible length for the longest rod?

Details and assumptions
A non-degenerate triangle is a triangle with positive area.

  • maths -

    is the answer 55

  • maths -

    no

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