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All the sides of a triangle are integers.  If the perimeter of the triangle is $3,$ then how many different possible triangles are there?  (Assume that the triangle is non-degenerate.  Two triangles are considered the same if they are congruent.)

 Sep 16, 2024
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Only 1 triangle is possible, and its side lengths are 1-1-1.  

Any other triangle with that perimeter won't have integer sides.  

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 Sep 16, 2024

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