Problem:
A set consists of triangles whose sides have integer lengths less than 5 , and no two elements of are congruent or similar. What is the largest number of elements that can have?
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Solution:
Denote a triangle by the string of its side lengths written in nonincreasing order. Then has at most one equilateral triangle and at most one of the two triangles 442 and 221. The other possible elements of are 443, , and 322 . All other strings are excluded by the triangle inequality. Therefore has at most elements.
The problems on this page are the property of the MAA's American Mathematics Competitions