Question
The numbers `1,2,3,4,5` are written at the vertices of a regular pentagon, with each number at exactly one vertex. A trio of vertices is called successful if it forms an isosceles triangle, where the number at its apex is greater than the numbers at the other two vertices, or where the number at its apex is smaller than the numbers at the other two vertices.
Find the maximum number of successful trios that can exist.
Difficulty level (1 very easy - 10 very hard): 5
Topics:
Proof and Example
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Constructing an Example / Counterexample
Combinatorics
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Case Analysis / Checking Cases
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Processes / Procedures
Geometry
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Plane Geometry
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Symmetry
Minimum and Maximum Problems / Optimization Problems
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