Difference between revisions of "2021 OIM Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | Consider a regular polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show that if <math>r(r | + | Consider a regular polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show that if <math>r(r - 3) \ge n</math>, then there exist at least two congruent triangles whose |
vertices are in <math>V</math>. | vertices are in <math>V</math>. | ||
Latest revision as of 03:02, 14 December 2023
Problem
Consider a regular polygon with 
sides, 
, and let 
be a subset of 
vertices of the polygon. Show that if 
, then there exist at least two congruent triangles whose
vertices are in .
Solution
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