Rmo 1993 Updated Jun 2026

One question focused on a 20-sided regular polygon, asking students to determine the number of possible scalene triangles whose vertices are polygon vertices but whose sides are not sides of the polygon.

So solution set: ( t \in [2,3] ).

( x = t^2 + 1 ), with ( t \in [2,3] ). So ( x \in [5, 10] ). rmo 1993

( x-1 \ge 0 \Rightarrow x \ge 1 ).

This is a standard inequality problem solvable via the Cauchy-Schwarz Inequality or the AM-HM inequality. One question focused on a 20-sided regular polygon,