Problem

Source: 2017 Iran MO 3rd round , second combinatorics exam P1

Tags: Iran, combinatorics



There are $100$ points on the circumference of a circle, arbitrarily labelled by $1,2,\ldots,100$. For each three points, call their triangle clockwise if the increasing order of them is in clockwise order. Prove that it is impossible to have exactly $2017$ clockwise triangles.