Problem

Source: Indonesia IMO 2007 TST, Stage 2, Test 5, Problem 3

Tags: combinatorics proposed, combinatorics



On each vertex of a regular $ n-$gon there was a crow. Call this as initial configuration. At a signal, they all flew by and after a while, those $ n$ crows came back to the $ n-$gon, one crow for each vertex. Call this as final configuration. Determine all $ n$ such that: there are always three crows such that the triangle they formed in the initial configuration and the triangle they formed in the final configuration are both right-angled triangle.