Here is a problem from Miklos Schweitzer competition from 2017.
Is it possible to partition a square into finitely many triangles such that no two triangles share a side?
I believe it is impossible. I tried proving that the polygon formed by triangles (without sharing any side) must have a concave angle ($>\angle180^{\circ}$), but... or maybe just making concave polygons with the triangles...
Help guys!