Problem

Source: (2022 -) 2023 XVI Dürer Math Competition Regional E3

Tags: combinatorics



Pythagoras drew some points in the plane and and connected some of these with segments. Now Tortillagoras wants to write a positive integer next to every point, such that one number divides another number if and only if these numbers are written next to points that Pythagoras has connected.Can Tortillagoras do this for the following drawings? In part b), vertices in the same row or column but not adjacent are not connected.