2015 Paraguayan Mathematical Olympiad: Problem 3
Source:
October 10, 2015
geometry
Problem Statement
A cube is divided into smaller cubes of the same size, as shown in the figure. Then, each of these small cubes is divided again into smaller cubes of the same size. This process is done more times to each resulting cube. What is the ratio between the sum of the total areas of all the small cubes resulting from the last division and the total area of the initial cube?