MathDB
N^3 unit cubes All-Russian MO 1995 Regional (R4) 10.7

Source:

August 26, 2024
combinatoricscombinatorial geometrygeometry3D geometrycube

Problem Statement

N3N^3 unit cubes are made into beads by drilling a hole through them along a diagonal, put on a string and binded. Thus the cubes can move freely in space as long as the vertices of two neighboring cubes (including the first and last one) are touching. For which NN is it possible to build a cube of edge NN using these cubes?