MathDB

a cube of edge 2^n is divided into 2^{3n} unit cubes , remove unit cube

Source: Polish second round 1999 p2

January 19, 2020

Tilingcombinatorial geometrycubecombinatoricsgeometry3D geometry

Problem Statement

A cube of edge

2

with one of the corner unit cubes removed is called a piece. Prove that if a cube

T

of edge

2^n

is divided into

2^{3n}

unit cubes and one of the unit cubes is removed, then the rest can be cut into pieces.