The cube $nxnxn$ consists of $n^3$ unit cubes $1x1x1$, and at least one of these unit cubes is black. Show that we can always cut the cube in $2$ parallelepiped pieces so that each piece contains exactly one black 1x1 square .
Source: Second Saudi Arabia JBMO TST 2018, P3
Tags: combinatorics
The cube $nxnxn$ consists of $n^3$ unit cubes $1x1x1$, and at least one of these unit cubes is black. Show that we can always cut the cube in $2$ parallelepiped pieces so that each piece contains exactly one black 1x1 square .