Question 14
(VIE 2) Prove that it is possible to place $2n(2n+1)$ parallelepipedic (rectangular) pieces of soap of dimensions $1\times2\times(n+1)$ in a cubic box with edge $2n+1$ if and only if $n$ is even or $n=1$.
Remark. It is assumed that the edges of the pieces of soap are parallel to the edges of the box.
Remark. It is assumed that the edges of the pieces of soap are parallel to the edges of the box.