IMO Shortlist 1978 problem 14
Dodao/la:
arhiva2. travnja 2012. Prove that it is possible to place
![2n(2n + 1)](/media/m/6/0/b/60b5829bd05e8f41e2e05cdb57afafae.png)
parallelepipedic (rectangular) pieces of soap of dimensions
![1 \times 2 \times (n + 1)](/media/m/f/b/9/fb904ff1a9e1a112b67a3470aaa62c17.png)
in a cubic box with edge
![2n + 1](/media/m/9/6/4/9645bec33da754f07d7a3eaf2b91eeaa.png)
if and only if
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
is even or
![n = 1](/media/m/6/0/b/60bd22f83584e59c0352d20be6119425.png)
.
Remark. It is assumed that the edges of the pieces of soap are parallel to the edges of the box.
%V0
Prove that it is possible to place $2n(2n + 1)$ parallelepipedic (rectangular) pieces of soap of dimensions $1 \times 2 \times (n + 1)$ 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.
Izvor: Međunarodna matematička olimpijada, shortlist 1978