Thirteen 1x1x2 bricks are assembled into a 3x3x3 cube with a hole in the cube. Where can this hole occur?

A 3x3 layer made of 1x1x2 bricks must necessarily have a hole in it. If we put together two consecutive 3x3 layers such that the holes are adjacent, we can place another 1x1x2 brick in it, essentially creating a full 3x3x2 solid. We then can place another 3x3 layer next to it, with the hole anywhere within the layer. As we rotate the cube, we can see that the hole can be located anywhere in any of the surfaces. In other words, anywhere except the center.

Correction-- Dej Mar is correct in that the 12 center-edges can't contain the hole either. That's because a single 3x3 layer made of 1x1x2 bricks can't have the hole in any of its center-edges.

Edited on April 18, 2007, 1:09 pm

Posted by Kurious on 2007-04-17 11:06:30