Take six identical cubes and place them on the table in such a way that each cube touches each of the other five cubes with some part of its side (touching only along edges or at corners doesn't count).
Here is what I did, though there is probably more than one solution.
I separated the cubes into two groups of 3. Then I took two cubes from each group and placed them side by side (EastWest), sharing a complete face. Then I took the third cube from each group, and placed on the North side of the other two, so that the third cube shared half a face with one and half a face with the other. I have basically constructed a cube pyramid, if you look at the top view.
From here on out, I will call the West cube Left, the East cube Right, and the North cube Top, even when I rotate them around (and Top isn’t actually on top anymore).
Now, since my two "pyramids" are oriented the same way, what I will do is rotate one of them 135 degrees clockwise. I will call this one the Rotated pyramid, and the other the Original pyramid.
I will pick up my Rotated pyramid, and place it on top of the Original pyramid. Next, I’ll line up the center of the Top cube on the Rotated pyramid with the center of the Right cube on the Original pyramid.
Now, every cube touches the others along a portion of a face.

Posted by nikki
on 20040811 15:09:19 