Start with 27 small cubes. Now put them together to make one larger cube. Without touching the sides of the larger cube, remove the cube in the middle to leave 26.

(Note: No one may touch the outer cubes or in any way do anything that would move or change them)

First, I assume the 27 small cubes will need to be the same size, but not necessarily identical.

What if I had 26 wooden cubes, 1 inch on a side, and 1 cube of ice, 1 inch on a side? Then I could place 9 wooden cubes on a table, 8 wooden cubes plus the ice cube on the next layer (with the ice in the middle), and 9 more wooden cubes on top of that.

Then I just sit and wait. Since the cubes are not perfect, there will be some gaps between them and the water can come dribbling out onto the table. You only said I couldn't move or change the OUTER cubes.

Hmmmm, but then the top cube would fall down on its own. Does that violate the problem?

Isn't there something you can do to a sugar cube to make it mostly gone, but the outer surfaces of the structure are still there. That would allow the top cube to be supported while MOST of the middle cube was removed.

My only last thought is a variation on the ice cube. If the ice cube were made around a wire frame that would stay behind and support the top cube after the melting occurred. Of course, this still means that only MOST of the cube was removed.

I wonder if I'm even close to the right track =)

Later!

Posted by nikki on 2003-10-24 16:20:51