The Touching Cubes Problem
How can you arrange a set of identical cubes so that as many as possible touch a single cube in the center? For cubes to be considered "touching" they must share some finite area face to face; they are not considered "touching" if they only meet at a corner or an edge.
Hint: This problem has several "pretty good" solutions, one "very good" solution, and one (hard to find!) "best" solution.