You have a 3x3x3 cube. You bore a circular hole, of diameter 1, from the center of the top face to the center of the bottom face. You bore a similar hole from the left face center to the right face center, and another hole from front center to back center. How much material was removed?

(In reply to re(5): picture of the center by Charlie)

As a further aid for combinatorial analysis, the following link points to a picture that could be considered of those points that are in exactly 2 of the cylinders or those that are in at least 2 of the cylinders, as the set that are in all three (the picture in the Wolfram link) is completely surrounded by these:

the picture of intersections of cylinders 2 at a time

Posted by Charlie on 2005-03-07 16:41:43