Posted 19 October 2011 - 12:04 AM

Hello, thank you for the awesome puzzle! Now, having read a lot of the discussion, I have come to think that there are actually 3 answers possible:

1,2) If the length of the hole is equal to the diameter of the sphere (6 inch hole, 6 inch diameter sphere) then the answer is either 36pi or 0. That is because in order to drill such a hole in such a sphere the diameter of the drill must be either 0 inches or 6 inches (again must think about the length of the INSIDE of the sphere after the hole's been drilled out. Like standing inside the hole - if there's anything visible left, then the hole is less than 6 inches).

So, if the diameter of the drill is 0 inches, the remaining volume of the sphere equals to the original volume of the sphere (36pi), as nothing was drilled away. If the diameter of the drill is 6 inches, the sphere is, of course, completely drilled away with nothing left, so you can only imagine the hole, and the volume is thus 0.

3) If the length of the hole is smaller than the diameter of the sphere (6 inch hole, 7 inch diameter sphere) then the answer is impossible to figure out logically, without computing it. And if the problem would have no answer that is possible to figure out logically, thus it would have no answer at all, given it is a logic puzzle.

So actually, there's three answers to this problem, given the aforementioned reasoning - 36pi, 0 and No Answer.

Please, correct me if my reasoning somewhere is wrong.

p.s. Actually, while writing this post I have lost my line of thinking several times, and rewrote it accordingly =p This is the final version that I can finally read without getting confused myself... Made my night *sleepy*.