3 ms·

I remember reading and solving this the problem as the end of the article (“A six inch high cylindrical hole is drilled through the center of a sphere. How much

I remember reading and solving this the problem as the end of the article (“A six inch high cylindrical hole is drilled through the center of a sphere. How much volume is left in the sphere?”) as a kid. I did it the hard way using the formula's, but the whole point of the puzzle was what this article called the "cheat" answer. It reduces the solution to utter simplicity by application of some elegant logic. It's not something of a cheat -- it's the whole point of the puzzle. I really was a kid. I was taken in by Gardner's April 1st column that claimed among other things that a proven solution for "Chess" indicated that white would always win and that the opening move was P-KR4 (h4 in modern notation).

sparky_z 12y ago
It only wouldn't be a cheat if the question were framed as "Surprisingly, the volume of the ring is constant, regardless of the radii of the sphere and circle. What is that constant volume?" Otherwise, you don't really know your answer is correct. Maybe, they wanted the answer in terms of R1 and R2. And if you are able to trick them into confirming it, then you're essentially using social engineering to leverage somebody else's work (the person who discovered the surprising result) in formulating your answer. There's no way that the original discoverer could have used that method. That's what makes it a cheat. Back in middle school geometry, I came up with my own strategy for proving theorems. "You wouldn't ask me to prove it if it weren't true, therefore it must be true. Q.E.D." It didn't go over well.
- eru 12y ago
  That's why in Uni they usually asked: prove this statement right or wrong (or undecidable).