I drew a circle with "dist=1" next to it, then put two little hash marks on the circle, one at six o'clock, and another little farther on in the clockwise direction. Then I wrote a couple of equations involving r1, r2, t1 and t2, and crossed them out. Then the phone rang, I came back to the paper, and wrote the same equations again (not noticing that they essentially identical to what I had before). Then I drew a little arc of a circle going counterclockwise around the circle and somehow got the idea that I had the right equations, although I wasn't sure. Then I decided to solve the equations even though I wasn't sure they were correct. Then I got the answer and spent another minute making sure it was correct, scribbling another circle and a few more r1's and r2's. I can't imagine myself being successful trying to do this problem without drawing the circle, even though it's useless in some sense --- it's just a circle On 8/6/07, Eric Angelini <Eric.Angelini@kntv.be> wrote:
it's the kind of thing that throws people because it sounds like there's not enough information.
Old Boniface he took his cheer, Then he bored a hole through a solid sphere, Clear through the center, straight and strong, And the hole was just six inches long.
Now tell me, when the end was gained, What volume in the sphere remained? Sounds like I haven't told enough, But I have, and the answer isn't tough!
----
There also is a meta-theoretic answer to this puzzle. Assume the puzzle can be solved. Then it must be solvable with a hole of any diameter, even zero. But if you drill a hole of zero diameter that is six inches long, you leave behind the volume of a six inch diameter sphere.
http://www.faqs.org/faqs/puzzles/archive/geometry/part1/
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