So we have spheres of various size. We have drills of various circumference, but all only 6 inches long. I'm still not getting it. How can a six inch long drill with a diameter of any size (1/2 in. or a mile) dirll completely through the earth. I'm picturing a small 1/2 hole and a larger 1 mile depression but still only 6 inches deep.

If you look at a doughnut cut through a sphere ( or a regular doughnut), it's height (when you put it on the plate) is about 5 cm.

Now the diameter of the original sphere (before the hole) is actually the diameter of the doughnut itself (the circle) maybe 15 cm!

The same with a hole through earth: The height of the doughnut cut is 6 inch, but the sphere has a much bigger diameter.

And the drill is not 6 inch long at all, the drill can actually be as long as you like but it's width (or radius) has a MAXIMUM* to be calculated in a way to leave a 6 inch doughnut in the sphere in question.

In the case of the earth, its radius has to be a small fraction less than that of the earth.

And in a 3 inch radius sphere, its width has to be 0 and the doughnut's height will then be 6 inch with no hole in the middle!

Of course with a sphere with less than 6 inch diameter, the puzzle doesn't hold.

* Why MAXIMUM? Well, the drill itself can be a regular drill with regular dimensions, but it's going to take a long time to drill through the earth and leave a 6 inch doughnut from the planet, not to mention there will be no place to stand!

**Edited by roolstar, 05 February 2008 - 10:36 AM.**