## 23 January 2010

### A simple math puzzle

A ball 13 inches in diameter has a 5-inch hole drilled through the center. How deep is the hole?

Found at Futility Closet, where it was credited to Henry Dudeny.

1. 12 inches. Just draw a diagonal across the hole - it forms a 5/12/13 triangle.

2. relevant: http://en.wikipedia.org/wiki/Pythagorean_triple

3. It's confusing. Is the hole 5 inches DEEP, or 5 inches WIDE?

4. Andrew, since the question asks how deep the hole is, it's reasonable to assume that the depth is not provided to you.

however, i guess it could technically be a trick question. in which case, the hole is 5 inches deep and 12 inches across.

5. But the ball's diameter is 13", meaning that at the point of entry for the hole it's only 13" at the very center. Since the hole is 5" wide (2.5" each direction from that center point of 13") and heads straight downward, then the edges will have a point of intersection lower on the circle than the 13" point. The edges will also emerge from the other side of that circle before a full 13" has been measured, as well.

I am not a mathematician (you can tell because I'm not going to do the complicated calculations to figure out the true answer :-D, but that's what seems logical to me.

I suppose it's not outside the realm of possibility that I'm completely wrong, either. :-D

6. I'm not an artist, either, but I put together a quick MSPaint illustration of my point:
http://www.flickr.com/photos/17314471@N08/4300872710/

7. @kateohkatie - I think a much simpler visualization is the way I did it - draw a line from the top of the left vertical line to the bottom of the right vertical line. That's a diameter (13") and the hypotenuse of the triangle. The other side of the triangle is the width of the hole (5"), so the depth of the hole - the vertical line - forms the third side of the triangle, and must be 12".

8. Yes but essentially my point boils down to - because the circle is 13" in diameter and the hole is 5" wide, then the sides of the hole are not going to be 13" long because they're not actually intersecting the diameter of the circle, but are 2.5" off center.

9. Oh. Wait. I get it. Nevermind :-D

(I figured I was wrong somewhere in there :-P)

10. See I was thinking that the ball was made of air (the problem didn't indicate it was a solid ball) so I thought well if you put any size whole into, say, a basketball, it would deflate and it's depth would be zero.

11. the depth of the hole is the distance from one end of the hole to the nearest object, measured by a line segment oriented parallel to the hole's length, through the hole. The length of the hole's wall is 12 inches. If you were to look at the sun through the hole, it's depth would be somewhere in the neighborhood of 93 million miles.

12. the answer is 12. Stop being nerds and move out of your parents basement.