*Mjollnir: Let’s say I have a straw, a tube from a roll of “Bounty” paper towels, and two balls the size of basketballs made of clay.

I poke the straw thru one ball, and the paper towel tube thru the other–both perfectly thru the center.

I now have two perfect spheres with cores of different sizes cut out of them.

And the volume of the remaining clay is the same.

Huh?

That was the way I read this riddle when it appeared in the paper, that the remaining volume would be the same regardless of the diameter of the core cut out.

What am I missing?*

They’re creating confusion, wrongly making you think of the volume of just the clay and the shaped clay as the same. (Tough to explain, example at end.)

Immersing either sphere in water before and after its coring and noting the displacements would show that the volume of clay is reduced in both cases, more so in the paper-towel-tube-cored sphere.

Example: Take a letter size sheet of paper. It’s area is 8.5" x 11" = 93.5 in[sup]2[/sup]. Now cut a 1" x 1" square piece out of the middle. The sheet *as a whole* still encompasses 93.5 in[sup]2[/sup]. But the amount of paper is 92.5 in[sup]2[/sup].

If you have a link to this question (it was in a newspaper?), post it and let’s see exactly what they’re talking about.