Here's a simple problem, illustrated simply, that will have you cocking your head and wondering how it's done. You won't be the first. Aristotle (reputedly) first took a whack at this, and Galileo gave it a try as well. See what you can make of it.

Not everyone agrees that Aristotle invented this little paradox, but everyone agrees that it would be just like him to come up with something like this. The paradox involves two different-sized wheels, one inside another. Think of the edge of your tire and the edge of the hubcap. The two rotate in sync, and they rotate over a certain distance. But should they rotate over the same distance?

If you look at the animated gif above, both wheels use their entire circumference to trace the same amount of distance - the red line. Clearly one circumference is smaller than the other. Either that means that the wheels have the same circumference, which they don't, or that different circumferences "unroll" to the same length, which they can't. (If they did, since this is true no matter how small the radius of the wheel, technically a wheel with the circumference of an inch should be able to go the same distance in one roll as a wheel with the circumference of a mile. The only thing that's keeping us from being able to drive across the country with one revolution of our tires, then, is that the tires aren't small enough.)