You have two spheres of different size — say, an apple and a grapefruit. (A proton and a planet will do.) You are going to core each of these fruits. The shape that remains from each sphere is what we will call the napkin ring.
Suppose we have a product of functions, uvw. Each component — u, v and w — changes with some additional variable, time, t. How will an incremental increase in time, dt, affect our product?
Imagine your original function, uvw, as a u × v × w box:
“You’ll have to leave a small deposit,” said the shopkeeper. “For security.”
I had just scribbled my mark at the foot of a three-page document, set in 6-point Courier Bold.
I set aside the stylus and met the shopkeeper’s eye. I must have looked worried. He smiled. …
The University of Toronto has posted this page and a half of brain teasers. How many can you solve?
Here’s the first:
Show that n⁷ − n is divisible by 42 for every positive integer n.
First, factor the polynomial.
I once designed a video game for a friend of mine. It featured him running back and forth, Donkey-Kong style, striking objects with the smoke from his pipe. My friend loved the game. But he missed the Easter Egg.
I had included with the game some awkwardly-written documentation. It was…