Infinite Series

Imagine you have a square-shaped room, and inside there is an assassin and a target. And suppose that any shot that the assassin takes can ricochet off the walls of the room, just like a ball on a billiard table. Is it possible to position a finite number of security guards inside the square so that they block every possible shot from the assassin to the target?

Imagine you have four cubes, whose faces are colored red, blue, yellow, and green. Can you stack these cubes so that each color appears exactly once on each of the four sides of the stack?

Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity?

When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?

Infinities come in different sizes. There’s a whole tower of progressively larger "sizes of infinity". So what’s the right way to describe the size of the whole tower?

In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?

If Fermat had a little more room in his margin, what proof would he have written there?

In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of?

If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?

What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.

What happens when you divide things that aren’t numbers?

You know the Golden Ratio, but what is the Silver Ratio?