If you had a wire as long as the circumference of the Earth and added just ten meters to it it would float 1.6 meters off the ground everywhere.
If you could fold a piece of paper 42 times you would reach the moon and beyond.
If you have 23 people in a room there's a 50% chance that two of them share a birthday. If you have 50 people in a room there's a 97% chance that two of them share a birthday.
(1/2)+(1/4)+(1/8)+(1/16)+(1/32)+...=1
An infinite surface area can enclose a finite volume.
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" It is to your advantage to switch your choice.
10! seconds is exactly six weeks.
If you properly shuffle a deck of cards, chances are the order in that deck has never been seen before.
Given a solid ball in 3dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. This is known as the BanachTarski paradox.
