Can all but one square of an n by n chessboard be covered by L-shaped trominoes? In general, it may...
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Seven Shuffles
How many shuffles does it take to randomize a deck of cards? The answer, of course, depends on what kind...
Continue reading...Gamma Function
The Gamma function is an amazing integral: Gamma(x) = INTEGRALt=0 to infinity tx-1e-t dt . Using integration by parts, you can show...
Continue reading...Tesseract
What does a cube look like in higher dimensions? Well, we can extrapolate by looking at lower dimensions. A 0-dimensional cube is a...
Continue reading...Arclength Surprise
Consider a unit circle, and any arc S on the unit circle in the first quadrant. No matter where S is...
Continue reading...Ants on a Stick
One hundred ants are dropped on a meter stick. Each ant is traveling either to the left or the right...
Continue reading...Ham Sandwich Theorem
Here is one of my favorite theorems from topology, called the Ham Sandwich Theorem. It says: given globs of ham, bread,...
Continue reading...Pass the Beer
Suppose you and a bunch of friends are sitting around a table. There are N of you. You have a...
Continue reading...Two Envelopes Paradox
I have two envelopes, and inside each I have put some money. In fact, one envelope contains twice as much...
Continue reading...How many Primes?
Are there infinitely many primes? We’ll give a proof, due to Euclid, to show that there must be infinitely many primes....
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