A magic square is an NxN matrix in which every row, column, and diagonal add up to the same number....
Continue reading...combinatorics
Euler Characteristic
Take out a sheet of paper. Pop quiz! (just kidding). Draw any number of dots on your page. Now connect...
Continue reading...Matching Problem
Suppose I return N homeworks randomly to my N students. What is the chance that no student gets back her...
Continue reading...Toggling Light Switches
Imagine 100 light bulbs with light switches numbered 1 through 100, all in a row, all off. Suppose you do...
Continue reading...Leapfrog Addition
Here’s a nice mathematical magic trick based on properties of the Fibonacci sequence. Give your friend a card with ten blank lines, numbered 1...
Continue reading...Proofs without Words
There are many facts which can be proved just by looking at a picture! For instance:x2 – y2 = (x+y) (x-y)is illustrated...
Continue reading...Pascal’s Triangle
Consider the triangle in Figure 1, called Pascal’s triangle. It consists of numbers where each entry is the sum of the...
Continue reading...Pigeonhole Principle
Here’s a challenging problem with a surprisingly easy answer: can you show that for any 5 points placed on a sphere,...
Continue reading...