## How to Understand Injective Functions, Surjective Functions, and Bijective Functions

1/25/2013

### One way to think of functions

Functions are easily thought of as a way of matching up numbers from one set with numbers of
another. The function `f(x)=x+3`

, for example, is just a way of saying that I'm matching
up the number 1 with the number 4, the number 2 with the number 5, etc. A different example
would be the absolute value function which matches both -4 and +4 to the number +4. Think of
functions as matchmakers. ...

## How to solve the Impossible Escape puzzle with almost no math

2/12/2015

You and a friend are imprisoned but have a chance for freedom. To earn it, you must walk alone into a separate room where a chess board is laid out with a coin per square randomly showing heads or tails. You are shown a particular square on the chess board, and are then allowed to touch one coin to flip it. Then you must leave without making any contact with your friend. Your friend enters the room and must pick the square which was pointed out to you. You and your friend may discuss a strategy before you enter the room. ...