# combinatorics

## Domino and Square Tilings

How many ways can you tile a (1 x n) board with (1 x 1) squares and (1 x 2)...

## Inductive Tiling

Can all but one square of an n by n chessboard be covered by L-shaped trominoes? In general, it may...

## Seven Shuffles

How many shuffles does it take to randomize a deck of cards? The answer, of course, depends on what kind...

## Sperner’s Lemma

Divide a triangle T into lots of baby triangles, so that baby triangles only meet at a common edge or a common...

## Rising Sequences in Card Shuffling

In Seven Shuffles we saw that it takes about 7 random riffle shuffles to randomize a deck of 52 cards. This means...

Place n points along a unit circle, in such a way that when you draw all lines connecting every pair of...

## Four Color Theorem

Are four colors always enough to color any map so that no two countries that share a border (in more...

## Six Degrees of Separation

The word graph has two different meanings in mathematics. One involves plotting the domain and range of a function, and another is...