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

Continue reading...# combinatorics

## Inductive Tiling

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

Continue reading...## Seven Shuffles

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

Continue reading...## 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...

Continue reading...## 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...

Continue reading...## Misleading Sequence

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

Continue reading...## Four Color Theorem

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

Continue reading...## 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...

Continue reading...## Making History by Card Shuffling

Did you know that whenever you shuffle a deck of cards, it is quite likely that you are making history?...

Continue reading...## Fibonacci Number Formula

The Fibonacci numbers are generated by setting F0 = 0, F1 = 1, and then using the recursive formulaFn = Fn-1 +...

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