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 +...
Continue reading...