Suppose you and a bunch of friends are sitting around a table. There are N of you. You have a...
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Two Envelopes Paradox
I have two envelopes, and inside each I have put some money. In fact, one envelope contains twice as much...
Continue reading...How many Primes?
Are there infinitely many primes? We’ll give a proof, due to Euclid, to show that there must be infinitely many primes....
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...Spherical Geometry
Remember high school geometry? The sum of the angles of a planar triangle is always 180 degrees or Pi radians. However, triangles...
Continue reading...Sums of Two Squares Ways
In the Fun Fact Sums of Two Squares, we’ve seen which numbers can be written as the sum of two squares....
Continue reading...Fundamental Group
You are abducted by space aliens and dumped, blindfolded, on a strange asteroid! Removing your blindfold, you decide to play...
Continue reading...Chords of a Unit Circle
Take N equidistant points on the unit circle. Pick one of those points, then draw chords from it to all...
Continue reading...Repunit Fun
A repunit is a whole number consisting of only 1’s, such as 1, 111, or 111111111. (It’s like a repeating unit.) These numbers have...
Continue reading...Sine of (1/55555….)
Take your calculator, and enter a number consisting of several 5’s, such as 5555555. Now take the reciprocal of this number. Now take the...
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