Probability 🎲

Intersections of chords of a circle

The picture above shows a regular polygon with 15 vertices, including all the diagonals between the 15 vertices, and all the intersections between the…

Jun 4 •

Anti-inductive dice

David and Goliath each have a six-sided die.

Apr 28 •

Random coprime numbers

Two integers are called coprime, or relatively prime, if they have no factors in common other than 1.

Mar 14 •

Chess and the number e

The number e=2.718281828459045… is one of the most famous irrational numbers.

Dec 16, 2024 •

Chutes, ladders, and Markov chains

The classic board game of Snakes and Ladders (or Chutes and Ladders) originated almost 2000 years ago in India, where it is known as Moksha Patam (see…

Dec 4, 2024 •

Solving a maze with two exits

Given a maze based on a square grid with an entrance at A and two exits at B and C, is there a navigational strategy that guarantees a 50% probability…

Aug 19, 2024 •

The infinite monkey theorem

The infinite monkey theorem is the observation that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will…

Mar 11, 2024 •

Benford’s Law

Benford’s law is the observation that in many real life sets of numerical data, the leading digit is likely to be small, and is equal to 1 about 30% of…

Sep 7, 2023 •

Loaded dice and unfair polynomials

If you throw a pair of fair dice, you are six times more likely to throw a total of 7 than a total of 12. This is because the only way to throw a 12 is…

Jul 19, 2023 •

The best denominations for coins

What is the best way to give change so as to minimize the number of coins used? The obvious way to do this using the widely used coins in the US (25…

Jul 7, 2023 •

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