23 April 2021

The Magic of the Pigeonhole Principle

Some of the best magic tricks are the ones that seem impossible, but involve the application of mathematical principles, they can reliably deliver a seemingly impossible outcome.

The following video from Mathologer involves much longer exploration of seven examples involving the pigeonhole principle in action, but we've cued it up to feature a card trick where the key to getting the magic to work involves understanding how the randomly selected cards can be ordered to encode a secret message from the magician's assistant to the magician about what card an audience member has selected:

The trick works in part because of the pigeonhole principle, which will seem blindingly obvious once it's pointed out. This second video does that in a little over 30 seconds, but continues for about another eight minutes to present examples of how it can be practically applied:

And that's how you get from a parlor magic trick to the kind of modern lossless data compression we use every day to more efficiently communicate large amounts of data across computer networks!