Episode list

If you're comfortable with percentages maybe you shouldn't be. Percentages can be counter intuitive as this puzzler demonstrates.

Most people think of paradoxes as unanswerable, contradictory questions deliberately designed to confuse you for no good reason. But they're actually a lot more complex than that; some paradoxes can be answered even if they seem impossible, and others are obviously wrong... but it may take thousands of years of human experience and the invention of calculus to prove why. Join Kevin, some action figures, three envelopes and a whole lot of whiteboard doodles as you discover the three types of paradoxes: Veridical, Falsidical and Antinomy, and why each one plays a unique role in how we process the world around us -- including finally learning how there's a mathematical explanation for why you should always switch doors in Monty Hall's classic game show.

Here are a couple games you can use to frustrate your friends by always winning. But to be sure you'll want to go first.

We're all familiar with standard pizza slices - one center slice and two 45-degree cuts and you're ready to party with 6 perfect slices. Throw in another cut and you've got 8. But what if I told you that you can cut a pizza anywhere on its surface -- not just across its diameter -- and get a perfectly fair, shareable pizza for two people by assigning alternating slices? Prepare to witness the most delicious, unexpected presentation of mathematical beauty: a proof without words. And bring napkins.

Here's a game where every chose is yours but is rigged to draw you into to making larger and larger losing decisions.

The Martingale Betting system claims that by doubling your wager after each loss, no matter how many times they lose in a row, a gambler is guaranteed to eventually win big. It's considered foolproof, and mathematically it is... until it isn't. With the aid of a faithful blackjack-dealing robot friend, Kevin puts this 18th-century France gambling strategy to the test. How does expected value play a role? What about exponential growth? Here's the real question: Does it actually work!?

An ant is placed on one end of a rubber rope and he begins walking at about 5cm per second. As he's walking, the rope gets stretched... and stretched... at a rate of 10cm per second. The rope is getting stretched faster and longer relative to the ant's consistent walking pace. Can the ant ever get to the end of the rope? Is he caught in an endless, impossible trek in which the end keeps getting further and further away? This classic paradox has very real implications to how we understand our position in a rapidly-expanding universe.

How many people need to be in a room before there's a 50% chance that two of them share the same birthday? Is it about 180, since that's around half of 365? Is it only 100? The real answer is surprisingly much, much smaller. If you have just 23 people in a room, the odds of whether two get presents on the same day is a coin flip. Get 50 people together and that shared-birthday probability skyrockets to 97%. A handful more and it's a virtual statistical certainty. Really? Yes, really. With the aid of tiny plastic babies and some mathematics, Kevin proves and visualizes this surprising veridical paradox.

Kevin explores the math and mystery behind a classic riddle that just... doesn't make sense. Three friends go out to lunch and split a $30 bill evenly. Each pays ten bucks. Then the waitress realizes the bill should've been only $25. She gives the busboy a $5 refund, but he can't figure out how to evenly divide five dollars three ways. The customers don't even know they've been overcharged, so he just takes a $2 tip for himself and hands the three customers one dollar each. If the customers only paid $9 each for lunch and the busboy pocketed $2, where is the missing dollar?!?