Explore all Real Numbers videos
Episode 1: Probability
The Perils of Dogsitting
In this first episode we present a warm-up probability problem about dogsitting a rambunctious poodle, and review the...
Episode 2: Probability
Always Take the Middle Taxi
The problem of the week in this episode involves the probability of a certain arrangement of random cars at a traffic...
Episode 3: Probability
A Perfectly Balanced War
In this episode, we ask you to compute the probability of losing an Ace when playing a turn of the card game War, and...
Episode 4: Probability
Passing Your Driver's Test
At the DMV, there are test takers who study, and there are those who pass. This episode’s problem investigates the re...
Episode 5: Probability
Grandma's Secret College Fund
A second Bayes’ Theorem problem is presented in this episode, as we sample a random bill from a piggy bank and try to...
Episode 6: Geometry
The Perfect Snow Cone
This episode kicks off a sequence of geometry problems, here we are figuring out the optimal dimensions of a snow con...
Episode 7: Geometry
Efficient Reshaping of a Snowball Into a Snow Cone
In this episode we continue with snow cone related calculations, with a bonus problem to use integration to compute t...
Episode 8: Geometry
Crossing the River
For your toy boat Wavey to cross the river, it must fight the current using its motor: where should you aim it?
Episode 9: Geometry
Crossing the River 2: Wavey's Revenge
We continue charting courses for Wavey at the riverbank, solving the previous episode’s navigation puzzle and posing ...
Episode 10: Geometry
The Art Thief at the Window
The problem of the week is to figure out which paintings will slide through an oddly-shaped window, the security of t...
Episode 11: Expected Value
The Unknown Monster
In this episode we define Expected Value and offer an introductory puzzle to the concept, along with bonus problem, a...
Episode 12: Expected Value
Photographing the Chaotic Marching Band
To get the perfect photo of the marching band, the rows have to be in-step, but are choosing their starting foot at r...
Episode 13: Expected Value
How Many Snowboards Need Sharpening?
Rachel has six snowboards, one of which gets chosen for each day. How many distinct snowboards did she expect to use?...
Episode 14: Expected Value
Finals Week
Jayden is preparing for finals week, and wants to know how much time can he expect between his two finals. Can you he...
Episode 15: Expected Value
The Half-Court Shot
We solve the problem of the expected time between Jayden’s two finals, and present the last problem of the first seas...
Episode 16: Expected Value
Finale
We finish off the season with a flurry of solutions to the problem of the number of half-court attempts required to m...