- Art Gallery Problem - Season 2, Episode 3, Obsession. 9:05 - 9:20. This is unfortunately a very short clip that doesn't really give a statement of the problem.
- Dijkstra's Shortest Path Algorithm - Season 3, Episode 23, Money for Nothing. 9:20 - 10:10. This gives a nice description of greedy algorithms in general (via the change algorithm, though without David E's more detailed comments) and an overview of Dijkstra's algorithm.
- Knapsack Problem - Season 3, Episode 24, The Janus List. 18:30 - 19:00. This clip gives a nice and mostly compete description of the problem in the context of "things you would bring on a hiking trip" based on weight and their importance.
- P vs. NP - Season 1, Episode 2, Uncertainty Principle. 18:30 - 19:00. The P =? NP problem is a theme running throughout this episode... but unfortunately there's no nice clip that summarizes the problem, just lots of shots of Charlie working hard and a mention of the Minesweeper Consistency Problem. The specific times I mention are as close as I could find to a useful clip for teaching purposes.
- Monty Hall Problem - This is a clip that's actually on YouTube, so I'll let whoever posted it take the blame for the copyright issues and just give a link.
- The Seven Bridges of Konigsberg - Season 2, Episode 9, Toxin. 24:30 - 25:20. If you imagine that this problem would look beautiful if well-animated and described, you're right.
- Voronoi Diagrams - Season 2, Episode 10, Bones of Contention. 29:45 - 30:25. A description of Voronoi diagrams in terms of "the closest place to find a cheeseburger."
I've been thoroughly enjoying watching these clips in class, and I think my students have too. Perhaps this will become a running series as/if I find more. If you know of any additional clips, from Numb3rs or elsewhere, please leave them in the comments.