Episode 408 - “Tabu” airdate: 11/16/07
In this episode, a high-profile heiress is kidnapped by a group intent on attacking her father. Don and the team try to save her before its too late.
The math….
Cake Cutting
In the episode, the FBI negotiator mentions that he had read some of Charlie’s work on cake cutting, to which Charlie responded, “Sometimes cake is a series of algorithms and sometimes it is just cake.”
For those of us not in on the joke, here goes…
Cake cutting in the literal sense is dividing a cake fairly so that everyone gets the maximum of what they want (i.e. if someone likes more frosting, then they would get an edge piece.) Another thing about cake cutting is that the last person does not cut the cake at all, they chose their piece. A real world example of cake cutting is the Allies dividing up Germany after WWII. Because Berlin was such an important piece “of the cake,” everyone wanted it. Therefore Berlin was divided up into very unusual pieces so that everyone was happy with their piece. Click here to view a map of this.
The activity from a previous episode and web sites below allow students to explore more about cake cutting.
- Numb3rs episode #: 317 - “One Hour” - Have Your Cake And Eat It Too
- Cutting a Pie Is No Piece of Cake – Story from weekly Math Trek column
- Applying Cake cutting to resolving conflicts – Web site
Tabu Search Optimization
While Don is tracking down the kidnappers, Charlie offers to help him by using something called a “Tabu Search.” A Tabu Search speeds up any search by allowing the searchers to use their memories and past experiences, not just to rely on a brute force approach. This means that a Tabu Search excludes places they won’t go and pinpoints the optimal stops along the way that will ensure their success.
The example below uses a method of finding the quickest path between any two locations called Dijkstra’s Algorithm. For a complete description of Dijkstra’s Algorithm as well as a WAUMED activity using it refer to Driving With Dijkstra from episode # 323 “Money for Nothing”
Consider the graph to the right where the edges are certain streets in Los Angeles, the vertices A – L are street intersections and the numbers on each edge is the time required to travel between the intersections. Our kidnappers start at vertex A and need to reach vertex L.
The shortest route following Dijkstra’s algorithm results in the tree to the right. The kidnappers would follow the path A – D – E – H – K – L and have a total time of 14 to reach L from A.
However, if there were police at vertex E, the kidnapers would avoid it. The shortest route using “Tabu” with Dijkstra’s algorithm results in the tree to the right. The kidnappers would follow the path A – D – G – H – K - L and have a total time of 19 to reach L from A.
This is but a simplified example of a tabu search. Imagine a much larger graph, the size of Los Angeles, where constraints could be added such as the following:
- once the length exceeded 2 hours, gas would be needed
- one way streets
- internet connection needed by 6 p.m.
- moving police cars on the graph
The activity from a previous episode and web site below allow students to explore more about tabu searching and Dijkstra’s Algorithm.
- Numb3rs episode #: 323 Driving With Dijkstra
- A PDF of a paper written by the inventor of Tabu searches which discusses their many applications as well as some examples is located here.
Go Jayhawks!!!
Pat Flynn
November 23rd, 2007 at 10:54 am
The full episodes on NBC should be there longer.
Also activities should be availible for the episodes in season 4!!!!!!
November 24th, 2007 at 9:25 pm
I have kind of a silly question…I watched Numb3ers last night and there was a quote I liked. I can’t remember all of it, if anyone could help I’d be so grateful.
It was when the reporter was asking the blonde guy about Charlie. The blonde guy said Charlie was “…social with many, and known to few.” I can’t remember the beginning of it, and missed who the quote orginated from.
Can anyone help?
thx.
November 25th, 2007 at 9:23 pm
I have read all of the blogs from this season and take partial responsibility as I was one of the teachers who did NOT respond to the request to take your survey (and I teach Statistics!) nor did I take the time to comment on how important I find the activities to my teaching. Like many of those who have written before, I do need the activities by air date as I do not show the whole episode but just the 3 - 10 minutes that relate to the topic I wish to explain. Many of my students choose to watch on their own. Since time and what math will actually stay in the episode seem to be of concern, perhaps knowing that the teachers can wait if we know that new ideas are coming would be helpful information. As was expressed by tomlinson in an earlier post, generating new ideas for the same topic IS the hardest part of the job. It is for the classroom teacher too. I think that is part of the appeal of your site. You gave not only fabulous reasons to encourage the purchase of TI products but real application problems that we could sink our teeth into and that our students could get excited about. It is o.k. if we notice that the the basic concept for the activity is not all that different from one covered in season 1 or 2. As teachers, we will appreciate having a variety of ideas to choose from or even levels of the same activity. For example, the concepts of basic probability are covered both in middle school and AP Statistics but at much different depths. Activities that recognize this would be very beneficial. Perhaps you could think about creating a summer internship for just this type of activity writing.
November 27th, 2007 at 3:28 pm
Ben Franklin said it.