Phone Tag (Solution)

by David Roe, Dimah Eroshkin, John Stumpo

The first thing to note is that the last names of the salesmen are names of American cities. Moreover, the extension listed in the voice mail message is the area code of the corresponding city.

Each directory gives an unordered list of other salesmen and an unordered list of area codes. Note that dialing the extension while in the directory does not take you to the person that's supposed to correspond to that mailbox. Instead, these directories reveal two parallel graphs on the same set of vertices. One graph corresponds to the names of cities, the other to their area codes.

Wagner and Willy L are clues to Arthur Miller's Death of a Salesman, which suggests looking at the traveling salesman problem on these two graphs. Solving the traveling salesman problem with the graph defined by the city names in the directory yields the path suggested in the voice mail messages. Solving it with the other graph (area codes), yields another path. Dialing through the phone tree along this path reaches a live person, who gives you the answer.

Secret graph solution:

```McAllen, TX
Lincoln, NE
Hampton, VA
Montgomery, AL
Flint, MI
Stamford, CT
Norman, OK
Yonkers, NY
Memphis, TN
Pomona, CA
Irvine, CA
Corona, CA
Eugene, OR
Stockton, CA
Hayward, CA
Chandler, AZ
Fargo, ND
Billings, MT
Buffalo, NY
McAllen TX
```

Total distance: 25872.5 km

Following the path either forwards or backwards leads to the answer, RIOT on the step before last.