Mr. and Mrs. Freeze live in Twotown. This is a great town except that you can't get ice cream anywhere in the town. The Freezes, being entrepreneurial, have decided to change this. They are going to build ice cream stands all over town so that people can buy ice cream. They decide that an ice cream stand on every corner would be convenient, but too expensive. They decide to build stands so that every person in town would find an ice cream stand either on the corner where they live, or at the very most, only one street away, so that they would only have to walk down one street to find an ice cream stand on the corner. On the map of Twotown, place ice cream stands so that a minimum number of ice cream stands are built and no one has to walk further than one street away to get ice cream.

How do you know if you have found the best answer? What method did you use to find an answer? If you succeed, do the same thing for Puzzletown, so that the Freezes can sell franchises and retire. (From This is Mega Mathematics, by Mike Fellows and Nancy Casey.)