Location of Services The Division of Motor Wyoming (DMV) in Wyoming operates several offices around the state. Citizens must travel to one of these offices to register a car, obtain a title, renew an operator's license, and perform a number of other minor activities. However, it is expensive for the DMV to operate a large number of offices, so the DMV has been keeping some offices open only three days per week and closing down other offices entirely in an attempt to reduce expenses. Recently, the suggestion was made to have one mobile DMV office which would operate out of a trailer and appear in a different location each day. The question then became: How much coverage could the mobile design provide? A possible standard was proposed: Locate the mobile office so that at least once a week, residents of the state could go to the DMV in their own county, or in a neighboring county.
1. Is it possible to locate the mobile office in such a way that for any county, the office will either locate in that county or locate in a neighboring county at least once per (5-day) week? If so, which counties should host the office for a day? If not, what is the minimum number of days required to provide all residents access within their county or a neighboring county?