Question 3.114

84. When two towns are within 145 miles of each other, the frequency used by a certain type of emergency response system for the towns requires that they be on different frequencies to avoid possible interference with each other. The following table shows the mileage distances between six towns:

120

E F G I S T
Evansville (E) 290 277 168 303 133
Ft. Wayne (F) 290 132 83 79 201
Gary (G) 277 132 153 58 164
Indianapolis (I) 168 83 153 140 71
South Bend (S) 303 79 50 140 196
Terre Haute (T) 113 201 164 71 196
  1. What would be the minimum number of frequencies that are needed for each town to have its emergency broadcasts not conflict with those of any other town using this system?
  2. How many different towns would be assigned to each frequency used?