How Many Different Channels Are Needed for Six Television Stations

Essay

How many different channels are needed for six television stations (A, B, C, D, E, F ) whose distances (in miles) from each other are shown in the following table? Assume that two stations cannot use the same channel when they are within 150 miles of each other? $$\begin{array} { c c c c c c c } & A & B & C & D & E & F \\A & - & 85 & 175 & 100 & 50 & 100 \\B & 85 & - & 125 & 175 & 100 & 130 \\C & 175 & 125 & - & 100 & 200 & 250 \\D & 100 & 175 & 100 & - & 210 & 220 \\E & 50 & 100 & 200 & 210 & - & 100 \\F & 100 & 130 & 250 & 220 & 100 & -\end{array}$$