How many different channels are needed for six television stations (A, B, C, D, E, F) whose distances?

Question

(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?
50, 85, 100, 125, 175, 200, 210, 220, 250

Answer 1

This is really hard to answer without the table. You have nine distances, which means that some of the stations show multiple distances from each other.

I'll answer as best I can.

If the stations are all in a straight line, then the answer is pretty easy. Start with one channel at the first station, a second channel at the second station, third, fourth, and when you get to the sixth station, 175 miles away from the first station, you can re-use that channel, because it is over 150 miles away. The next station must use a new channel because it is 200-50 = 150 miles away from the second station, and that is too close. The station after that can re-use the second station's channel.

However, I have a feeling that these stations are not laid out in a straight line, but are scattered hither and yon. In that case, start with one edge and put different stations in the ones closest to it.

Without seeing the diagram, you're on your own, and mostly it's going to be trial and error: "Will this work? No, drat it!"
If it's any consolation, this is part of a class of problems related to the four color map problem that was not solved until the mid-1980's, and required computers.