How Many Different Channels Are Needed for Six Television Stations

question 35

Short Answer

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? $$\begin{array} { c c c c c c c } & A & B & C & D & E & F \\A & - & 85 & 175 & 100 & 50 & 100 \\B & 85 & - & 125 & 175 & 100 & 130 \\C & 175 & 125 & - & 100 & 200 & 250 \\D & 100 & 175 & 100 & - & 210 & 220 \\E & 50 & 100 & 200 & 210 & - & 100 \\F & 100 & 130 & 250 & 220 & 100 & -\end{array}$$

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Definitions:

Celiac Plexus

A complex network of nerves located in the abdomen, sometimes referred to as the solar plexus, playing a key role in innervating many of the abdominal and pelvic organs.

Sympathetic Neurons

Nerve cells that are part of the sympathetic nervous system and involved in the body's involuntary responses to stress.

Propulsion

The act of driving or pushing forward, in biological contexts often referring to the movement of food through the digestive system.

Segmentation

The division of some animals and embryos into a series of repetitive segments, or a process of dividing data or objects into parts for analysis.