if you wanted to paint the home with the given floor plan so that no two adjoining rooms are the same color…
if you wanted to paint the home with the given floor plan so that no two adjoining rooms are the same color, find the minimum number of colors you would need. note that you cant paint the outside. the minimum number of colors you would need if you wanted to paint the home with the given floor plan so that no two adjoining rooms are the same color would be
Answer
Explanation:
Step1: Understand graph - coloring concept
This is a graph - coloring problem. We can represent each room as a vertex of a graph, and an edge exists between two vertices if the corresponding rooms are adjacent.
Step2: Analyze the worst - case scenario
For planar graphs (and a floor - plan can be considered as a planar graph in this context), according to the four - color theorem, any planar graph can be colored with at most 4 colors such that no two adjacent vertices (rooms in our case) have the same color.
Step3: Try to find a lower number
We can start coloring the rooms. By trial and error, we find that we can color the rooms in the given floor - plan with 3 colors. For example, we can color the rooms in a pattern such that adjacent rooms have different colors.
Answer:
3