Dr. Purplesheep discovered a new class of materials, which are useful in converting solar energy to electrical energy. She has designed 25 unique materials that belong to this class, and she would like to identify the top 3 out of these 25 materials in terms of their effectiveness. Unfortunately, however, she does not have an experimental method that can be used to quantify the effectiveness of a given material. Instead, she can run comparative experiments such that each experiment provides a ranking of 5 materials in terms of their effectiveness (from most effective to least effective). Running these experiments is rather expensive, so she would like to minimize the number of experiments she runs. Required:
a. Can you help her design a strategy that will identify the 3 most effective materials among 25 materials by performing the minimum number of experiments?
b. What is the minimum number of experiments needed to conclusively determine the 3 most effective materials? You do not need to write pseudo-code; a verbal explanation, possibly supported by graphics, will suffice