Problem $2$

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. 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? 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.