There exists one student X in the class in which the following statement is true:
No student in the class has more hairs on his/her head than X.
We will never know who X is, but we know he/she exists.
Who is X?
I'm having trouble wrapping my head around how to narrow down the selection to one person, and how that would even be helpful for the solution since it all seems theoretical. Any help or ideas would be appreciated
On
Maybe a proof by induction will help. You wish to prove that for every class with $n$ students, there exists at least one student with at least as many hairs on their head as on any other student's.
When $n=1$, this is obvious. Suppose that the claim is true for $n=k$. You will need to show that it is also true for $n=k+1$.
I'll leave the details to you, but feel free to leave a comment if you face any difficulty. I'll also leave you with the following hint. Pick one student, and leave them out. You now have a class of $k$ students, and can now use the assumption that the claim is true for $n=k$.
Suppose there are $n$ students in the classroom. Let the number of hairs on the students be $$ h_1, h_2,...,h_n$$
This set has a maximum which we call it $h_k$ The studen number $k$ is the hairiest one.