Say you're given a set of objects, and you don't know the value of any of the objects, but, given a pair of two objects you are always told which one is bigger.
For a set $\{x_1, x_2, \cdots, x_n\}$, what is the minimum number of comparisons that will suffice to put all of its elements in ascending order of size: i.e. of the form $$\{y_1, y_2, \cdots, y_n\}$$ where $y_i\lt y_{i+1}$ for all $i$?
Obviously this is easy to determine for small $n$ (by trial and error), but as $n$ increases, I'm not sure which comparisons are redundant.