Given a list of positive integers a, b, c, ... z, you can calculate the superpower a^b^c^...^z. [Note that this is a^(b^(c^(...(y^z)...))).]
What's the largest/least superpower value you can get with the list 2, 3, 4, ... n?
Based on the idea that you make a number much larger when you use it as an exponent over a small number rather than use it as a base raised to a small number (i.e., 1.01^1000 > 1000^1.01), it would seem to follow that you want to arrange the numbers from smallest as the ultimate base to largest as the ultimate exponent. However, this may fail at the final (highest power-ed) step, so a manual check should be made (e.g. in the case of 2 and 3, 3^2>2^3 wich breaks the above general rule). This works for the few, small number, small sets that I tested with; expanding beyond these trials and proofs are beyond my abilities.
Intuitive guess
