Determining last digit of power with $2015$ exponents without parenthesis

Question

This question was posted on a quiz recently, however I am unsure if there were parenthesis involved or not. The question was to determine the last digit of the number

$$ \huge 2^{3^{4^{...^{2016^{2017}}}}} $$

Any thoughts?

Answer 1

The last digit of $2^n$ is 2, 4, 8, or 6, depending on $n\bmod{4}$.

Here $n=3^{4^{\dots}}\equiv (-1)^{4^{\dots}}=1\pmod{4}$, so the answer is $2$.