Complicated Powers

Notice that the last digit of $a^{4k+1} (a,k\in \mathbb{N})$ is always the last digit of $a$ . Using this simple trick, we have:

$Q=2222^{7777}+3333^{7777}+4444^{7777}$

$Q=2222^{4\times 1944+1}+3333^{4\times 1944+1}+4444^{4\times 1944+1}$

$Q=...2+...3+...4$

$Q=...9$

So the last digit of $Q$ is $\boxed{9}$