Find the remainder when \[6^{\underbrace{66\cdots6}_{100 \text{ times}}}\] is divided by 10.
8
For any positive integer exponent $k\ge1$, the last digit of $6^k$ is always $6$. Therefore $6^{\text{(any positive integer)}}\equiv 6\pmod{10}$, regardless of how large the exponent is (here it's the 100-digit number consisting only of sixes). Hence the remainder upon division by $10$ is $\boxed{6}$.
Find the missing code:
L1#1O2~2, J2#2Q3~3, _______, F4#4U5~5, D5#5W6~6