The remainder when 6666..∞ is divided by 10 is :

Answer: Option B

$$\begin{array}{rl}& \text{Since},\\ & \frac{6}{10}\to \text{remainder}\text{is}\text{6}\\ & \frac{6^6}{10}\to \text{remainder}\text{is}\text{6}\\ & \frac{6^{6^6}}{10}\to \text{remainder}\text{is}\text{6}\\ & \frac{6^{6^{6^6}}}{10}\to \text{remainder}\text{is}\text{6}\\ & \frac{6^{6^{6^{6^6}}}}{10}\to \text{remainder}\text{is}\text{6}\text{and}\text{so}\text{on}.\\ & \\ & \text{Thus,}\text{in}\text{all}\text{the}\text{such}\text{cases}\\ & \text{The}\text{remainder}\text{will}\text{always}\text{be}6\end{array}$$