Question 11
What are the last 5 digits of the sum
$$3+33+333+\cdots+\underbrace{333\cdots333}_{2005\text{ digits}}\,?$$
$$3+33+333+\cdots+\underbrace{333\cdots333}_{2005\text{ digits}}\,?$$
IMSO Maths · IMSO 2005 Mathematics Contest in Taiwan – Short Answer