1. Camilla is very patient and is writing out, in full, the entire number $1000^{1000}$. How many digits does she have to write in total?
(A) 1000
(B) 3001
(C) 1000001
(D) 1001
(E) 1004
Problem 1. The answer is (B).

The number $1000^{1000}$ is equal to $\left(10^{3}\right)^{1000}=10^{3000}$, which is written as 1 followed by 3000 zeros. The total number of digits is therefore 3001.

(Problem proposed by P. Francini)