1. Laura has received 200 dice as a gift, of a very special type: each die has four faces with the number 2 and two faces with the number 5. Laura is about to roll all 200 dice at once, then she will sum the 200 numbers that come up. How many possible values can this sum take?
(A) 201
(B) 1000
(C) 601
(D) 600
(E) 1001
Problem 1. The answer is (A).

Let $n$ be the number of 2s that come up, the sum will be $2 n+5(200-n)=1000-3 n$, with $0 \leq n \leq 200$. Since the possible values of $n$ (from 0 to 200) are a total of 201 and since, varying $n$, the aforementioned sum varies, the possible values of this sum are indeed 201.

(Problem proposed by P. Francini)