In a certain class, in any distribution of 200 candies, there will be at least two students who receive the same number of candies (possibly none). What is the smallest number of students in such a class?

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Let there be no more than 20 people in the class, then we will give nothing to the first student, one candy to the second student, two candies to the third student, and so on. In this case, no more than $0+1+2+\ldots+19=$ 190 candies will be distributed. The remaining candies will be given to the student with the most candies. Thus, we have indicated a way to distribute the candies so that there are no two students with the same number of candies. Therefore, there must be more than 20 students in the class.

If there are 21 students in the class, then the minimum number of candies required for all students to receive a different number of candies is

$0+1+2+\ldots+20=210$. Since a total of 200 candies are distributed, the condition is satisfied in this case.

## Answer

21 students.