If a class of 30 people is seated in a movie theater, then in any case, at least two classmates will end up in the same row. If the same is done with a class of 26 people, then at least three rows will be empty. How many rows are there in the hall?

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The first condition means that there are no more than 29 rows in the hall. Indeed, if the number of rows were not less than 30, then obviously, a class of 30 students could be seated with no more than one student per row. The second condition means that the number of rows in the hall is not less than 29. Indeed, if the number of rows is not more than 28, then seating the students of a class of 26 people one by one on empty rows, we will get that either at some point all the rows will be occupied, or all 26 students will be sitting on 26 rows, one per row, and in this case, no more than two rows will remain free.

Therefore, the cinema has 29 rows. Obviously, in this case, both conditions are satisfied.

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