1. 50 students from fifth to ninth grade published a total of 60 photos on Instagram, each not less than one. All students of the same grade (same parallel) published an equal number of photos, while students of different grades (different parallels) published a different number. How many students published only one photo?
Solution. Let each of the students publish one photo first, during which 50 photos out of 60 will be published. There are 10 photos left to be published, which we will call additional photos. We have a total of five different classes (parallels), and these 10 additional photos must be published by different students from different classes, and in different quantities. It remains to note that $1+2+3+4=10$, i.e., one additional photo can be published by only one student from some class, two additional photos by another student from another class, and so on, a total of four students from four different classes. Therefore, 46 students from some class (parallel) published one photo each, and four students from the other four classes published the remaining 14 photos, one published two, one published three, one published four, and one published five.

Answer. 46 students published one photo each.