KöMaL 2020 K673

The students in a class (we do not know how many of them there are) decided that everyone would buy some small present to everyone else for Christmas, and they would also buy some present together for each of their 11 teachers. Unfortunately, the Christmas party was cancelled. Then they decided to divide the presents equally among all the siblings of the students. (Each sibling gets the same present.) Was that possible if the total number of siblings was 15?