Question 117
Let $n \ge 2$ be a natural number. Laura's mathematics teacher likes group exercises. In Laura's class the teacher composed new groups in every lesson of statistics. When all of the statistics curriculum had been covered, it appeared that every two different students had belonged together into exactly one group and every two different groups had contained exactly one student in common. On the day when correlation was studied there were precisely $n$ students besides Laura in her group. How many students were in Laura's class if their number was larger than $n + 2$?