### Discrete Mathematics Problem - Grouping Students

Source: Sent to me by Vinayak Gagrani (CSE IITB Alumnus 2013) Problem: There are 289 students. We have to divide them into 17 groups of 17 each every day. The groups have to be such that no two students who have been previously on some group together can be formed a group again. How many days can we do this ? Extension: Can this be generalized for any N^2 students?