I have a counting problem for work that we've been trying to solve for a bit now, and have finally come here for help. Here is the problem:
Given 100 people, split the 100 people into groups of 4. Now we have 25 groups of 4 people. The question is, how many times can the 100 people be split into 25 groups of 4 so that no one is in a group with the same person twice?
Ideally, we are looking for a general solution to the problem. We have worked out a couple of smaller versions by hand. For instance, for 16 people split into groups of 4, the groups can be made 3 three times.