Suppose that n citizens of a town wish to form as many clubs as possible under the following rules:
86067
A Variation of the even-town odd-town problem
34645
Requirements for a clan war?
50679
Induction problem: "if the group has at least one player who is better than Messi, then all the members of the group are better than Messi"
49366
Group of order 30 can't be simple
13263
A Pronominal Proposal
124354
How many entities in an area?
44620
Reference for combinatorial game theory.
51847
Showing that only $(n+1)^{n-1}$ of all the possible $n^n$ choices assure a full car park
14531
How group action works.
155654
Is starting a group with 5 newbies (DM included) possible?
62049
Conway's Game of Life, counting neighbors
74310
In how many ways can a committee of $4$ people be selected from a club of $6$ men and $9$ women?
55451
Are Quidditch teams restricted to 7 players in a squad?
72052
Combinatorics the number of options for $k$ different balls in n different cells, with at least $1$ ball in each cell
137586
A familiar limit, but in general form .
77128
Necessary and Sufficient conditions for $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.
31687
Classification of groups of order 30