Question 4
The National Marriage Council wishes to invite $n$ couples to form $17$ discussion groups under these conditions:
1. Each group consists entirely of males or entirely of females.
2. The sizes of any two groups differ by $0$ or $1$.
3. Every group has at least one member.
4. Each person belongs to exactly one group.
Find and justify all values of $n\le1996$ for which this is possible.
1. Each group consists entirely of males or entirely of females.
2. The sizes of any two groups differ by $0$ or $1$.
3. Every group has at least one member.
4. Each person belongs to exactly one group.
Find and justify all values of $n\le1996$ for which this is possible.