The National Marriage Council wishes to invite n couples to form 17 discussion groups under the following conditions:
1. All members of a group must be of the same sex; i.e., they are either all male or all females.
2. The difference in the size of any two groups is 0 or 1.
3. All groups have at least 1 member.
4. Each person must belong to one and only one group.
Find all values of n, n <= 1996, for which this is possible. Justify your answer.