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Marriage Council

[ Sunday, 11 October, 2009 ]

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.

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