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 female.
(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. combinatorics unsolvedcombinatorics