APMO 1996 Problem 4

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 $n$ , $n \leq 1996$ , for which this is possible. Justify your answer.