Question 96
There are $n$ rooms in a sauna, each has unlimited capacity. At one time a room may be attended by people of the same gender (males or females). What's more, males want to share a room only with males that they don't know and females want to share a room only with females that they know. What's the biggest number $k$ such that any $k$ couples can visit the sauna at the same time, knowing that two males know each other if and only if their wives know each other?