51 rooms will suffice for any 100 people. Here's why: First of all regardless of how many couples there are, there will always be an even number of people besides the couples to accommodate. That's because there will always be an even number of people contained in the couples. 100 people minus any even number will leave an even number of people. It's easy to see that if there are an even number of single men and an even number of single women, that only 50 rooms will be needed, regardless of the number of couples. However, if there are an odd number of single men and an odd number of single women, then there needs to be a 51st room. That's because when all the single men have been paired up in rooms, and all the single women have been paired up in rooms, 49 of the rooms will be filled. There will be one single man and one single women left over. They can't share the 50th room, so there must be a 51st room, so that the extra man can be alone in the 50th room and the extra single woman alone in the 51st room (or vice versa). Edwin