Thanks to Anirudh Baddepudi for contributing this puzzle. I also do not know the answer yet and hence looking forward to enjoying this one.
At a party, seven people know seven others, and the remaining people each know 5 other people who are at the party. Knowing is mutual, so if person A knows person B, then person B knows person A as well. From this information, what is the smallest number of people that could have been at the party?