I did this in my head and multiplied two numbers with a calculator to get 184 = 8 x 23.
At a party, everybody is friend with exactly 22 of the other persons present.
1) The way I thought it out was if there were 23 people at the party then each person would be friends with the other 22.
Whenever two persons are friends, they do not have any friends in common.
2) There could be n groupings of 23
Whenever two persons are not friends, they have exactly six friends (present at the party) in common.
3) Which tells me there can be a minimum of 8 groupings. (2 groupings contain the two non-friends, the other 6 groupings contain the 6 common friends from Person from Group1 and Person from Group2.
Here's a picture, imagine each black circle contains 23 dots.
Red dots signify the two non-friends.
Green dots signify the common friends of each of the red dots.