I'm asking for a help with the following problem:
With 5 people on a party, how many possibilities that in each triplet there will be both friends and strangers?
I've found that the graph's look that satisfies problem condition will be always identical (aka pentagon), and the answer will be to set all possible names for verticies of this graph with respect to neighbour's position, which will lead to 5!/5 = 24 possibilities.
Am I right? I'm not sure that this is correct, but i can't find other way to solve or prove this. Thanks.