The scene is social, but the problem has a more rigid structure than it seems. It is worth asking what restrictions the distribution of squeezes actually imposes before answering.
The squeeze party
Riddle statement
At a party there are \(n\) people, with \(n\ge2\).
Each person writes down how many handshakes they gave during the party.
Is it possible that the \(n\) numbers recorded are all different?