We Like ... But We Don't Like ... Game
Someone starts by thinking of a rule to follow, such as [We like everything that does not start with the letter 'S'].
Then, he says "We Like Winter but we don't like Summer."
"We like Mindy but we don't like Suzy."
"We like Acting but we don't like Skits."
He keeps coming up with more statements until someone wants to come up with a statement they believe follows the rule. If the statement is correct, the leader tells them it is and they can continue to come up with more.
It's possible that they were just lucky or are thinking of a different rule, so the leader has to verify every statement made by others.
When everyone has guessed the rule or has given up, have a new leader do a round with a different rule.