Tom and $$8$$ of his friends went to Mr Tan\textquotesingle s house to play. Mr Tan gave each of them a hat with a two-digit number on it. All $$9$$ numbers are different and the students are able to see their friends\textquotesingle{} numbers but not their own. Mr Tan wrote a number on a slip of paper and ask the $$9$$ students: "Those of you that knows for certain that your number \textbf{is divisible} or \textbf{not divisible} by this number, please raise your hands." $$4$$ students raised their hands. Mr Tan then asked again:" Those of you that knows for certain that your number \textbf{is divisible} or \textbf{not divisible} by $24$, please raise your hands." $$6$$ students raised their hands. Tom raised his hands in both rounds and in addition to that, all students are smart and would not lie. What is the sum of all $$8$$ numbers that Tom saw on his friends\textquotesingle{} hat? 
Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering