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When three professors are seated in a restaurant, the hostess asks them: “Does everyone want coffee ?” The first professor says: “I do not know.” The second professor then says: “I do not know.” Finally, the third professor says: “No, not everyone wants coffee.” The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?

Assuming, All the $3$ professors who are seated in a restaurant are the truth-tellers means they always tell the truth.

Now, Question is "Does everyone want coffee ?"

The $1^{st}$ professor says : "I don't know".

Now, Consider the cases for $1^{st}$ professor,

Case $1)$ Suppose, $1^{st}$ professor wants coffee

Since, he himself want coffee but he does not know the status about other $2$ professors whether they want or not. So, saying "I don't know" is perfectly valid when he want coffee.

Case $2)$ Suppose, $1^{st}$ professor does not want coffee

Now, when the hostess asks him "Does everyone want coffee ?" , He would say :- "No" , not "I don't know".

So, conclusion from cases (1) and (2) is :- when  $1^{st}$ professor says "I don't know", It means he wants the coffee.

Same logic is applicable for $2^{nd}$ professor. So,when  $2^{nd}$ professor says "I don't know", It means he also wants the coffee.

Now, Comes to the $3^{rd}$ professor,

He says : "No, not everyone wants coffee". Since, We already concluded that $1^{st}$ and $2^{nd}$ professors want coffee and when $3^{rd}$ professor says "No, not everyone wants coffee" , It means he is the only professor who does not want coffee.

So, Conclusion is :- $1^{st}$ and $2^{nd}$professor want coffee but not $3^{rd}$.

So, Hostess will give coffee to $1^{st}$ and $2^{nd}$ professors only.