At a gathering, invitees arrived, including Mr. Balogh. Besides them, there is a journalist who wants to talk to Mr. Balogh. The journalist knows that no one knows Mr. Balogh, but Mr. Balogh knows everyone. The journalist can approach any of the invitees and ask if they know any other person.
a) Can the journalist definitely find Mr. Balogh with fewer than questions?
b) How many questions does the journalist need to find Mr. Balogh if they are lucky?
The journalist, pointing to someone (let's call this person ), asks another person () if they know them. If the answer is YES, then cannot be Mr. Balogh, as no one knows him. If the answer is NO, then cannot be Mr. Balogh, as he knows everyone. Therefore, with each question, exactly one person is eliminated, and at the end, after questions, only one person remains, Mr. Balogh. Thus, he can definitely be found with questions.
He will be lucky if he can find Mr. Balogh with as few questions as possible. However, no matter how he proceeds, he can only find Mr. Balogh after eliminating people, and with each question, he can only eliminate one person, so he will always need questions.
Keve Kurucz (Révkomárom, Selye J. Gimn., 10th grade)