So it was a good idea to sign off my message saying "I am not sure if the exact calculations are correct for each round but overall this is the logic" :D. True..so the first round does take 100 questions, the second round takes 50 questions and then 25 and then so on... This results in 100 + 50 + 25 + (12 + 1) + 6 + (3 + 1) = 198 questions. I have forgotten that in the old solution that there is no need to ask any questions in the last round since there will be only two true professors. Now, the interesting part (I am not sure about this too...:D ). If we kept track of all the solutions, we can back track all the good professors by noting who all the selected person said as good and who all they said as good and so on. This might work out nicely like the tournament method. Thanks for pointing out the flaw in the previous argument. See if the new one works (else I have my safety clause attached to this mail too ...:) )
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