This also belongs to a topic puzzles and paradoxes in math induction. We will discuss the puzzle and logic behind solving it but not mathematical induction.
I am pasting in the image of the question here:
Do not scroll past this if you do not want to see the answer.
I will not repeat the question so you better read it well. I am going to write answer below, if you do not want to look at the answer yet do not scroll.
Answer: All of the professors will resign.
Expanded answer:
1. Professors will meet for the last time in the last meeting of the year
2. They look at each other and realise the other person is not resigning
3. Deduce they must be the one who made the mistake and they all resign at the same time.
If you get it then you need not read the below.
Q. barbossa knows that jack isn't aware of his mistakes so how does he expect him to resign?
Let us consider that the two professors are Captain Jack Sparrow and Captain Hector Barbossa. They are sitting across the table
Let us run through jack's train of thoughts:
1. He sits at the table and looks at barbossa.
2. Professor X said one of you has committed a mistake
3. As jack knows barbossa has committed a mistake he says to himself "aha! barbossa be the black sheep" and sits back to drink his rum.
lets look at it the other(Opposite) way.
Jack thoughts:
1. If barbossa has NOT made a mistake then jack would NOT know about barbossa's mistake
2. He then says himself "One of us made the mistake, if he has done it then I'd known it. I haven't heard about his mistake. So I'm the one making the mistake".
3. That we know professor X's words "Which has been discovered by others in the department".
4. As soon as jack understands this he resigns.
The above did not happen and thus barbossa has made a mistake and jack knows it.
Barbossa then realizes this and the exact same seconds jack does too as barbossa too knows about his mistakes and then both of them resign!
All of this can be applied to as many sets of professors / pirates as you'd like. And the final result, every one resigns. Think about it you'll get it sooner or later!
Extra info:
When I was looking to add in images, funny enough I couldn't find one without copyright notice but I found a wikipedia article on pirates(the real ones), cool one. Have a look at it once you are done reading this. https://en.wikipedia.org/wiki/List_of_pirates
This puzzle is taken from http://www.math.cornell.edu/~mec/2008-2009/ABjorndahl/ppmi.pdf
I do NOT claim it as my own. All Copyrights to the respective owners.
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