someday, some math teacher decided to test the logic deduction capacity of the class consists of 32 students. When the class began, he showed a letter to each student between A to E and said:
"There will be the final exam in an hour in the middle of the semester, there will be only answer sheet, this is a pop up Final!
I actually gave you one of multiple choice’s answer to each one of you, from question 1 to 32 by the give away order. i am generous, so the exam will be out of 128 and every right answer has same point.
I will give you a chance to communicate with at most 3 people at the board and you can share your answers. No cheating more than that is allowed! no talk, no chat, nothing else but taking notes from others.
Every time you come together and share notes, you will come to the board and take notes from each other only and I will count how many times you gather up. and everybody will lose $1$ point every time you gather.
now you have an hour! go!”
What is the maximum average point they can get as a class?
What is the highest point they can get if every student wants to know all answers?
Fyi: Students want to share what they know all the time.