thinking problem (math)

I think that it's probably not a strategy that makes the teacher win every time since the student can just pick randomly and should have 12.5% chance of a win each time if 4 coins and a very, very small chance each time if 16 coins. (first coin doesn't matter, 50% that he'll do right at the 2nd, 50% on the third etc).

Student could maybe find a way to increase his chances of winning by deciding how many coins to flip each round (he know that there's 3-1,2-2 or 1-3 I guess so he should always flip one or two or one or three I think).

Also, is there 4 coins in each corner or just 4 coin, one in each corner.

I think it's one of those that gets down to the fact that the probability to get it right is fairly small, but given an unlimited amount of tries he should win at some point.

Although, I'm not good with math anymore.

Lets create another scenario where the person is able to see the faces of the coin before being blind folded. If it is head/head/head/tail(3-1) or tail/tail/tail/head(1-3), the correct play is to flip only one coin (25% of being correct) and ending the game. But if the game does not end then the person knows for sure it is now 2-2 (head head tail tail) and the correct play from then on is to flip 2 coins until the game is over (50% of being correct). Now of course in the problem the person cannot see the original position of the coin. But now we know we have to get to 2-2 positioning somehow. That is all I thought about so far maybe it can help.

As Dusty said, at each round, the blindfolded person can turn the coins he wants. By doing it randomly (obviously never flipping 4) he has 1/8 to win. So to your first Q : no, there is not.
And yes, your second question is the same than your first. If there is a strategy for the student to win, there is no strategy for the teacher to make the blidfolded unable to win.

So I guess, your problem is not well presented.

Is there a more efficient way than picking randomly for the blindfolded person ? I guess so but only if the teacher has to define a strategy which is not dependant on the blindfolded's actions.

Hmmmm yes I may have missed some part because Dusty is right as it is now the student can win that way. But i feel like i remembered it all hmm

and it was 1 coin in each corner, 4 total

Can we place all coins in the same corner? :O

If I were the teacher I would just face every coin in the same direction hoping for the blindfolded person to always flip 1-3 coins.

when does the blind player win? instantly when the coins are in order or when he says out loud that he thinks the coins are in order and is correct?

btw if the rounds go till infinity then he ll win eventually

I dont understand the question :/