Rubik's Cube Riddle

Question

When I was toying around with a Rubik's cube, I got a inspiration for a Maths puzzle, and I find it extremely difficult to answer. This riddle was all by me.

Imagine you are blindfolded and a randomly oriented Rubik's cube is placed in front of you by one of the hosts of this riddle. Your task is to guess on which face the white center is, but you only have 4 guesses. Is it possible to win every time? The host can also hear in your strategy and try their best to thwart you.

I tried to come up with strategies to solve this, and all failed, but I cannot yet prove this is impossible. If it is, I'll try to soften the riddle a bit. The variation is that after your first failed guess, the host points out a face that doesn't have a yellow center other than the one you picked. If that's still impossible, the host will point to another face that doesn't have a yellow center.

Answer 1

1. With 4 guesses and no feedbacks, the chances are as good as a random guess. Only 6 guesses are a sure way.
2. With 4 guesses and feedback over yellow on first attempt, there are 2 cases:

• If that face is not white, the rest of the 3 guesses can be made on each of remaining faces.
• If that face is white, you will need 5 guesses.

So this situation would still need 5 guesses.

3. Proceeding similarly for 4 guesses and feedback over yellow on 2 faces, you should be able to find that 4 guesses are sufficient.