12. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. Present the minimum number of weighings and your answer clearly. In the problem, remember that I do not ask you to find the fake coin among 8 coins using the scale. You dont need to find out which coin is fake. The question is that you should be able to identify whether the fake coin is heavier or lighter than the real coins.

12. (2 points) [Puzzle] Assume that you have 8 identical-looking coins and a two-pan balance scale with no weights. One of the coins is fake, but it is not known whether it is lighter or heavier than the real 7 coins. Describe your idea to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others. Present the minimum number oif weighings and your answer clearly. In the problem, remember that I do not ask you to find the fake coin among 8 coins using the scale. You don't need to find out which coin is fake. The question is that you should be able to identify whether the fake coin is heavier or lighter than the real coins