If you have 9 coins: Divide into 3 groups of 3 coins each. Weigh two groups: If balanced, the fake coin is in the third group. If unbalanced, the fake coin is in the heavier or lighter group. Take the group with the fake coin (3 coins) and weigh 2 of them: If balanced, the fake coin is the one not weighed. If unbalanced, the fake coin is the heavier or lighter one. You can find the fake coin in 3 weighings or fewer.