You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect precision that shows how much difference between weighs you put on. For example, if you put 10 g on the left side and 20 g on the other side, it will show -10, otherwise +10.
You are asked to find a fake coin among given 99 coins:
- You know that all genuine coins have the same weight but you do not know their weights.
- You also know that every fake coin is heavier or lighter by 1 gram than any genuine coin.
So, what is the minimum amount of weighing which guarantees to find any fake coin you are looking for? (The fake coin you are going to find might be heavier or lighter, it does not matter, you just need to find any fake one.)