Follow up question to my other question, but totally different methodology required.
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 know that all genuine coins have the same weight but you do not know their weights.
- You also know that every fake coin could be heavier or lighter by 1 gram than a genuine coin. So Some fake coins could be 1 gram lighter and some other fake coins could be 1 gram heavier than genuine coins
- The weight of genuine coin is integer valued.
What is the minimum amount of weighing which guarantees to tell whether if any coin you choose is a fake or not?
In other words, you will choose a coin you want; after weighings you are going to tell that if that coin is a fake or not for sure. That's the aim of the question. The coin you choose could be a fake or genuine, it doesnt matter.