Homework problems

Problem 1. Create problems similar to problems 4. and 7. from the lecture changing the numbers.

Problem 2. We have a balance scale that measures the difference between the sides. We are given 101 coins - 50 of them are counterfeit. Every counterfeit is one gram less or one gram more than a genuine coin. All counterfeit have the same weight, all genuine coins have the same weight as well. Take one of these coins. Can we decide with one measurement if this coin is genuine or counterfeit?

Problem 3. It is an interesting question to study how many different solutions does this problem have depending on the fact if the weights are integers. Create problems using that.