You have two sets of five coins. Each set has four real 30g coins and one 31g fake coin. It is easy to find the fake coins using a balance scale a total of four times, two weighings for each set.
Can you find a strategy which uses only three weighings?
While drinking my morning coffee I read through my "solution" a second time and immediately saw the flaw in the statement that "If these coins balance the not replaced coin on the right side is fake" I had failed to take into consideration that the initial comparison could have compared only real coins. At age 75 I should know better than to rely on my short-term memory. In the future I will resort to pen and paper to diagram my solutions, and hopefully remedy this sort of error, before submitting another "solution".