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?

Solution: Compare three coins from one group with three coins from the other group. They will either balance or not balance. In that the solution to the more difficult case of balanced coins includes the method to solve the less difficult case, I offer only that solution. Begining with the left and rigth side balanced three coins each: Using the two off-scale coins from the left side replace two of the on-scale coins on the right side and using one off-scale coin from the right side replace one on-scale coin on the left side and compare this arrangement. If the scale balances the not replaced coin on the right side is fake and comparing it with one of the not replaced coins on the left side will solve. If the left side weighs heavy the on-scale replaced coin on that side is fake. Then compare two of the three off-scale coins on the right side to solve. (if one of these dosen't weigh heavy, the other off-scale coin is fake) If the left side weighs light the off-scale replaced coin is fake,etc.