Welcome! This is Vaidy, a graduate student in mathematics. If you are an undergrad at Ohio State and have mathematical questions , feel free to contact me. MINIMUM INFORMATION PROBLEM: There are 12 balls (11 original and 1 counterfeit) in a bag. An original ball weighs a gram whereas the counterfeit weighs 2 grams. You have a Roberval Balance (http://en.wikipedia.org/wiki/Roberval_Balance) and you can use it no more than 3 times. How can you find the counterfeit ball? If you can solve this, try solving the problem if the weight of the counterfeit coin is unknown (could be higher or lower than 1 gram). Also, in the latter case, I would really appreciate if you can find whether the counterfeit ball is heavier or lighter than the rest.