you have 13 bags of gold wins. out of 13 bags gold coins, there is one bag gold coins lighter. assume that one real gold coins is 10g and the fake is 9g. now, you are given a electronic beam balance. find the most minimum ways to figure out which bag of gold coins is lighter.
Try to get a "bit" (binary digit) of information with each weighing. This divides the possibilities as close as possible in half.
Start by weighing 6 bags at a time. If they both weigh the same, then the remaining bag is the fake. If not, divide the lighter set in half and weigh again. From this weighing, take the lighter set and weigh 2 and 1. If the one is not fake, then you only have one more weighing to go.
At the max, how many weighings is that?