Ten bags in front of you on the floor are each full of newly-minted 1oz platinum bars. All of the bars look exactly the same, but all the bars in one of the bags are rejects and each bar weighs 1 gram less than a certified bar. You have an extremely accurate scale capable of measuring weight to the gram, but you are only permitted to use the scale once to make only one weighing. Using the scale only once for one weighing, how do you determine which bag has the bad bars?
You come upon 3 chests containing coins. You cannot see inside any of them. Each has a hole in the top and a sign on the front. They are labeled "GOLD," "SILVER," and "GOLD AND SILVER." Each is labeled incorrectly. You are permitted to reach into one box and remove and inspect one coin. You may not peek or feel around inside any chest. Staying within the rules given, how do you label each chest correctly?