Having just picked some apples from my tree, I placed them in a basket, and took them around to my friends. I ate one and then gave a third of the remaining apples to my friend Mike. I then drove to Joe's home, but ate two apples along the way. I gave Joe half of the remaining apples. After Joe's I met Lucy, and gave her 10 of the remaining apples, which left one apple. I ate this one later. How many apples started out in the basket?

You have 8 marbles that weigh 10g each, and 1 marble that weighs 12g. You are unable to determine which is the heavier marble by looking at them. You have a weighing scale that consists of 2 pans. How can you determine which marble is the heaviest one using the scale, using only two weighings?