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?

Answer: 37

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?

Answer: Place 3 marbles on each pan. If they balance, remove the marbles from the pans and place 2 of the remaining unweighed marbles on the pans, one on each pan. If one is heavier, it is the heavy marble, but if they balance, the remaining unweighed marble is the heavy one. If your first weighing does not balance, remove the marbles from the lighter pan (because it can't be one of these), and place one marble on each pan from the heavier pan. The heavier one is the 12g marble, but if they balance, then the third marble left over is the heavy one. Simple!