Solution to: Weighing Marbles
Number the ten bags from 1 up to and including 10. Then take one marble from bag 1, two marbles from bag 2, three marbles from bag 3, etc. Place all 55 marbles that you took from the bags together on the balance. The number of grams that the total weight of these 55 marbles differs from 550 grams is equal to the number of marbles of 9 grams that are among those 55 marbles, and that is equal to the number of the bag that contains the marbles of 9 grams!