An unemployed man walks into a shipping warehouse on the wharf. He goes to the foreman and asks for a job. The foreman says he’ll give him a job if he can figure out a problem with 10 bushels of apples. Nine of the bushels are full of apples weighing 1 pound each, but one bushel contains apples weighing 1.1 pounds each. All of the bushels contain the same number of apples. The foreman wants to know which bushel has the heavy apples. There is a scale, but he can only make one measurement on the scale. Making only one weight measurement, how can the man find which bushel contains the heavy apples? He can include any combination of bushels or apples on the scale.
Answer
The man takes one apple from the first bushel, 2 apples from the second bushel, and so on through the 10 bushels. He then weighs all of these apples. Since each apple in the heavy bushel weighs an extra .1 pound, the weight of the apples would be between 55.1 to 56.0 pounds. The portion over 55 pounds would tell you which bushel has the heavy apples. If the weight is 55.4 pounds, then the bushel with the heavy apples is bushel #4 and so on.
