40 lb. Stone

A farmer had a 40 pound stone that he used to weigh 40 pounds of feed with, you know, he had a balanced scale, you put the stone on one side and the feed on the other side, and when it balanced, he knew he had 40 pounds of feed on the one side. A neighbor of his, Frank Staples, I think, borrows the stone and when he returns it, he says I’m terribly sorry, I dropped the stone and it broke into four pieces. The farmer says don’t worry, you actually did me a favor and he explains that the pieces of the broken stone could now be used to weigh any item, assuming those items were at one pound increments from one pound to 40 pounds. So, if he wants to weigh something that’s one pound, two pounds, three pounds, four pounds, five pounds, he can do it with those four stones, four pieces and the balance scale. Here’s the question: What are the weights of the four pieces of stone.