Interesting problem to explore: Stones & Balances


Here is the full problem, from 10/22/11 Car Talk radio show:

A farmer had a 40-pound stone that he could use to weight 40 pounds of feed, hay, or whatever else he wanted to sell from his farm. He had a balance scale, and he put the stone on one side and piled the other side with feed or hay, and when it balanced, he knew he had 40 pounds.

One day, a neighbor borrows the stone, but he had to apologize when he returned it, broken into four pieces. The farmer who owned the stone later told the neighbor that he actually had done him a favor. The pieces of the broken stone could now be used to weigh any item, assuming those items were in one-pound increments, from one pound to 40.

The question is, what were the weights of the four individual stones? And if you want to weigh one pound, six pounds, 11 pounds, 22 pounds, 39 pounds -- how would you use the stones, the thing you are weighing, and the balance scale?

And here's the Hint: how would you weigh two pounds?

See the CarTalk website for the solution: