# Solution: The 40 pound stone puzzle

This is the solution to The 40 pound stone puzzle. If you haven’t read the puzzle yet, click here before you read the solution.

This puzzle similar to some of the puzzles in my book Interview Puzzles Dissected.

The key to this kind of puzzle is to remember that you can put weights in three places: in the balance’s left pan, in the right pan, or in neither pan. For example, suppose you have a 2-pound weight and a 3-pound weight. Then you can measure 1 pound of beans by placing the beans and the 2-pound weight in the left pan and the 3-pound weight in the right pan.

The correct weights for the pieces of stone are powers of three: 1, 3, 9, and 27. Using those four weights, you can measure any number of pounds of beans (or whatever). For example, to weight 20 pounds of beans, place {1, 9, beans} in the left pan and {3, 27} in the right pan. The weights 1 + 9 + 20 = 3 + 27, so the pans balance.

Interview Puzzles Dissected has more to say about this kind of puzzle. It proves that this solution works and discusses variations on the puzzle that you might use in an interview or that you might encounter if you’re a job applicant. The book also describes hundreds of other interesting puzzles and their variations. Go to the book’s web page to see a few other sample puzzles.