You are given fifteen stones which look and feel identical. One of them contains a valuable gem worth $ 500,000 which is yours if you can correctly identify it. The gemstone is slightly lighter than the other 14 stones (but not enough lighter to detect by lifting or comparing). You have a balance scale which you can use no more than three times. After three uses the balance scale can never be used again. How can you be certain to find the stone with the gem. If you guess at any point you lose the chance to win the gemstone.