1. Using balances efficiently

3. In Amazing Race, my partner and I
are in a foreign country where balances are still used in
the marketplace to sort out the valuable gems from the
worthless stones. As a part of this challenge, we are given
9 stones and we have to figure out which stone is really
the valuable gem. We are told that although they all look
the same, the valuable gem is slightly heavier than a
worthless stone, and that the 8 worthless stones we are
given all weigh the exact same. If we use the balance
more than 2 times, we are penalized and have to take 1
hour off of our travel time. That would cause us to lose the
game since this is a very close race. We are determined to
figure out a way to identify the stone without using the
scale more than 2 times. Please help. Explain how we can
identify which is the valuable gem using it only 2 times.