There are 15 gold coins. One of the gold coins is a fake. A fake gold coin is lighter than a real one. You have a “balance machine” without any scale. Can you identify the fake coin by using the “balance machine” at most three times?
put 5 left and 5 right. If the scale balances, the unweighed coin is one of the 5 unweighed coins. Otherwise, it is one of the 5 lighter group.
Repeat with 2,2 and then 1,1