I wanted to buy silver coins for Diwali. On visiting a shop selling such coins, I had an odd feeling. The coins were supposed to be of perfectly equal weight. I chose 15 coins, but I somehow knew that one was fake. The only way to know the fake one was that there was
a very small weight difference (towards higher or lower side) which could only be measured with an accurate scale. I took the coins to a gold smith next door, but he was charging some money for letting me use the scales of his shops. But since his scales were perfectly accurate, I had little option. Also, the gold smith did not let me use any other weight or any tool along with the scales.
What was the minimum number of times I used the scales so that the cost us using them was minimum and I could figure out the fake coin?