Counterfeit Coin

You are a market salesman. Every week you sell your wares in a beautiful authentic market stall. People travel from faraway lands to buy your signature product: fermented shark. Of course, such a delicious product should only be exchanged for a vast amount of shining, valuable coins.

Sometimes customers try to fool you by paying with counterfeit coins. You always spot them, of course; you take out your trusty scale and weigh the coins to determine if any of them are of different weight.

In this particular instance, a rather notorious customer by the name of Peter Rog Rammer, famous for his "off-by-one errors", has just paid for a fermented shark dish using $n$ seemingly identical coins. However, you are sure that there is one coin that is not quite the same as the others. As the line of customers is getting rather lengthy, you do not want to spend too much time finding the odd one out!