The Counterfeit Coin
Working at a reserve bank in beautiful Puzzlania, you are in charge of the destruction of counterfeit tender. Due to bad planning and a lack of originality bordering on plagiarism on behalf of the Puzzlanian treasury, the Puzzlanian dollar looks a lot like a U.S. penny. Right down to the "UNITED STATES OF AMERICA - ONE CENT" on the back. In fact, the only difference between them is the grade of the copper. As a result, a Puzzlanian dollar doesn't weight quite the same as an American penny.
Well, you can probably guess what the number one source of counterfeit currency in Puzzlania is. So day after day you have thousands of (Puzzlanian) dollars worth of U.S. pennies melted down to provide the raw materials for real Puzzlanian dollars.
One day, on impulse, you pocket one of the counterfeits as a souvenier. While working in with the analytical balance on a batch of real dollars, you accidentally mix the counterfeit coin with seven real coins near the end of your shift.
It is imperative that you remove the fake from the real coins, or you'll lose your job (and go to prison!). Because the analytical balance uses very expensive electronic sensors, each employee has a limited number of "balancings" per shift.
Each weighing on the balance will tell you which of two samples is heavier, or if they are equal in weight. Puzzlanian dollars are identical in weight to within several micrograms. American pennies, with their imperfections, are invariably heavier or lighter. Using the balance, you can compare any two piles of coins with each other; however you only have the eight coins at your disposal.
What is the fewest number of weighings which will tell you correctly which is the counterfeit coin?