Which Is the Heavier Coin?

Here is a detailed examination concerning Which Is the Heavier Coin.

There are 16 coins, 3 of which are slightly heavier or lighter than the others. The counterfeit coins have the same weight but it is not known whether they are heavier or lighter than the genuine ones. Using a balance scale, what is the minimum number of weighings in order to determine whether the counterfeit coins are heavier or lighter?

How to figure out if a coin is real or fake?

The following diagram explains the procedure. The middle case (G1) = (23) is self explanatory, i.e. 1, 2, 3 are genuine and 4th coin can be figured out lighter or heavier in one more trial. The left side of tree corresponds to the case (G1) < (23). This is possible in two ways, either 1 should be lighter or either of (2, 3) should be heavier.

Can you put a fake coin on a balance scale?

Solution. One weighing. Place one coin on one side of the balance scale, one on the other, and put one coin aside. If the scale balances, the coin that we put aside is fake. If one of the sides of the scale is heavier, the fake coin is on that side. Example 2. One of the nine identically looking coins is fake.