You have a pile of 24 coins. Twenty-three of these coins have the same weight, and one is heavier. Your task is to determine which coin is heavier and do so in the minimum number of weighings. You are given a beam balance (scale), which will compare the weight of any two sets of coins out of the total set of 24 coins. How many weighings are required to identify the heavier coin?
It can be done in three weighings.
Weighing 1: Break the coins into three piles of eight. Weigh one group of eight against another group of eight. If the scale balances, then the group that hasn't been weighed has the heavier coin. If the scale tips, then that group contains the heavier coin.
Weighing 2: Break the group of eight that has the heavier coin into three groups (three coins, three coins, and two coins). Weigh one set of three against the other set of three. If it balances, the group of two has the heavier coin. If the scale tips, then that group has the heavier coin.
Weighing 3: If the heavier coin is in the group of two, then just weigh one coin against the other to determine the heaviest coin. If the heavier coin is in a group of three, then take two of those coins and weigh them against each other. If the scale balances, the coin that hasn't been weighed is the heavier coin. If the scale tips, then that is the heavier coin.