| Case 1 | We are given 1 good coin, 1 suspect coin, and a balance. A suspect coin is either too light, or too heavy, or is good and of the same weight as the good coin. Give a method to use the balance 1 time to find out which of these 3 possibilities is the case. |
| Case 2 | We are given 1 good coin, 4 suspect coins, and a balance. A suspect coin is either too light, or too heavy, or is good and of the same weight as the good coin. At most one coin is no good. Give a method to use the balance 2 times to find out which of these 9 possibilities is the case. |
| Case 3 | We are given 1 good coin, 13 suspect coins, and a balance. A suspect coin is either too light, or too heavy, or is good and of the same weight as the good coin. At most one coin is no good. Give a method to use the balance 3 times to find out which of these 27 possibilities is the case. |
| Case n | We are given 1 good coin, k suspect coins, and a balance. A suspect coin is either too light, or too heavy, or is good and of the same weight as the good coin. At most one coin is no good. Find the largest k for which one can give a method to use the balance n times to find out if there is a bad coin and, if there is one, which one and whether it is too heavy or too light. Describe the method. |