逻辑问题，不知道有没有简单一点的方法

A history test has three questions on Presidents of the United States. Here are the answers six students give.　 1. Polk, Polk, Taylor 2. Taylor, Taylor, Polk 3. Filmore, Filmore, Polk 4. Taylor, Polk, Filmore 5. Filmore, Taylor, Taylor 6. Taylor, Filmore, Filmore　Every student has at least one correct answer. What are the answers? 知道可以列出所有的27种可能然后一个个删除。可是，应该有简单一点的办法吧