Final answer:
In the logical puzzle presented, Zippy and Betty are knaves, and Sally is a knight, as deduced by analyzing their statements and applying the definitions of knights and knaves.
Step-by-step explanation:
The logical puzzle presented involves determining who is a knight (one who always tells the truth) and who is a knave (one who always lies) based on their statements. Zippy states that Sally and Betty are different. If Zippy were a knight, one would be a knight and the other a knave.
Conversely, if Zippy were a knave, Sally and Betty would both be of the same type. Betty claims that it is false that Sally is a knave; if Betty is a knight, then Sally is also a knight. If Betty were a knave, her statement would falsely indicate that Sally is a knight, meaning Sally would be a knave.
Lastly, Sally states that Zippy is a knave. If Sally were a knight, then her statement would be true, confirming that Zippy is a knave. If Sally were a knave, she would be lying, indicating that Zippy is a knight.
By analyzing these statements, it becomes clear that Zippy is a knave, Betty is a knave, and Sally is a knight. This solution aligns with all the statements when considering the nature of knights and knaves.