1. Construct a finite-state machine for an electronic door lock that implements the following rules: A user enters a string of three digits, one digit at a time. If the user enters the correct three digits, the door will unlock. When the user enters an incorrect string of three digits, the electronic lock will make a beeping sound (but only after all three digits have been entered).
2. A pet owner is taking three of her pets to the vet: one dog, one cat, and one mouse. She was able to put all of them in her car and is now ready to take them to the vet's office. The pet owner has suffered a terrible accident and only has one hand. Thus she can only carry one of her pets at a time. If she leaves the dog and the cat in the car, the dog will attack the cat. If she leaves the mouse and the cat in the car, the cat will eat the mouse. On the other hand, the dog and the mouse will leave each other be. How can this pet owner bring all three animals to the vet's office? Represent your answer with an FSA and justify your answer.