Abaddon,
I didn't know there were two possible answers until I saw that nowisee's answer would also work. The source of this puzzle is a book titled "Math Wizardry for Kids" published by Barron's.
I double-checked all of the clues at the start of this thread and they have been correctly stated on a basis consistent with the book.
Leolaia,
Clue 2) - You are right. The "name of the pet" means the "name of the type of pet".
Clue 7) is not superfluous, as explained below.
Golden Girl,
Priceless! I laughed like hell.
Little Toe,
You are right, with a little help from Google. Clue #2 should be the "name of the type of pet". I regret the book did not present the clue with the proper clarity.
The approach to solving this problem is to set up a Grid or Chart to help you make the proper matches. As soon as you find one match, you can cross out other possibilities. For instance, if Pet #1 turns out to be a Mouse, then Pet #1 cannot be a Dog, Cat, or Parakeet. Use logic to find the matches.
Dog Mouse Parakeet Cat Fluffy Spot Mickey Vickie
Buffy
Duffy
Rickie
Danny
Fluffy
Spot
Mickey
Vickie
The above chart should alos have vertical lines to create boxes or squares inside of which you can insert "X's" as you go thru the processes of elimination, applying each of the clues.
Now, follow the clues about the pets and people like this:
1) If no person's name rhymes with the name of his or her Pet, then you know that Fluffy does not belong to Buffy or Duffy. You also can tell that neither Mickey nor Vickie belongs to Rickie. Make "X" marks on the grid by each name.
2) If no person's name begins with the same letter as his or her Pet (type), then you know that neither Danny nor Duffy has a Dog.
3) If Mickey is not a Mouse and Fluffy is not a Cat, mark "X" on the grid by those spots.
4) Danny's pet is neither a Mouse nor a Parakeet. You already know from Clue #2 that Danny's pet is not a Dog. There's only one pet left. Danny's pet must be a Cat. If Danny has a Cat, then the other people, Buffy, Duffy and Rickie do not have a Cat. You can "X" out those spots on the grid.
5) If the pets with rhyming names are not Parakeets, then neither Mickey nor Vickie is a Parakeet. Mickey and Vickie also do not belong to Duffy. Look at the "X" marks on your grid. Spot is the only pet name for Duffy. Spot must belong to Duffy. Now you also know that Spot does not belong to Buffy, Rickie or Danny.
6) The Parakeet does not belong to either of the people with rhyming names. Therefore, the Parakeet does not belong to Buffy or Duffy. Mark your grid.
7) Make an "X" to show that Mickey does not belong to Duffy.
As the grid fills with "X" marks, you can make the rest of the connections between Pets and People.
Rod P.