You are at the pet store to pick out a puppy. There are 9 cages in 3 rows of 3. Each cage has a different breed and different number of puppies. Figure out which cage each breed is in, and how many of each breed there are.

1. Chihuahuas are Northwest of the Spaniels, whose number is the square root of the Pomeranians.
2. The Terriers are Southeast of the Spaniels.
3. There are twice as many Corgis as there are Yorkies, who are West of the Schnauzers and North of the Spaniels.
4. The 7 puppies North of the Pomeranians barked at the 2 puppies South of the Spaniels, and the puppy East of the Poodles was all alone.
5. There is 1 less Chihuahua than Collies, who are Northwest of the Poodles.
6. The 8 Corgis are Southwest of the Spaniels, who have half the number of the Collies.
7. There are 6 puppies West of the Spaniels.