What side of a cat has the most fur?
The reason is simple. On most domestic cats, you can see the back of their tails.
When the cat sits, the tail hangs down the side.
From there, it is a very easy step to see that the cat will be sitting up to watch you, so you see a bit more on the back than on the sides.
This applies to all cats, regardless of their breed, colour or size.
The only thing that matters is how much of the cat is in view.
If it is difficult to see all of them, I would say the back has the most fur.
This is a great question, and a great opportunity to illustrate why we need to teach our children about wildlife. :)
The "right answer" would probably be a matter of personal opinion.
I'd suggest that you consider each of the cat's 4 legs:
The forelegs are shorter than the hind legs, so they're a bit closer to the body. They have more fur, because they can feel more comfortable. They're also more prone to damage (like scratches), so they tend to have less fur. So, I'd say the forelegs would have the most fur, but I'd be hesitant to say for sure.
The hind legs have the strongest muscles, so they have the most fur, but since they're further away, the fur tends to be more short and thick.
Of course, this is just an educated guess.
Also, your question implies that cats have fur, but we can't be absolutely sure. While it's true that cats are covered with hair, it is not actually "fur", since they aren't mammals.
The closest animal to a cat (besides people) that is covered with fur would be a dog. However, dogs have much larger, softer coats, and much more hair. As such, I'd say dogs have much more fur than cats.
According to the BBC:
Domestic cats (Felis catus) have more body fur than dogs, which is more body fur than ferrets (Mustela putorius).
I also know that the American Veterinary Medical Association's 2013 edition of the Canine and Feline Species Description and Characteristics describes the cat as having a coat of "long, soft fur."
So, it looks like the answer is:
The cat has the most fur on its back.