It could be a) worms b) a flea problem or c) anal gland issues (as someone else said, if she has had runny poo it could be the anal sacs haven't been emptying properly and they're a bit clogged up).

Take the cat to the vet, it's the only way you'll be certain what it is. I've had bum rubbing on the carpet issues and with my kitten and she had to have her anal glands expressed a couple of times. If this is the problem with your little one it's important to get it seen to otherwise they can end up with infections or abscesses.

He's booked in for 2 weeks on Saturday for his next set of vaccinations, but I'll get an earlier appointment and ask them about the things you've all suggested!

Thanks for the responses and advice!

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"Each generation imagines itself to be more intelligent than the one that went before it, and wiser than the one that comes after it."

A very good idea to take the kitty to the vet and get all the possibilities investigated that other posters have suggested.

All I would add, is that if when everything else has been tried there is still a problem my suggestion would be to take the kitten off dry food completely and just give him good quality wet food for a while. It could be the case that his stools are not the right consistency (e.g. perhaps slightly too dry, or slightly too loose) for him to be able to pass them out in neat 'parcels' when he does his toilet, and as you have observed small clumps are left sticking to his bum afterwards. This would no doubt make his bum feel sore or irritated hence the reason why he rubs it on the carpet. I once had an adult cat who did this, but stopped once we changed his diet to wet food only.

Meanwhile until you get the problem resolved I would suggest perhaps you could use unscented pet wipes to help him clean up after toiletting. (Or just a piece of loo paper!).

I hope you get it resolved before your carpets are ruined