I have had numerous cats, like dogs their level of intelligence varies greatly.
My first when I was a small child was extremely clever, at the time we also had an Afghan Hound which despite being 10 times the size was terrified of the cat due to always losing in fights and getting shredded regularly. On one occasion the dogs nose was cut so badly we had to take her to the vets.
In my teens we had two tom brothers, both were very large short hairded moggies. The alpha was was thick as s**t, had no concept of inanimate objects and was constantly breaking things but was the toughest cat in the neighborhood. The other one taught itself to open some of our windows (never did learn to close them afterwards), regularly raided cupboards, was strong enough to get into the fridge and used our toilet. His best trick was to pierce the top of a milk bottle, knock it over, lap it up as it came out at a reasonable pace, then leave the rest to flood the kitchen.
My current feline is most definitely at the lower end of the scale but an awesome hunter despite a predominantly white coat.
In my experience cats do not display what we would describe as intelligence, they are comfort seeking, driven by instinct, and think with their stomachs. There are individual exceptions but the same can be said for any species.
No problem is so large it can't be fit in somewhere.