But being Intelligent doens't mean you can solve puzzles very well. I am above average intelligence and I suck at some puzzles. Maybe your character is very good at memorization (thus the Intelligence is geared toward retention and recalling facts then creative thinking). Maybe a Knowledge: Riddle skill(O no not another knowledge skill) could be used in a Riddle heavy campaign.
Yes, and some people have great reflexes and considerable grace of movement, but cannot play darts or juggle - so do they have a high Dex, or not? The person with great upper body strength, but a weak lower back? The person who doesn't bruise easily, but who catches colds like clockwork? And what about those characters who are the opposite, and are great with puzzles but not at memorization?
The D&D stat system is very generalized and abstract. The action of the human mind really isn't accurately reduceable to a single number, or even a small collection of numbers. Such is life.
While it is possible to start making up sub-skills to cover every possible task, since characters have a limited number of skill points, so havng the skills available really doesn't help much. Personally, I think the generalized Intelligence score in the game works well enough. The headache acquired for aiming for too much veracity isn't worth the effort.