But, if you have low scores, your brains don't matter, because you fail.
D&D is a very cut and dry game of "high numbers win, low numbers fail". If you want to play a game where creative gameplay and interesting application of weaker abilities still results in successful gameplay, D&D is not the game for that.
You're not going to get what you what doing what you suggest in D&D. You're going to either fiat away the rolls with player-skill and knowledge, which makes the low scores you wanted meaningless, or you're going to fail a lot and get frustrated that you, as a player, saw that coming but your character just can't pass the checks.
I'd suggest looking to a supers or a detective-styled system, and I'd stay away from the d20.