I'm generally in agreement with those who advise a healthy mix between the two schools of thought: player-centric, and character-centric roleplaying.
I personally assert that the player chooses the actions for a character, whose abilities are then taken into consideration through skill checks and the like to determine the outcome of those actions. Example: the player decides that his character will attack the otyugh by taking a five-foot step and a full attack. The character performs the action, the result of which is determined by his attack and damage rolls.
Similarly, the player approaches a puzzle and decides to solve it. The character puts his knowledge and reasoning ability to use, generating hints for the player and such.
That's how I would do it anyway.
The kind of puzzle I would suggest is something akin to one used in "Indiana Jones and the Last Crusade." Indy comes to a grid and deduces that he has to walk only on the lettered tiles which spell the name of God. This is something for the player to figure out, just as he would decide that his character is going to take full defense and provide cover for the wizard against enemy archers. Indy then recalls the name of God, Jehova. He begins to step on the J, which crumbles. Then he remembers that in the time that the crypt was built, the Latinate alphabet was being used, and I was used instead of J. This is where the character's abilities should be taken into consideration. One can assume that Harrison Ford rolled up a knowledge (religion) check for Indiana, and the result was high enough to remember that by this point the name of God was often considered to be Jehova. It was not high enough, however, to determine the proper spelling. After making his mistake, he took a moment to consider further (another check) and proceeded to solve the puzzle.
Like combat, a good puzzle shoudl combine player and character abilities. The player determines the method by which his character will approach the situation, and the character's abilities determine the outcome.