If you make your players figure out the puzzles themselves in the game, that's like making your players run a race to find out who wins the race in the game. Or making them actually bench press weights to figure out if they can lift the gate. Or actually stabbing them when the goblin stabs them.
Puzzles have their place, but I don't think that place is nessecarily in a game where you're playing a role. The role should be challenged. The player's involvement should be in playing the role, and in figuring out the role's reaction to the challenges presented. Combat is an obvious challenge to the role -- it can cancel the role. But other things, can, too, from rumors of townsfolk to the royal dinner.
Puzzles can break the verismilitude VERY easily, just like riddles can, if the players themselves are expected to solve them. Like I said, that's just like forcing them to get up and run a race in the middle of a chase scene. Or actually playing a game of chess to figure out the outcome of a game of chess. It becomes a game-within-a-game, and almost by definition, that is a metagame.
ML gives the best advice on how to use puzzles that aren't really puzzles -- that challenge the characters, not the players. The
reader never had to figure out how to get into Moria. The
characters did. In D&D, this can be a significant problem -- if the
players have to figure out a riddle, it's not part of the story anymore.
My thesis (which is based on definitions at dictionary.com is that characters are built to use their players smarts.
This is like saying my thesis (which is based on definitions used at the Jeffrey Dahmer Trial) is that we should all eat humans.
Look, your definitions are largely inadmissible, because they're not formed within the context of the game in front of you. You're arguing semantics when the real problem is at the table. The game is in the playing of the role, not in the using of smarts. It's more of a dramatic test, more of an improvosational game, closer to
Whose Line Is It Anyway than a crossword puzzle. Combat is just another way to play a role (and a very action-packed and edge-of-your seat way to play that role). The moment I start demanding my players figure out the puzzles as players, and not as characters, I'm also going to demand they show me that they can lift a real sword when they say "My barbarian hefts the sword."
And if I'm demanding that they figure out the puzzle as characters, it's entirely applicable to have them roll for the results. And if they don't find it...hell, that's where the challenge of improvosation comes in. Is there a sage? Is there an ally? Are there explosives? There are many ways around the obstacle as there are logical ways to interact with the world, after all.