Giving hints

I have a single PC campaign, and the player has not yet caught on to the little "hints" in descriptions that are made to let a clever character get an advantage. I generally get more and more obvious about the hint until they catch on, trying to get them to recognize this thing next time. Do you think this is a bad idea? It can be good because it teaches them to catch on, but it can be bad because they may depend on you and not feel any adverse effect from not catching on. I'd like to year people's opinions.

Here is an example:
Lets say that the character is at a large hill with cliffs on each side, with a cave near the top of one cliff. The obvious way of entering the caves within is to take follow a party of monsters to the secret enterence. The clever way to enter is to use their Rope of Climbing to make their way, step by step, up the cliff with the cave. I may hint in the description "There are scattered ledges large enough to stand on, and places where you could tie a rope to, if you could only reach them." If the character doesn't take the hint, I would make it more and more obvious until I finally tell them to take a closer look at their inventory.

I personally don't take that approach. Once I describe a scenario adequately, I leave it up to the playerss to decide what their characters do. And if they decide to take an approach which isn't the most clever or ingenious, so be it. They are running the characters after all, so they should react as the players see fit, not based on any predetermined ideas I have of how they should act. At most, I will provide character information based on the given PCs and their skills/abilities, but I will definitely not be hinting that something is the smart thing to do.

My real question is whether it is good to hint in order to "train" the character to think cleverly or if that just wreaks it because they become dependent. Because I am a fairly new DM, I do not have the experience to know what is a better idea.