I am a professor of (theoretical) mathematics at a state university in the US. In recent years I have advised a number of graduate students: so far, one master's student and three PhD students have written theses under my direction, and I currently have two PhD students.
Just now I tried to look back over these six students and recall if any of them ever just solved a problem I gave them with no intermediate discussion or help from me. This definitely happened once: one of my students did something brilliant over the course of a couple of weeks that became the main core of his PhD thesis. There is another case where a group of students working in a research seminar with me quickly and completely independently came up with a clever, computationally-intensive way of answering a question soon after I raised it in the seminar. And my first student was exceptionally strong: to my mind his thesis work was done mostly independent of me, but that did not stop him from asking a steady stream of technical questions both of me and his co-advisor.
I could complement each of the stories above by half a dozen more involving the same students, in which they got very substantial help from me, or -- even more commonly -- simply abandoned the problem because they did not have the prerequisites / could not make progress / was not to their taste / was too difficult, too technical or otherwise poorly chosen by me. I won't tell such explicit stories, of course, but you should be aware that virtually every graduate student in mathematics could. In my opinion, thinking that you need to talk to your advisor only after you've solved a problem (even a "small" one, or even a single step of a problem) is a major misunderstanding of what the student / advisor process is like in mathematics. I don't know how it is in other academic fields, but as a student in mathematics when you start (trying to) do research you don't have a clue. Somehow you need to get from not having a clue to research success in the span of several years: you do that by getting a lot of help from your advisor.
When I was a PhD student (at one of the top programs in the world, with one of the most eminent advisors in the world) I was very independent. I would usually meet with my advisor less than once a month. When I met with him more often, I felt like I was telling him an incomplete story: you asked me about this, and I am trying this, and it is starting to look like it won't work, so maybe next I will try that...I wanted to go through the entire process of acquiring background and trying to solve a problem in all the ways I could think of by myself: by talking to him sooner than that, I felt I wasn't giving him my best effort. In retrospect I really think I played this mostly wrong: my approach fanned the flames of my independence, but at the cost of much of the help and insight I could have gotten from my world-renowned advisor. In recent years my professional confidence has grown a lot, and I am much more willing to tell someone "You know, I thought about what you told me [for, say, a day or two] and couldn't work it out. Here's where I got stuck. Can you tell me a little more about...?"
Now I work with PhD students and often wish they would check in more often -- both more often chronologically and more often in terms of steps of their own thought process. I've had so many meetings where it turned out that students were spinning their wheels for 4-6 weeks on something that gets cleared up immediately upon meeting: either I resolve the point they're stuck on (there is no shame in that, by the way; I would much rather a student spend three months on a problem, getting stuck every so often and allowing me to unstick them than spending three years solving the problem completely independently) or they misunderstood what I told them and are going down the wrong track or it turns out that what I suggested definitively doesn't work.
The point is that getting help from your advisor -- substantially and often -- is much of the value gained from being in a PhD program at all. You should not at all feel embarrassed about asking your advisor for help. Instead you should work on asking for help in a way which shows knowledge and professionalism: don't just say "I'm stuck." Explain where you're stuck. Better yet: when you leave any meeting with your advisor you should have been given at least one specific thing to try out, and when you come back you should report on that (very small, usually) thing. If it worked...but seriously, it usually won't work, in which case you should endeavor to try to explain why it didn't work. Just coming and saying "I couldn't do this" to your advisor is not very helpful. At best, it is liable to elicit your advisor telling you what she thinks will work to solve the problem: this could be helpful...or she could solve the problem before your eyes.
Let me finally say that most thesis advisors I know have relatively poor ideas about the true difficulty of a problem and how long it will take a student to solve it. (To be fair, you can give the same problem to two students of ostensibly equal background and abilities, and very often one of them will spend months or years longer on it than the other.) An advisor who thinks that a problem is "quick" or "easy" probably means that it is quick or easy for her. Also, there may well be (and arguably should be, at least eventually) unforeseen difficulties. Finally, academics are famous for underestimating the amount of time it takes to do anything: the same advisor who is looking down her nose a little bit at you for taking several months to solve an "easy" problem may well have just sent an email explaining that her referee report will be several months late.