Two anecdotes that I claim have something in common:
Scene: me at office hours having worked on an algebra problem for 3+ hours.
TA: The solution involves matrices
Me: <realizes answer>
Scene: friend asking me for help solving a reasonably difficult CS problem that I don't know the answer to.
Friend: I tried X, Y and Z and nothing is working.
Me: Well, can't you just do A? Seems like it should work.
Friend: ...yeah that works.
In the example case, I already knew the solution involved matrices, but telling me "there exists a solution" let me solve the problem almost immediately. In the second example, someone was like "can you help me solve this?" and I figured out how to do it faster than I would have normally
The important part of the first example is that telling someone "there exists a solution" is implicitly telling them "there exists a solution and I expect you to be able to find it." The important thing about the second part is that asking someone to help you with something suggests that you expect them to be able to help.
It's all about expectation, you see.
When someone expects me to be able to solve a problem, then I start thinking about the problem in a different way. I go from trying-to-solve to just solving. I stop thinking about how I might approach the problem, and just start approaching it. I stop wondering about the tools I might need and just do the obvious thing.
To turn this into a technique, you need to figure out a way to reliably generate expectation for yourself. People's brains work differently - there is no reliable and consistent way that works for everyone. Sometimes, the standard resolve cycle can accomplish this for you. If it does not, there are other tricks to try:
1. Tell your friend that you're going to solve your problem in N minutes
2. Pretend your friend is the one with the problem and they're asking you for help
3. Pretend someone you trust has told you that your problem has a solution they expect you to be able to find
A caveat with this technique is that if you can't solve the problem after you've expected yourself to be able to solve it, then it hurts. In order to leverage your full power to solve a problem, you have to expect to solve it. The corresponding implication is that if you don't solve it, then you will feel the pain of failing to live up to expectation.
Try and find a method to generate expectations about yourself, then use it to solve one of the problems in your life in a shorter amount of time/effort than you would have otherwise.