Can we stop the brain from processing a particular task? Imagine a task of high involvement and great complexity, but one that is not very important, e.g., a strategic computer game. Because of high involvement, the brain continues to process the problem to find solutions after playing the game. Because of the task complexity, I believe there is no right way to solve the problem, and the task is processed by the brain for a very long time but with no solution. The problem is absolutely non-important in 'real life' terms.

Is there a way to "tell" the brain not to process tasks anymore in order to prevent the uncomfortable feeling of having an "unsolved" task?

UPDATE: One of the commentators posted a good additional example of what may happen when your brain continues to process a task:

"A while back I played a game called diplomacy, which is very complex strategically. When I went to sleep that night, thinking about the upcoming turn, my brain was going through all possible combinations of turns and outcomes. One by one. For about 3 hours as I could not fall asleep because of this. While I did find the correct solution, it was quite unpleasant , non normal sleep."

I believe this one is the one of the most unpleasant results of an unwanted task processing. To some extent, a similar thing may happen during the day or even days after the task was "implanted" in the brain. It's just like in a middle of a day, you spontaneously start thinking about that task. So brain was processing that task all the time, it's just you were more busy with other things to not feel it and not start aware thinking of it.

Regarding night time task obsession, I was trying to focus on different things, lying with open eyes, aware thinking of something else, trying to stop the brain, but this doesn't help at all, only makes things worse (because you can't do anything). The solution I found is to not to go to sleep immediately, but to do something different or just rest (do nothing) for approximately an hour, you'll feel after that your brain is calmed a lot. This somehow diminishes that brain task activity and despite, you still may receive task thinking attacks, they won't be so severe, long and pressures.
One answer is through turning off these messages or "tasks" via mindful awareness and focused attention on another task requiring much less cognitive load - like breathing. 

Look up Dr. Jeffery Schwartz's book "You Are Not Your Brain" for scientific data on this.

Basically, latest scientific research shows that we can use our mind to stop the brain (or really work around the task, observing it, until it slowly diminishes activity in the bran).

It's the old saying; "mind over matter" - where the brain is also matter.