I think perhaps the solution to every problem is trivial, if only you know the domain in which the solution lies. Of course determining that domain is the hard part of finding a solution. Two examples from the newspaper led me to this hypothesis.
One is the crossword puzzle in the daily paper. Once you get a sense of the types of words they tend to use, you can more quickly and easily solve a puzzle. For instance the words Era and Eon appear frequently. Once you know this, any clues that remotely result in one of these words makes the puzzle easy.
Another is the puzzle for children in the comics section that asks you to find six differences between two similar scenes. Once you realize the types of differences they mean, it is very easy to solve such puzzles. For instance someone’s arm is slightly bent, or their hair is slightly longer. On subsequent puzzles you simply look for similar kinds of differences.
These solutions seem to lie in particular domains, such that once you stumble upon them, the problems are easily solved.