One of the things that keeps my mind active is the daily Target puzzle:
E T A
A B D
R M O
Try form words of four or more letters from the given ones above (no proper nouns or plurals ending in S). Today's target: "29 words, good; 43 very good; 57 excellent" - that is, try to get half, three quarters, or all the words they identify from their dictionary (Chambers).
Of course, they miss a few words that aren't in Chambers, but for some reason they sometimes miss some common words.
I usually get the nine-letter word - but not always. Sometimes it comes to me as soon as I look at the set of letters; sometimes I work out a few of the smaller words, and it emerges from there. Sometimes, of course, I go for obvious prefixes, suffixes, or compound words.
But sometimes I have to actively stop seeking. I can't get it, so I move on to something else. Then I look back at it, and it can come to me immediately.
We've all had experience of that - and it's been confirmed as a specific neurological phenomenon, according to a letter published in New Scientist. It refers to a 2003 article in an American journal of cognitive psychology, the Psychonomic Bulletin and Review (specifically, v10 p730 - full paper here).
Well, that's not quite neurology. But they describe the conscious mind activating a wrong pathway, and that pathway being cemented in the mind, over-riding the pathway to the correct answer. Only when that process subsides can the pathway to the correct answer be activated.
Another correspondent notes that as an engineer, he encounters this so often that he deliberately sets himself design problems before he goes to sleep, and very frequently wakes up with the answer before him. He ascribes this more specifically to the amount of clutter inhabiting older peoples' minds. There is a strong inference that younger people are more likely to immediately either know the answer or not.