Here is the first verse of the poem Kubla Khan by Samuel Coleridge:
In Xanadu did Kubla Khan
A stately pleasure-dome decree:
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea.
There are an amazing number of patterns and connections within this verse. There's the rhyme, of course. There's the fact that it scans. There's the eerie harmony of all the imagery. Less obvious but no doubt contributing strongly to the poetic effect is the subtle alliteration at the end of each line: Kubla Khan, dome decree, river ran, measureless to man, and sunless sea. Another non-obvious aspect of the poem is its consistent rhythm: the repeating pattern of short syllables in the pattern of "in Xanadu". If you imagine beating on a drum for each syllable, it comes out musically "right", with that same four-beat rhythm all over the place: It also appears in "did Kubla Khan", "-ly pleasure-dome", and more.
How could a mere human mind pull together words from the vastness of the set of all available English words and all the possible ways of combining them (a set that includes everything there is to say), into such a harmonious order? As every school kid who's tried to write a poem knows, as you try to get the rhyme to work, you usually mess up the meter; if you fix the meter, you break the rhyme; the meaning often suffers while you work on the other aspects; when you fix the meaning, you break something else; and so on. How did Coleridge manage to find a combination of words that fit all of these criteria at the same time?
That, friends, is the subject of heuristic.
It seems clear that if you sat down with a dictionary looking for words that fit together so well, you could not possibly put together the first verse of Kubla Khan in any feasible amount of time. The number of words and ways of combining them is just too vast. Some people use a rhyming dictionary to help them write poetry. This is indeed a resourceful heuristic move: to find a word that rhymes, you need only look on one page, and that page will include all the words that rhyme with a given word. This is a classic search space reduction. But if you've read a poem after it's been manufactured by someone who depends solely on a rhyming dictionary and doesn't bother to relate words to one another, you'll discover it is easily forgotten.
Somehow, to write a poem like Coleridge's, you'll need to be able to search by many, many factors all at the same time. One would have to weave words like a weaver threads a tapestry on a loom. How it could be done defies our best understanding of computer science to this day.
Coleridge himself told how he did it, though there is some evidence to suggest that he wasn't being entirely truthful. He said that the poem came to him whole in a dream that he had after he took some laudanum. When he awoke, he immediately began writing it, as we know it today, from memory. He stated that there was more to the poem but the rest slipped from his memory. This suggests that there wasn't any in depth re-writing and editing done, as is common with most literature. This story seems unlikely, yet, as it happens, the myth has out lived the facts. The myth is fact. But this fact is not a tangible marker to extrapolate a universal strategy from this poem.
As far as heuristics is concerned, it demonstrates how vast a puzzle can extend itself: almost beyond the hand of man. Almost, but not quite. Since Coleridge's only strategy appears to be that of intangible serendipity, it is certain another happy accident will happen without knowledge of the when and where. At least, not without scientific observation.