"Threes" in storytelling

Continuing to pick away at Christopher Booker's monumental work on storytelling: The seven basic plots.
His chapter on The Rule of three is particularly revealing. He outlines four (!) ways that threes are used in archetypal storytelling:

1. Cumulative three: each of the elements has the same value - all three have to be brought together in order for the plan to work. eg: the three treasure caves that Aladdin must go through before he gets to the lamp.
2. Ascending (or descending) three: where each is of more value (or more dangerous) than the last. This is a natural progression that leads to a climax. eg: Little Red Riding Hood's three questions: what big eyes, what big ears, what big teeth, or the three little pigs.
3. Contrasting three: where two of the three are there to give counterpoint to character or gifts of the third. eg: two ugly sisters are the contrast to Cinderella.
4. Dialectical three: This is the most sophisticated, where the first two are wrong or flawed for different reasons, before the best, or middle way is found in the third. eg: Goldilocks - the bears' porridge, chairs and beds, where two are tried and found faulty for different reasons, before the third is found that is just right.

This threeness finds its expression not just in story devices, and character interplay, but also in terms of the whole action of the plot.