How to make writing engaging?

One of the most engaging book genres are recipe books because you only refer to the book when you have a goal in mind (to cook something). However to bring about two engagement factors through writing alone can be difficult, and takes some skill. Someone who manages this quite well is Douglas Hofstadter. Here is a quote from the beginning of Metamagical Themas:

In the following sentence, the Epimenides quality jumps out only after a moment of thought: "This sentence contains exactly threee erors.",

He gives both a tool (by prompting you to think about it) and a space (the example sentence). This creates curiosity and may lead the reader to count the number of errors, realize that there are only two, then understand that the third error is that there are only two errors. Throughout many of his books he creates curiosity and engagement by providing both a space and a tool to explore it (see: Engaging mediums encourage thought)

While Hofstadter often inspires curiosity, the combination of each two pairs of engagement factors will likely create different forms of engagement.

Questions

• Examples of each of the Three approaches to engagement through writing?