Ever since I struck out on my own, I have done far more job interviews and storytelling than my entire carrer thus far. Most of the interviews for development and testing contracts are talking through problems. You must tell a story, as this is how people internalize your attributes and form emotional investments. I can talk about the lessons I have learned or the design of a thing until I am blue in the face, but it won't matter unless people know where they come from. This is because people don't engage the predictive engine in their hindbrain if you don't tell a story.  People don't get into camshaft thinking (imagination) without emotionally investing in knowing how it works, and as such are in "internal monologue" mode.  A story is the only thing this mode of thought can comprehend or output, and is a necessary prerequisite to get into the mode of thinking where imagination "fills in the blanks".  By the time they get there, diagrams and so forth are unnecessary unless you are interested in mass production which comes for free with software.

When you tell a story, people "think past the sale", and start to see themselves doing business with you unconsciously. If you don't tell a story, people default to their lower consciousness which is stimulus-response. In this case, if you aren't attractive from a "mode 1" (judging a book by it's cover) point of view, good luck. For knowledge work, this is only the case for established intellectuals with some degree of fame. This is why everyone has to do this "online brand" thing; eventually somebody fishing will see you in the net and haul you in.

That said, your online brand can only get you in the door. From there people in the knowledge trades have an innate skepticism beaten into them via the scientific method. This has to be overcome, and the way this is usually done is by telling stories which the interlocutor identifies with. The whole goal is for both the interviewer and evaluator to be congruent with what each expects from the other. This is why it always ends up being the senior development staff that does the heavy lifting here. They've heard this story enough times to sniff out the little details that break them out of their suspension of disbelief (also known as "benefit of the doubt"). This has a high rate of success, as it is difficult to fake having reasoning skills, and being able to practically apply them. It's also difficult to fake the little details which we encounter in the course of our daily toil. Difficult, but not impossible.

I remember setting up those little programming puzzles on hackerrank for the candidates to chew through. My colleague who was working on this with me on it at the time had some anxiety as to whether they were being specific enough in the description of the problems. I thought of how the application process ought to feel both to the applicant and evaluator in order to maximize the potential they can show and give ample opportunity to display their deficiencies. The job-seeker's story is supposed to be a gauntlet of increasing difficulty, hopefully revealing the core qualities needed in our work.

In that vein, I suggested we nail down problem 1 as well as possible, while leaving the second vague. This gives people the ability to show both how efficiently they operate when things are concrete and how quickly they pick up on our "trick" question which is ill-defined and start giving us options. The two hardest problems in software are choosing optimal algorithms and reducing vague requirements into concrete, testable execution constraints. Everything else is straightforward testing, investigation and annealing.

This is not to say that software organizations don't have other (mostly logistical and marketing) problems to solve, but that these are the core ones of interest to engineering. As an interviewer you have to lead the horse to water and see if they'll drink. The interviewer should focus on getting them interested enough in their stories that the evaluator shares some back. Reciprocity is the best sign of developing emotional investment.

You may have noticed I'm telling a story right now. It's uncanny how well this works on you even when you know how the sausage is made! I've been on both sides of the table when it's clear that "they know you know, and you know they know" based on the responses. In these cases breaking the fourth wall is even more convincing of a story as it too is a story.

This is unfortunately a rarity on both sides. All the world's a stage, and we are merely players. A performance cannot truly be great unless both sides can believe it and find more significance therein than their reality! This is despite foreknowledge that it's a performance and not a demonstration. To succeed, one has to get fully sheep-dipped into the hyperreality you want to hop into.

On that note, I will be putting out a series of war stories soon both as practice for upcoming contracts and for your enjoyment.