“they started by thinking and mentally designing”

Right, and that’s exactly what you can’t do in a typical hack-a-thon.

I have heard of companies that have done things similar to hack-a-thons, with two differences: 1. they last longer. A week, rather than two days, say. 2. they focus on fleshing out the idea, rather than trying to throw together a completed project.

In addition, these exercises are often geared towards developing ideas that could turn into viable long-term products/projects within the organization. To me, that’s a much more valuable approach than the frantically-churn-out-code variety.