Seemingly simple solutions often have important underlying concepts which we tend to skip.
There is a fun logic riddle involving prisoners on an island. I came across it few years ago. A somewhat modified version of it can be found in this Ted-Ed video:
This riddle came up in one of my recent conversations with a friend, and it soon blew up into an intense and mind-numbing logical debate. My friend seemed to think that there is a fundamental flaw in the entire explanation. The simplistic solution given in the video didn’t satisfy him. Before long, we were breaking down the problem into various scenarios.
According to him, the induction logic broke down when we transitioned from 3 to 4. His arguments were quite convincing (the details of which I will skip, since they were ultimately wrong). For a long time, we were stuck in a phase — I would demonstrate how the problem made perfect sense from one perspective, and then he would ask me to consider his method of deduction which made everything seem chaotic. Neither of us could readily figure out loopholes in the other’s logic.
However, once the dust settled and both of us were satisfied, I realized that the simplicity of the puzzle had few intricacies hidden under it. It demonstrates how we might not understand a problem fully even after solving it.
Some relevant questions should come to mind:
- The outsider is not providing any new information. What is her actual role in the problem?
- Is the transition from 3 to 4, 4 to 5 (and so on) really as intuitive as it seems?
In any case, pondering over the seemingly simple solution provides some nice insights.