12 Balls

Ben Heim
4 min readJan 17, 2022

For the past few years, a close friend of mine has been trying to get me to solve a logic problem: you have 12 identically looking balls and a scale. One of those twelve balls is either heavier or lighter than the other balls (you don’t know whether it is heavier or lighter). What’s the fewest number of weighings to unequivocally determine which ball is a different weight and also determine whether it is heavier or lighter?

This problem killed me. I admit that I spent about 90 minutes playing with rocks (to represent the balls) on the side of my street trying to solve it. Alas, eventually I cracked the code.

https://www.popularmechanics.com/science/math/a26259/riddle-of-the-week-25-pool-ball-problem/

Finally solving the problem was satisfying. But, even more than the solution, I enjoyed the pursuit. Creating postulates and running different scenarios was fun. It tested my mind to take on new perspectives to get at the problem. And it made me wonder what makes a good problem solver a good problem solver? Are there certain traits that help you find solutions and can those traits be trained?

Before revealing how we can improve our problem-solving skills, let’s tackle what problem solving even is.

In general, problem-solving skills assist in finding out 1. why an issue is happening and 2. how to resolve the problem. Many sources also tried to ascribe a process to problem-solving. However, I think the linear structure these systems apply to problem-solving falls short of grasping the nuance of true problem-solving: a messy, unpredictable pathway characterized by sporadic regression, pauses, and progression.

Some google searches revealed that most people treated this problem solving concept as a nebulous, distant, unsolvable riddle. If there was any reason that some problem solvers excel while others fail, the best way to ostensibly discover why was to rely on intuition. Yet, there were one insight that I walked away with that I found both empirically supported and intuitive. And the answer is found in distance.

How Distance Accelerates Creativity

Construal Level Theory (CLT) argues that anything we are not doing here and now is psychologically distant. So, a problem that we are actively trying to solve has little psychological distance (PD). Its effective PD is 0. It’s right in front of our minds. A problem that someone is having in another state is very psychologically distant. You may have heard about it on the news, but it takes up little to no space in your mind. Its effective PD is much higher than 0.

Researchers in CLT suggest that we can induce psychological distance by attempting to take another person’s perspective or thinking of something as if it is unreal. In these scenarios, despite the problem taking up mental space, the fact that we aren’t engaging with the problem or experiencing it at the moment means that it has a significant psychological distance. Surprisingly, psychological distance has a distinct relationship with creativity: namely, when we increase psychological distance, our creativity also increases.

Jia et al. from Indiana University discovered that making problems seem farther away than they actually are increases creativity when approaching the problem. The researchers used insight problems (these problems are solved with an ‘aha moment’) to show this relationship. They provided participants with these insight problems and either told them they were developed at a research institute in California (2,000 miles away) or in Indiana (where they already were). Those who were told the questions were developed in California solved more problems than participants who were told they were developed in Indiana. The same relationship is found when relating to temporal distance.

Taking a distant approach to a problem will enhance your creativity in solving it. This may example why walking away from the source material (such as a tough math problem) may induce you to find new solutions.

This relationship also suggests the importance of asking for help from others in solving your problems. In Barbara Sher’s Ted Talk, Isolation is the dream-killer, not your attitude, she enumerates several examples in which sharing your dream with other people bolstered others to share what they could do to overcome the obstacle and achieve the dream. She suggests that you present your problem and obstacle. Immediately, human minds start trying to solve your problem.

Not only may these people have significant information to solve the problem, but they also have the psychological distance to enable abstract thinking for solve the problem.

I don’t really think either of these pieces of advice would help on the 12 balls problem. Yet, the steel balls are so far from reality that maybe it doesn’t really matter. When it comes to real, consequential problem-solving, the best thing to do may simply be going for a walk or asking for help. So, stop grinding and get outside.

--

--