Experience Report

One evening, my mother asked if I was interested in a puzzle. It was “22 + 4 = 2”. I received no further information or clues, nor was there a specific question attached. The equation was easy to remember, so I found myself spontaneously pondering over the next few days what the puzzle meant.

I was curious about the solution and probably motivated just by that. Had I been standing at the board in school needing to come up with something quickly, I would have just turned red.

I tried all sorts of things. It was a wild train of thought without knowing what I was doing. Suddenly, football came to mind, as there are a total of 22 players on the field, plus the two coaches, and also my mother’s boss, who had given her the puzzle, was a football enthusiast.

While working at a distribution hub for the ALDI supermarket chain, I observed all sorts of objects within my field of vision. Sometimes, I watched the forklifts go by, and at other times, I looked at pallets full of buttermilk. I even searched my work clothes for clues. Finally, I kept thinking about various fields of knowledge, like literature, science, movies, series, etc., hoping to be inspired somehow.

After several days, I had given up. I had resigned and was completely relaxed again, going about my routine. Around noon, my gaze fell on a large wall clock because the radio was not playing, and I had neither a cellphone nor a wristwatch with me: On the dial, the three on the right, the six at the bottom, the nine on the left, a little higher up the ten or in the evening as twenty-two and four hours later, after midnight, thus on the next day, two o’clock at night – that was it!

The solution made sense. Checking with my mother seemed completely unnecessary. I was unusually satisfied and cheerful and quickly sought out a coworker to ask if he wanted a puzzle.

The next day, the euphoria had long faded. Instead, I was disappointed and even frustrated. All those years of learning, in kindergarten, school, university, etc., and all the knowledge from books, movies, and series – and then I was confronted with a kind of children’s puzzle and had no idea what to do.

This experience report superficially shows how my problem-solving process went. Back then, I was relatively inexperienced, proceeded unsystematically, and without special methods. Maybe someone can recognize themselves in this?


Analysis

Let’s now examine the experience report! In doing so, we uncover the underlying processes and gain a better understanding of what happened.

Task vs. Problem

A flat tire is annoying, but most people roughly know what to do; the basic steps to change the tire are somewhat known. Needed are a jack and a tool to loosen the screws, etc. Yet, many find the change very problematic and prefer to call roadside assistance or go to the workshop. If the steps from the current state, the flat tire, to the desired state, the changed tire, are known, then we speak of a task. With the puzzle “22 + 4 = 2”, however, I had no idea what to do. I wasn’t even properly aware of what was expected of me, except maybe to provide an explanation. The transformation to the desired state was in the dark, and therefore it was a problem. If the steps from the current state to the desired state are known, it is a task, otherwise a problem. Of course, this is relative and not immutable; what is merely a difficult task for one person is a problem for another.

Motivation and Stress

It is not an exaggeration to talk about motivation, even with seemingly insignificant things like a small puzzle. In fact, just such small challenges can provide important insights into our psychological and creative processes. While certain activities like walking, running, or peeling potatoes can indeed be performed almost automatically and without much conscious effort, creative processes require a different kind of engagement.

The underlying unconscious processes required for creative thinking need to be activated, and belief in success plays a role like a spark. My own curiosity and optimism provided the necessary drive, even though I was excited and under stress. When this stress subsided because I had given up, I could think more freely and found the solution. It is true that under high pressure, creative thinking often suffers, and this can lead to blockages or avoidance behavior.

When it comes to dealing with stress, it usually means developing strategies to reduce stress, not necessarily to work more creatively under the same level of stress. It is a misconception to believe that someone can perform better creative work under the same stress level. Instead, it is about learning how to optimize the conditions for creative thinking, which often involves reducing the perceived pressure.

Brute-Force Method and Trial-and-Error

A bicycle chain with a number lock and three digits as the code is cracked at the latest on the thousandth attempt. Starting at 000, one reaches 999 on the thousandth combination. If a website password consists of three digits to be guessed and a hacker has an unlimited number of attempts, then access is achieved in fractions of a second.

Computers are particularly good and fast at this kind of unsystematic trying out of all possibilities. And I used this so-called brute-force method, this mindless trying out, this thinking of all possible things and jumping from one thought to the next, first and unfortunately without success. I didn’t know any better. Indeed, I also switched to the so-called trial-and-error method, which bears some similarities to the first method. It is based on repeated learning from mistakes. In a maze, I would choose directions at random at crossings, go back at dead ends and change direction, exclude wrong ways and thus gradually approach the exit. With the brute-force method, I would systematically try out every possible route without adaptive learning from previous mistakes, and then only accidentally find the exit at some point. We already see that neither of these methods works particularly well in solving puzzles, i.e., problems. At least I would use them consciously only very limitedly.

Analogy Principle

Most people probably search Google for help with their difficulties. They wonder: Has my problem or a similar one already been solved and can I transfer the solution to my situation? Alternatively, they search their memory for similar situations or challenges and try to make a connection to the present.

In a maze, for example, I might remember a previously conquered maze and that I always walked along the right wall there. Or I might recognize a known structure or pattern, like a tree diagram. A story could also inspire me, like that of Theseus and the Minotaur, where a thread is used.

On my journey through the warehouse, I may have compared about a hundred objects and looked for similarities. Likewise, when mentally sifting through various fields of knowledge, I searched for parallels.

Invariance Principle

When my gaze finally fell on the wall clock, of course, it did not show 22 o’clock only to then jump four hours to 2 o’clock. But I saw a variation of my puzzle, for it would be permissible and as a puzzle only insignificantly changed if asked about the meaning of “23 + 2 = 1”. Sometimes permissible changes of some parameters of a system make us aware that certain things do not change and these invariances can provide insights into the entire system. Incidentally, Einstein originally did not speak of the theory of relativity but of the invariance theory of light. The fact that the speed of light never changes provides insights into how space and time work. In the example of our puzzle, the practiced problem solver might ask for a variation of the puzzle. The invariance here lies in the way time is treated cyclically: after 23 o’clock follows 0 o’clock, which is the case in variants 1 and 2. If there is already a suspicion regarding this rule, then it is confirmed in variant 2.

Enlightenment

When I found the supposed solution, only my feeling told me: Yes, that’s it! It was as if a ball rolls on a flat surface into a small hollow and stays there, and the previously indifferent state suddenly becomes stable. The unexpected euphoria was rooted in the intrinsic reward. Both, the unfounded certainty and the positive mood swing, are typical for the successful completion of a problem-solving process.

Correction of Self-Image

The small puzzle made it very clear to me that I was not as smart as assumed. It showed me that I had previously mostly completed tasks and was not well prepared for dealing with real problems. Like most people, I used only two or three thinking tools. The crucial thing is that I have 22 tools available just from the field of heuristics for solving quantifiable problems.


Summary and Motivating Outlook

Let’s summarize the insights from my problem-solving attempt and give a motivating outlook:

  1. With tasks, the solution path or the transformation from the current state to the desired state is known, but not with problems. If I don’t know what to do, it’s probably a problem.

  2. Puzzles and general problems can hardly be solved mechanically; they require motivation, firm belief, or confidence. Stress inhibits creativity, while relaxation or even a certain indifference promotes it.

  3. The brute-force method is well suited for computers and cracking passwords but less so for solving problems. With the trial-and-error method, we get further.

  4. With the analogy principle, we look for already known solutions and thus transform problems into tasks.

  5. With the invariance principle, we introduce permissible changes of some parameters and observe whether parts of the system do not change and what they can tell us about the functioning of the entire system.

  6. We humans can effectively compete with a beaver in felling trees by using a tool like an ax or a chainsaw instead of relying on raw physical strength. Just as we cannot compete unprepared with an eagle in energy saving per kilometer traveled unless we use a bicycle. Similarly, in the realm of thinking, numerous tools are available to us that we can learn quickly and easily to significantly improve our problem-solving ability. This allows us to influence our mental potency ourselves and overcome previously seemingly insurmountable intellectual obstacles.

Go to: Learning Platform (LMC)