“What is this,” I thought to myself, “another one of those silly internet arithmetic challenges?” At closer inspection, I could see it was more complicated than most of the others, as there were a much larger number of guesses in the comment section. There must be more than meets the eye. The challenge I was faced with has evolved over the years. It may have first appeared on November 30, 2017 in a tweet from People’s Daily, China (@PDChina) that posed this problem:
Eventually, I got it right, but it took me more than a few attempts. The problem captures the beauty of mathematics in general, in that math can be very frustrating at times. You need to pay attention to all of the details, and be able to keep all those details organized. After quickly solving for what a pair of shoes, a cat, and a pair of whistles all equal, you begin to plug them in. Then you all of a sudden notice that we’re multiplying instead of adding on the last part… are we supposed to do that first? Oh, and wait, there is only one red whistle. The problem that it has evolved to is only slightly more complex. See if you can see why the answer to the above problem is 16.
Using mathematics to solve problems has taught me much about life. There are some problems I cannot solve, no matter how much time and effort I put into them. Some problems, if there is not a mentor to guide me by telling me I’m getting closer or if my thinking has begun to go off track, I eventually have to look at a solution to see where my reasoning went wrong.
Indeed, I remember walking into my would-be thesis advisor’s office after we received a difficult test back in order to work through a test problem. He had an uncomfortable look about him, because he was having to give me an A- for the class rather than an A. I recall being baffled, letting him know I didn’t give a shit about the grade, I just wanted to know how to do the problem. He was both relieved and impressed. I had tried to convey this mentality to my students over the years once I became a professor.
Many of my students I’m sure would be frustrated with me on a certain level. I wrote many of my own problems, which means you could only succeed at finding a problem similar to it if you resorted to Google. I’m just as guilty of resorting to Google to get quick answers from time to time. However, I feel that I rise above mediocrity when I dive into a problem with my mind, instead.
There are all kinds of problems that arise in our life that we can’t simply find an answer to by using Google. The Stoics teach us that we should prepare ourselves for these obstacles mentally, and rather than view them as in-the-way, simply accept them as the new path that you have to take.
When obstacles arise in our path, those that have developed their problem solving skills will rise to the top and lead us through that obstacle, which is most likely present as a result of those that are only interested in the answers.
It is unfortunate that many of our leaders are those that are only interested in answers. It is even more unfortunate that they not only cause more obstacles to present themselves, but then take credit for any of the solutions that the real problem solvers provide while pointing blame to others for the obstacle in the first place.