About

Welcome to my blog

The purpose of this site is to explore and solve as many of the problems from Ronald Hoeflin’s high-range intelligence tests and similar puzzles as I can, insofar as they genuinely interest me. Hoeflin’s tests contain a remarkable collection of mathematical problems, many of which are unusual in ways that I find especially compelling. Some are elegant mathematical puzzles; others require persistence, experimentation, or a particular insight. Even when a problem turns out to be flawed, ambiguous, or more complicated than it first appears, I find the process of investigating it worthwhile.

My fascination with Hoeflin’s puzzles began largely because problems of this kind are surprisingly rare and common at the same time. They are rare in the sense that not everyone on the internet is trying to solve them, and common in the sense that they are strikingly similar to those of the Great Martin Gardner. When I encountered these problems, I found myself wanting to understand not merely what the intended answer was, but why it was the answer, whether it could be proved rigorously, whether there might be a better solution, and sometimes whether the problem itself had been formulated correctly.

That curiosity is one of the main reasons this blog exists.

I am particularly interested in approaching these problems mathematically. When possible, I try to give complete explanations, proofs, alternative methods, and computational or combinatorial arguments rather than simply stating an answer. I am also interested in examining the assumptions behind a problem and distinguishing between an intuitive solution and a rigorous one. In some cases, this leads well beyond the original puzzle into areas of mathematics such as combinatorics, geometry, number theory, probability, logic, and discrete mathematics.

There is another important part of my story: English is not my first language. My English may occasionally be imperfect, but I want to communicate ideas as clearly and precisely as I can. I hope readers will bear with any linguistic mistakes while I continue improving.

My academic background is somewhat unconventional.

I completed my undergraduate studies in Natural Sciences before enrolling in a Master’s program in Applied Physical Sciences. Through coursework such as statistical mechanics, I developed a deeper appreciation for math. That experience gradually transformed my interest in mathematics from something peripheral into something much more fundamental to me.

I don't want to give a wrong impression. Since my master's thesis was directly related to advanced physics, although my main work resembled more that of a technician, I was advised to take courses that were compulsory for physicists, such as the one mentioned earlier.

Nevertheless, I was not able, for the most part, to follow the math that was being presented (simply because I did not have the required background), which at the time caused me a lot of frustration, but it allowed me to be exposed a little bit more to the methods and epistemological standards of this science. 

Eventually, I decided to follow that interest seriously. I intentionally left the Master’s program to pursue mathematics as my primary focus. Yes, I dropped out. It was not necessarily the conventional or safest decision, but it was a decision I made because I wanted to try to become a mathematician.

At the same time, I became increasingly aware of how many gaps existed in my formal mathematical education. Rather than treating those gaps as something to hide, I decided to start again from the foundations and learn mathematics more systematically. My own autistic perspective has also influenced the way I approach this process: I tend to become deeply absorbed in unusual problems, patterns, structures, and questions that other people might simply pass over. That way of thinking has been both a challenge and a source of fascination for me.

I am therefore currently pursuing a degree in mathematics, while continuing to study mathematics independently.

This blog sits somewhere at the intersection of those interests: mathematical problem solving, recreational mathematics, high-range intelligence testing, and the investigation of difficult or unusual problems simply because they are interesting. My knowledge of math is not that advanced, so whenever possible I privilege elementary solutions.

I do not expect every problem discussed here to have a beautiful solution. Some will turn out to have surprisingly simple answers; others may require substantial machinery. Some may expose ambiguities or weaknesses in the original formulation. That is part of the fun.

The goal is simply to explore them, solve the ones that capture my interest, and learn something along the way. I warmly welcome anyone to join the conversation—please feel free to share your ideas, questions, alternative solutions, or constructive feedback in the comment section.

I hope you enjoy exploring them with me.*

*I originally intended this blog to be a placeholder for the website I'm currently building to present a new high-range IQ test. However, I decided against that because I got disillusioned with "Hoeflin's approach to high-range intelligence testing" because of the epistemological problems it raises more than the typical statistical criticism of his tests (which I will explore in a future essay), and because of the advances in LLMs to solve many of these types of problems, allowing individuals to cheat. The website, however, will still be available for another purpose.