Clickbait title: Not everyone can make good puzzles.

I don’t know how common this experience is for other’s who have “always been interested in maths”: All my life, people who wanted to gift me something have defaulted to puzzles. Sudokus were probably the most popular. I don’t think I ever solved a single Sudoku in my life (maybe as homework at age 7?).

I do not want to sound ungrateful for any gifts I received (despite my generally low opinion of gift giving as a mandatory tradition), people put in as much as effort as they could bear to give me something. And for a lot people I think mathematics looks very similar to “logical thinking puzzles”. But my interest has always focused on the former, whilst disregarding the latter.

Puzzle authorship

The main distinction I like to draw between mathematics and puzzles is one of authorship. Mathematical problems spring forth from the general construction of mathematics, and are often the most satisfying to solve at an immense level of abstraction. Puzzles, especially as a commercial product, tend to have a specific direction in mind to be solved. They tend to aim for an “ah-a” moment, the good ones at least.

So the puzzle’s quality basically relies on the author. I find most puzzles to be an exercise in trying to read an author’s mind. You can solve a lot of medium-quality puzzles by just thinking “what would be the coolest thing to happen right now”. Low-quality puzzles tend to have the solution be completely arbitrary. High-quality puzzles are subjective, but in my opinion tend to push into the realm of mathematics.

General Audiences and Effort

Pushing more into acknowledging mainstream puzzles as products: They tend to try and present a “challenge” for anyone looking at them. This means they often create some sort of arbitrary system of rules. If everyone knows Sudokus, how dare you make a system that reminds people too much of Sudokus, because then your friend who is good at Sudokus is not sufficiently challenged.

Now, I don’t want to imply that puzzles are purely made something you can use to torment your friends with. There are people who really like puzzles as a mental exercise. My personal problem is that I see little use in any mental exercise that an algorithm can solve for me. It feels like wasted effort.

Sudokus lost basically any appeal they had left for me when I learned about SAT solvers. The only question left to ask really is if you can make a specialised solver just for Sudokus that is faster than a SAT solver. But I think an average person would still complain that I “let the computer solve it for me, instead of putting in the effort”. Probably me inventing a straw-man.

Intelligence

Let’s talk about chess. Chess is solvable, computationally. It is a combinatorial game, so theoretically there is a set of moves that always wins (disregarding repetition rules that can force draws). But of course we don’t have big enough computers to compute that perfect solution, so it remains an interesting problem, for all of humanity.

The best way I’ve seen someone describe why they dislike chess revolves around the cultural baggage attached to the game. In pop culture chess is seen as an intellectual battle to the death. (Actual chess players will of course tell you that it’s mainly an acquired skill.) The pressure of these expectations, especially if you’re around “normal people” will make the evening stressful rather than entertaining.

So why is chess such an easy short-hand for intelligence? Mainly market-penetration. People know the rules of chess and have played it themselves. Plus the combative nature of chess means that it’s somewhat “measurable”, there’s no way for someone to weasel themselves out of having lost a chess match (I am not going to write you-know-what here).

As this is my article I will assert here that I am very shaky on any existence of some sort of “fluid intelligence” (vs. crystallised intelligence). So I find any sort of tests devised to measure it dubious. But I think even someone who disagrees with me on that, accepts my complaint that something as specialised as chess is a stupid measurement of intelligence of an average person. Why? Because chess just measures how good you are at chess. This is what makes it “just a puzzle” to me. (Whereas the efforts of writing good chess robots interest me very much, as long as they sideline chess-specific considerations)

Competition

I think the main reason that puzzles remain so relevant is accessibility. But an underrated reason I think is because a lot of people see mental achievement as a competition. I think school and grades are mainly to blame for this. Being able to pick out a specific instance of a generalised problem and letting people compete against each other is exciting. A published algorithm that can solve the problem in any configuration less so. Plus verifying the algorithm by intuition is probably impossible for the average person, whereas verifying a specific solution can be quite easy.

What I find sad about this is the fact that it sidelines the important part of science: cooperation. Abstractions tend to very good tools to create further abstractions. The library of mathematical theorems created by humans may be the best example of this.

Finding the solution

Zooming back in. When I am given a puzzle, I tend to think of it as a conversation with the author. Except I probably do not know the author, so it might just be that they’re talking nonsense. So when I am failing to solve a puzzle, I sometimes think “maybe it’s not me, maybe this person is just talking gibberish”. The answer is of course often that no I just haven’t followed the signs they have given me. I am not smarter than most puzzle authors.

If I am working on an “unsolved problem”, not that I’m actually high calibre enough to handle important unsolved problems, I have nobody to blame but myself. And my selection of a problem. And if I dislike the problem I can move on. If I move on from a puzzle I feel myself being judged from the outside as not being able to solve something that objectively has a solution.