I'm not sure the title of this question is the best one - feel free to edit it - but I have a question on puzzles in general:

Most puzzles I know (and surely most puzzles on this site) fall into the category of

rational puzzles

By this I mean, that one can use rational thinking and reasoning to find the answer.

As such, mathematics can act as puzzle-language and is most often an excellent tool for solving them. Where analytical maths can't help, numerical maths aka brute-force 'simulation' via programming comes to the rescue.

But there are surely also different categories of puzzles:
One, I can think of, are

knowledge based puzzles

These puzzles require that the solver has a certain specific knowledge, and only in this context the puzzle becomes solvable. Without that knowledge, the puzzle appears arbitrary and ill-defined.

A lot of riddle-type puzzles with very specific, topological hints (i.e. certain music groups / actors /...) fall into this category. (Google to the rescue!)

But if you think of it, also any Chess-puzzle without specifying the rules of Chess would really be of this category. The same for most/all cryptographic puzzles. ( A Ceasar cipher is not logical in any way! )

Those two examples are generally accepted on this site, because the required knowledge (such as Chess rules or how to use Internet searches) are assumed to be general knowledge.

But this category would also accommodate more obscure examples, and I wonder of the fate of such puzzles on this site.

Example: Historic paintings. Those paintings often used symbols with very, very specific meaning which could encode a message or puzzle very nicely. People of that period and culture (or historians) would see, understand and appreciated the puzzle - and they would firmly believe there is a unique and clear solution to them.

There are, in fact, a lot of different expert-knowledge requiring puzzles, if you think of it.

This now leads me to my actual question:

What other general categories of puzzles do exist?

In particular:

Are there any puzzles which are not based on rational (left brain) thinking, but on creative / associative / emotional (right brain) thinking?

Can you give an example?

If they exist, how can you proof the solution is correct? What does correct mean in this context?

If this all sounds a bit too philosophical, well maybe it is.
But it is a genuine question and interest of mine, and I hope I will get some good, thought-provoking answers.

The question somehow came to mind out of observation: I consider myself a "left-brain" thinker, i.e. when I see a problem, I first try to apply some logic/rational thinking to it. And I enjoy it.
But I know a lot of people who do neither enjoy, nor think about problems this way. But it's exactly this group of people, which in other types of "puzzles" (/riddles/associative guessing games...) quickly find answers/solutions I wouldn't have dreamt of.

I was hence wondering, how one would best build a puzzle customized for such people.

  • $\begingroup$ Was [puzzle-logy] intentional, or was it a typo? $\endgroup$
    – user20
    Commented Dec 30, 2014 at 23:17
  • $\begingroup$ It was intentional (sort of), as I was lacking a better suitable tag. I've suggest a tag-wiki, but I'm in no way 'attached' to this tag. If someone could came up with a better, it would be fine with me. ( puzzle-research seemed too academic and misleading in another way. ) $\endgroup$
    – BmyGuest
    Commented Dec 31, 2014 at 8:50
  • $\begingroup$ All questions on Puzzling.SE are, by definition, about puzzles. So that tag is completely unnecessary. $\endgroup$
    – Doorknob
    Commented Jan 1, 2015 at 15:57
  • $\begingroup$ @Doorknob冰 while the tag might not have been the best one, just removing it didn't do much good neither.This question is not primarily about puzzle-creation, so it is now clearly missing something. But I'm going to post this separately on meta... $\endgroup$
    – BmyGuest
    Commented Jan 1, 2015 at 19:28
  • $\begingroup$ @Doorknob冰 see this meta-post $\endgroup$
    – BmyGuest
    Commented Jan 1, 2015 at 20:29

2 Answers 2


This is a very interesting question.

http://www-sre.wu.ac.at/ersa/ersaconfs/ersa14/e140826aFinal01568.pdf is an example of serious research surrounding what the authors call "relation logic" or "relational logic" - see p. 15 or p. 29 for examples. The idea is that a puzzle (which figure doesn't belong?) can be answered in different ways by different types of thinkers, and the paper draws a distinction between what you call left brain and right brain types as categorical vs. relational thinkers. It also relates back to Nisbett's theories on "geography of thought," suggesting that difference in ancient Greek vs. ancient Chinese logic have persisted through today creating Western vs. Eastern thinkers that somewhat align with your left and right brain ideas. According to this theory, Westerners are supposed to be more categorical by thinking of items in terms of their individual attributes, while Easterners are supposed to think in terms of relationships between items placed together.

Whether one puts a lot of stock in these ideas, they do suggest a possible way forward for puzzle design - if you're more of the left brain, Westerner-type, then you would do well to steep yourself in puzzles of "Eastern" origin. This seems to me to be the idea of fuzzing one's eyes to look at the whole - don't focus on individual pieces and try to get them to fit together, but look at clues as a whole as see if they remind you of any systems or relationships (familial, predator-prey, religious). For instance, a man with 12 followers, or a man, woman, and child, or a hammer and nail evoke certain contexts on their own, regardless of the details of the individuals or things involved. Correctness comes from the solver repeating the same relationship that was originally intended, or at least that can answer all the available hints in the puzzle.

I think you're right that uniqueness of the solution becomes harder to pin down in these cases - the paper I mention actually uses disagreement about the correct solution to a particular problem as its main measure of types of logic employed. Perhaps working backwards from the solution will ensure that all clues foreshadow correctly, or certain clues that are so exacting as to rule out close misses by narrowing down the possible relationships between items? Nonetheless, there are many examples on this site of multiple answers to a single riddle where some solutions fit closely but not exactly with the writer's intended solution. Experience seems a valuable guide in pinning down what uniquely defines a relationship to different people.

I hope there's something of use in this long response for you. A very interesting topic to think about, and I'd love to hear more of your own thoughts on the matter.

  • 1
    $\begingroup$ Thanks for extensive answer. Another piece of information for me to think about for a while. I very much like the two odd-one-out examples in the paper. Your answer in particular reminded me, that psychological papers might be a good source to look through for interesting puzzle ideas. $\endgroup$
    – BmyGuest
    Commented Dec 31, 2014 at 8:47

I heard about the following example of non-rational problem solving.

A dog holds a stick in his mouth. He wants to pass beween the bars of a fence. How can he do it?

I am sure you can explain the solution in very rational terms. But the way people find the solution is by just "seeing" the solution.


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