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I want to develop a difficult--but also fun and memorable--puzzle, but I'm not sure how hard is too hard. I don't want to post it and everyone just think it's "confusing." You know, Einstein once said

“If you can't explain it to a six year old, you don't understand it yourself.”

I believe a good Einstein-ian approach to the writing of puzzles is the correct form when trying to win an audience with mixed levels of understanding, but how do you balance wanting to post a hard problem that will bring something new and fulfilling when solved and also be able to explain it in a way that a six year old could not only understand, but not be bored with the notion?

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For what it's worth, this has always been a concern for me. I decided to write a bunch of puzzles aimed to be kind of medium difficulty. The idea was to write quickly, without spending too much time on any one puzzle so I could get a feel for what was hard and what was easy and develop my puzzle writing skill at the same time. I thought after I had that figured out, then maybe I would go for something complex and ambitious.

It's been a year and a half (I think) and I still don't have it figured out but I do have some ideas:

  1. Multi-step puzzles are exponentially harder than single-step. Structure them so that it's clear what the solver is supposed to do next.
  2. Don't be hard in more than one way at a time. If working out the solution is difficult, (say there is a bunch of calculation needed) then be as clear as possible what type of puzzle this is and what sort of solution you are expecting. Contrariwise, if you have an enigmatic type of puzzle, it's best to have something that will be obvious as soon as it flashes through the reader's mind.
  3. Originality is good but don't be shy of borrowing. Have a look at some puzzles that are like yours in some way. How quickly were they solved? What did people come up with in partial solutions if there are any? What kind of clues or hints did the composer add that steer the solver in the right direction without giving it away?
  4. Instead of six year olds, talk to some people who are not that much into puzzling. Don't show them the puzzle, ask them what they think about the idea of the puzzle. I find that if you show them the puzzle, they want to solve it and get frustrated when they can't. If you show it and explain it immediately, then it's like saying you don't think they are smart. Instead, say something like: what do you think about a puzzle where I describe my travels and then ask what my name is and it turns out that if you draw the route on a map you've written a name? It's not infallible but it should give you some sort of idea whether people will feel satisfied when they get to the solution.

As I say, I haven't really figured this out myself but I hope this will be of some use.

One other thing that occurred to me later is that people are willing to put in a lot more work if they can tell they are making progress or if they have a very good idea of the type of thing they are looking for. The classic bad puzzle is a cipher: a string of numbers and digits followed by "can you decode this message?" Maybe the answer is a famous quotation, maybe it's a sentence specially constructed to have unusual letter combinations, or maybe it's "SHAQONEALFTW". Even if the coding method is not killer hard, it probably won't be solved because it could be arbitrarily difficult. If, however, you spin a story around it and say that the solution is a state capital then people will be much more willing to work on it. It could be harder than the first cipher but it is more likely to be solved because the reader has reason to expect that it is doable.

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What exactly do you mean by "hard"?

Puzzles that are challenging

There's absolutely no problem with this. We've had immense complex puzzles that take hours or days to solve, and they're usually extremely well-received by an impressed audience of voters.

As long as they're still doable, of course. Don't go so far into the realms of difficulty that you end up with a puzzle whose solution nobody could reasonably be expected to work out from the information given in the question. That counts as a "guess what I'm thinking" puzzle and is likely to be closed.

Puzzles that require lots of external knowledge

Then there's an entirely different brand of "hard". A puzzle might require extensive knowledge of algebraic topology or cell biology, but still not be very challenging for people who have that knowledge. Puzzles like this can also be on-topic, but might not be well-received. There's a fine line between a puzzle that requires advanced knowledge in some field of science and an exercise in that field.

In the specific case of puzzles involving advanced mathematics (which tends to be the most relevant for PSE), this has already been hotly debated a few times - see e.g. What tricky mathematical questions are on topic here? and Proposed policy on mathematical questions.

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