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Ideas for posting good Logic problems

Recently, I've been asked by the some members of community on where do I get my questions from and how do I frame the questions. Here are some points that I personally find useful in making good Logic problems.

\(\text{1.} \)Everyone starts at a bad point

I believe that this is the very first Logic problem that I've posted, as you can see, this is not a good problem but everyone starts off with writing bad problems. This problem is not good because it lacks proper mathematical basis and originality.

The first thing to do, is to find problems that you really really like yourself and try to rephrase the question, even the slightest bit will do. For example,

Most of the problems I've posted are slight variations of the original one I've found. Take this problem as an example, I took a standard 2 beaker problem and turn it into a 3 beaker problem instead and tried to make the solving technique harder.

\(\text{2.} \) Find the root of the problem

After solving any problem you come across, you should always try to obtain the essence of the problem. That is, understand why its set up in that particular fashion, why the author chose one particular approach as opposed to the other. After you have done that, create a harder variation of that problem but still is able to engage the readers. Here are two examples which takes plenty of cases checking but is still simplistic enough to engage the readers.

Are you, like, a crazy person?, and Classic Futoshiki.

The main gist of the problem to be working on it to make sure your problem appears original and is not a ripoff from other questions, though there will times where you can't deviate much from the original question, and we're left with the something very similar. E.g: Rudiments of tallying?.

\(\text{3.} \) Finding the source of the problem

Most of the problems I've created was inspired from other platforms like AOPS, Reddit, puzzle books, Wolfram MathWorld, OEIS, heck in problems from Brilliant itself! But the main issue is not where I found it but I used the essence of the problem and develop out a brand new problem. There's no point in copying other problems you found elsewhere, unless the setup could not be deviated. To entice the readers, we can use other means like the title, picture, choice of words, etc.

Here are some of my favorite problems which I came across from other platforms and have been modified greatly

\(\text{4.} \) Framing the question

Take any problem you can find and identify the essence of the approach. Then, find ways to make his question more interesting. For example, can we generalize this? What happens if the constraints are altered? What is the main intention of the original problem and what follow-up questions could be asked?

Take this problem as an example. I've asked myself questions like:

  • "What if we add 0's into it?",
  • "Can we explore base conversion (which Ivan Koswara already got that covered)?",
  • "Can we go above 9?"
  • "Are you sure there is a unique solution to this variation?"

Note that most of the time, the questions I've asked myself are not posted in Brilliant, this is because they do not engage the readers anymore and it becomes really tedious/dry.

\(\text{5.} \) Do not worry if all your problems are not well received

Everyone got their own niche appeal when choosing the problems to engage with. You should not make sure all the problems you've post to be well received by the community, but it's better to provide a diverse amount of different problem to improve your solving techniques. This also does not give you an excuse to degrade the quality of the problem. I too, have created a few problems that I personally like but it did not do well with the community. For example:

\(\text{6.} \) Keep practicing

Like what Ivan says: "The best way is to try solving as many puzzles as you can". Eventually, you will know what questions to ask to make your problem more interesting.

By the way, please follow Ivan Koswara and Maggie Miller. They post very good quality problems as well!

If you have any question or feedback, please leave it in the comment section below.

Note by Pi Han Goh
1 year, 2 months ago

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Thank you! :) Nihar Mahajan · 1 year, 2 months ago

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Awesome view Joseph Bidias · 1 year, 2 months ago

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I wouldn't count Futoshiki as "heavy case checking". (My solution was fairly smooth with not much case checking, but then I'm more experienced in such puzzles, so I might be biased. Good puzzle by the way.) Ivan Koswara · 1 year, 2 months ago

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@Ivan Koswara Oh, I'm fairly new to this. All my methods are trial and elimination within trial and elimination. Like the Fillomino puzzle, I can't (or haven't) figured out systematic ways for approaching it. So I thought it's very tedious.

By the way, I've noticed that for problems with puzzles like Sudoku, Fillomino, Hidato, etc. The solution poster only gave the final output of the complete grid. Don't you think that users (in Brilliant) should provide necessary steps in identifying where the crucial steps are? Take this page as an example, I think that it's sufficiently thorough with its explanation but without going through all the necessary steps. Any thoughts about this?

Take the solution in this problem as an extreme case.

By the way, what other puzzles have we not tried in Brilliant? I reckon Slitherlink, but I don't see a nice / immediate way of framing the question. Any thoughts? Pi Han Goh · 1 year, 2 months ago

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@Pi Han Goh Re trial and error: As an experienced solver, I have several "laws" that I can apply instinctively, hence why I don't really think I did trial and error or such. Other people's experiences may differ, ence why.

Re solutions: I'm considering to put full solutions (walkthroughs, in a puzzler's terminology, since the "answer" is called a solution). It's a rather tiresome process, however. Just as an example, this is one that I wrote a few years ago; that's what you need if you want to be thorough. Writing walkthroughs to puzzles is an art, just like writing solutions to math problems; the former appears much more rarely than the later, though, so it's hard to learn.

Re new puzzles; I don't see why Slitherlink can't be posted. Fillomino is a rather complex type (at least I still can't figure out how to put the instructions in short), but I posted two. Ivan Koswara · 1 year, 2 months ago

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@Ivan Koswara Re Re trial and error: I'm curious to see some of these "laws" that you have. =D

Re Re solutions: Wow, nice walkthrough! Post more! I asked this question because it almost appears to be trend for people to just post final answer for puzzle, which will most likely bring dismay for unfamiliar users.

Re Re new puzzles: I don't see a nice way to ask the question. Should we ask something like "Solve this slitherlink puzzle, find the sum of numbers outside of these closed polygons."? On the other hand, are there any other puzzles that you think it's easy to post to Brilliant? For example, hashiwokakero is difficult to ask in this site, but numberlink will be easier. Pi Han Goh · 1 year, 2 months ago

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@Pi Han Goh Re trial and error: One simple example is in Fillomino, if there are two diagonally touching 2s, the other two squares making up a 2x2 square cannot be 2s. Things like that, small patterns that one can check. Slitherlink has a lot of such patterns.

Re solutions: That's the problem; they are really tiresome to write. :P Writing this kind of full walkthrough is a long process, and usually there are only few interesting parts; compared to a math proof, there are more interesting parts during writing math proofs than puzzle walkthroughs. Explaining particular difficult spots might be doable, though. I'll see if I can post walkthroughs or similar to such logic puzzles. (EDIT: I posted a solution to the first Fillomino. That's more or less my standard for complete walkthrough. That also gets boring quick.)

Re new puzzles: You should try participating in online puzzle competitions. (One that is coming up is Indian Puzzle Championship.) Here, puzzles have "answer keys": submit something that you get from the solution to indicate that you've solved it, to compensate that usually the solution cannot be typed in full. I used this approach in my Fillomino puzzles ("write the contents of the marked row/column"); this is also often used in Sudoku and other Latin square-based puzzles (including Futoshiki). For Slitherlink, most commonly it's something like "write the lengths of the horizontal segments along this gridline row" or "write the lengths of cells inside the loop along this row of squares". (IPC 2015 uses "write the longest horizontal segment along this gridline row".) Hashi is pretty indeed pretty difficult; I'd use something like "write the number of horizontal double bridges", or "write the vertical bridges that intersect this gridline row, using 1 for single and 2 for double".

While on this point, I'm considering to tag all such puzzles with a particular tag so we can search for them from a single tag. What would be the good tag? "Puzzle" is kind of too broad, while "Sudoku" and all other specific puzzle genres are too narrow (I want to see all, not only one type). (Besides, if we can agree for this, I can go through all the puzzles existing in Brilliant and maybe write up stuff.) Ivan Koswara · 1 year, 2 months ago

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@Ivan Koswara Re Trial and Error: Haha, that's what I called common sense! I find Slitherlink much more obvious for spotting patterns. I still couldn't solve the third one the list.

This is what I had so far, after a couple of iterations, and I'm pretty sure I made an error somewhere.

I'm only confident of the numbers in the orange circles. The others are trial and elimination within trial and elimination without any concrete results.

Re solutions: Yeah, but it's definitely worth the effort to write one complete solution.

Re new puzzles: I'm tried these puzzle championship before but I do not like the setup where time is a constraint. I prefer to take my time to solve puzzles that I'm not familiar with. Plus, most of these puzzles have really unusual constraints that doesn't appeal to me. Thanks for the tip on Slitherlink and Hashi, I will definitely try it some time when I had a chance to find a good puzzle.

Re tags: I've considered doing that as well. I've asked Calvin about this and he said we can look at StackExchange and search for the relevant tags. Off the top of my head, here are some of the tags:

Grid puzzles, Lateral thinking, polyomino, dissection, ...

Yes, I definitely agree on this, can we get started on this project? Pi Han Goh · 1 year, 2 months ago

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@Pi Han Goh Re Fillomino: That is a difficult Fillomino, but it's surprisingly pretty enjoyable. Hint: You might want to draw lines connecting squares to indicate that they belong to the same polyomino, like my solution below:

Re solution: That's true. If I have an hour or so to burn, I'll consider writing up solutions to puzzles.

Re new puzzles: Yes, sometimes time being a constraint puts off some people. When you want to appreciate the puzzles, it's better not to have times. On the other hand, with that you can also use some "questionable" tricks, meta tricks that depend on the puzzle having a unique solution: if you do something and find that you'll get multiple solutions, you know that you've made a mistake somewhere, and you don't have to wait until you find a later contradiction (that will be bound to happen, otherwise there are indeed multiple solutions).

Re tags: "Grid puzzles" is an interesting tag, although it might be confused with logic grid puzzles. "Lateral thinking" doesn't really fit; I equate lateral thinking with inductive reasoning, and lateral thinking puzzles clearly cannot be asked in Brilliant's form (except maybe in notes). "Polyomino" and "dissection" only hold for certain puzzle genres (like Fillomino), not all of them (like Sudoku). Ivan Koswara · 1 year, 2 months ago

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That's a great list. Thanks!

Under 2/3, I would like to add the cases of

  • If the problem was hard, simplify it
  • Add additional conditions / special scenarios
  • Remove a certain condition
  • What happens when we change a value?
  • Can this be generalized?
  • What happens in a similar situation?
  • Are there any interesting facts that you came across while solving the problem or reading the solution?

That's how I create my list of "Inspired by XXX" problems. Calvin Lin Staff · 1 year, 2 months ago

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@Calvin Lin I don't usually implement this feature: "If the problem was hard, simplify it" but I see the appeal to it. Thanks, I will give it a try! Pi Han Goh · 1 year, 2 months ago

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Thanks!! Apoorva Raj Bhadani · 1 year, 2 months ago

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That' what I was waiting for! Thanks Siddharth Singh · 1 year, 2 months ago

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Thanks :) Good insides Suneet Bendre · 1 year, 2 months ago

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Thanks for sharing! Deepak Kumar · 1 year, 2 months ago

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Enjoy your problems and solutions
By the way may I ask what do you do Are you still a student ?... Des O Carroll · 1 year, 2 months ago

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@Des O Carroll We are always learning, so no. Pi Han Goh · 1 year, 2 months ago

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