# Looking for a Logical Puzzle with Scalability

I hope I am in the right place to be asking a question like this!

That being said, I am experimentalist in need of a 'good' logical puzzle. There are aspects of the puzzle I would like and other aspects I am trying to avoid due to too many potential confounding factors. Below is a list of these characteristics:

Things I am looking for:

1.) A logical puzzle that tests general intelligence/'talent' 2.) Highly visual e.g. geometric, pattern, etc.. 3.) Has scalability e.g. a puzzle that can easily be increased in difficulty, hence, increased size, number of objects, etc,.

Note: I am looking for basically an 'easy' version of a puzzle that comes with a 'harder' version that would be more cognitively loaded, but ultimately the puzzle needs to be the same.

Things I want to avoid:

1.) Potential for subjectivity on an inference level. I want to avoid any kind of logical puzzle that has a lot of verbal explanation or cultural context. These can create framing effects, differences in common language/semantics, cultural differences. I am trying to keep the process leading up to the answer as objective as possible. Therefore trying to avoid all verbal reasoning/logic puzzles.

I did think the 'Josephus Problem' was a really good potential puzzle, but it is really sensitive to increasing the number of static objects in terms of difficulty. I was also concerned with some subjects having a math advantage in comparison to others, but I highly doubt undergraduate math students know recursive algorithms.

Any other puzzles that would fit the above criteria would be awesome though! Need some serious help!

Thanks for the help in advance!

• Hi and welcome! How do you think about Raven's Progressive Matrices? – athin Apr 29 at 11:25
• Do you need just one "easy" and one "hard" version, or a whole spectrum shading smoothly from "very easy" to "requires superhuman intelligence", or what? – Gareth McCaughan Apr 29 at 12:25
• I suspect that different kinds of puzzles will scale up with different kinds of difficulty. What I mean is that for some making them larger will simply require greater powers of concentration and memory (e.g., multiplying larger and large rnumbers in one's head), for some it will be all about visual imagination, for some it will be a matter of reasoning that becomes more intricate, etc. So what sort of puzzle you want may depend on what faculties you want to tax more as the puzzle gets harder. – Gareth McCaughan Apr 29 at 12:27
• A finite set of maybe 5-6 variants scaling in difficulty would probably be appropriate. We are hoping that the hard task has around a response time of one or two minutes. – nl003 Apr 29 at 12:28
• I think we are probably looking more for visual imagination and fluid intelligence. Our primary analysis is not on the data associated with the subjects doing these puzzles. This is just a pre-test, where we will use the results from the pre-test subjects and put them in front of the primary subjects for the main analysis. – nl003 Apr 29 at 12:31

## 2 Answers

How about pre-constructed Minesweeper positions?

As for the desired features:

1) + Pure logic
2) + Purely visual
3) + Arbitrarily scalable (consistency checking proven to be NP-complete)

As for the disliked features:

1) + No words required
2) - Almost, but not quite, everyone already knows minesweeper

• This would probably be a good puzzle actually! I will put this on the list! Thank you! – nl003 Apr 29 at 13:56

If you're looking for a simple and pure visual puzzle, you can use:

"Spot The Twin" a.k.a "Find Two Identical Image" Puzzle

It ranges from an easy one like this...

... to an intermediate one...

... or even to a hard one...

... or if you want to make it in a single style, you can use something evil like this ;)

• Shouldn't the answer to the second one be 7 and 12 instead of 7 and 9? :) – KevinT Apr 29 at 14:34
• @KevinT Yep, you're correct! We should contact the author, ratselmeister... xD – athin Apr 29 at 14:37
• This does fit what I’m looking for, but I’m mildly concerned that the scaling of difficulty resembles the same puzzle, but in different artistic styles/environments. I’m trying to keep the puzzle symmetric across different difficulties. I will sit down and try to take one of the 3 you have shown and make simple/harder variations all else equal. :) – nl003 Apr 29 at 14:51
• @nl003 I'm updating my answer for that :) – athin Apr 29 at 14:58