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Bongard problem

Source: Bongard problem #112 by Douglas R. Hofstadter

I've scoured the internet, and I've yet to find an answer to this puzzle. (edit: It has been given the title of "Hardest Bongard Problem" presented on like 50 sites, without solution)

In a Bongard problem, you are given 12 pictures, 6 on one page and 6 on the other. The pictures on the left page conform to a rule, and the pictures on the right page conform to a different rule. Furthermore, a picture on one side cannot conform to the rule on the other side. The goal is to determine the rules.

You can find plenty of examples here: http://www.foundalis.com/res/bps/bpidx.htm

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  • $\begingroup$ Reminds me of the hour/minute/second hands on a clock. $\endgroup$
    – Ian MacDonald
    Aug 30, 2016 at 21:41
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    $\begingroup$ Ironically enough, the very same site you linked to has the solution -- but I'll let more people work on it, it's a deceptively simple rule. $\endgroup$
    – ffao
    Aug 30, 2016 at 21:55
  • $\begingroup$ Really? It doesn't seem to me that his site contains a list of solutions to the problems. $\endgroup$
    – greenturtle3141
    Aug 30, 2016 at 21:58
  • $\begingroup$ I've seen a solution elsewhere on the internet (I forget where). I find the rule rather an unnatural one and don't feel too bad about the fact that I didn't solve it before getting bored and looking at the answer :-). $\endgroup$
    – Gareth McCaughan ♦
    Aug 30, 2016 at 22:20
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    $\begingroup$ Well maybe I am unnatural; I know I'm difficult :p $\endgroup$
    – Jonathan Allan
    Aug 30, 2016 at 22:51

1 Answer 1

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It looks to me like

The two vertical distances (right) or two horizontal distances (left) separating the three dots in each image are the same, but not both (left page, right column, middle row is kind of a close call for matching both rules though)

Here is an image which

actually shows that top right of the right page seems a little off, (and clears up the left page, right column, middle row - only one pixel out though, and the dots don't exactly have obvious centres - they are quite fuzzy):
horizontal and vertical lines

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    $\begingroup$ Now that it's out in the open, I can link explicitly to the list of solutions to the first 200 problems of the foundalis site: foundalis.com/res/Foundalis_dissertation.pdf (scroll all the way down to appendix A). $\endgroup$
    – ffao
    Aug 30, 2016 at 22:25
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    $\begingroup$ So, now we will get a post of each of the others? $\endgroup$
    – Jonathan Allan
    Aug 30, 2016 at 22:49

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