# Can you solve my meta-problem?

This is a metapuzzle of Bongard problems. Rules (quoted from here)

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.

This is the problem:

I use the following reference system:

Feedback is appreciated.

• Is the answer simply.. rot13(Gur yrsg fvqr fubhyq or n inyvq Obatneq chmmyr, juvyr gur evtug fnvq vf vainyvq.)? Feb 10 '20 at 3:32
• @athin yes. it is easy if you already know BPs.
– JAGO
Feb 11 '20 at 9:56

The Bongard problems on the 1 side of the Meta-Bongard are all easy to solve (Numbers are OP's reference system):

1A:

Nothing | Something

1B:

White shape | Black shape

1C:

Square | Non-Square Rectangle

1D:

Big thing | Small thing

1E:

Threesome | Foursome

1F:

Black Circle | White Triangle

The 2 side is significantly harder... (Bold Numbers are Meta-Bongard box, Italic are Bongard)

2A:

Here, the two sides are exactly the same, so there is no possible rule to differentiate them.

2B:

Here, there is an apparent rule: Arranged | Scrambled.
Unfortunately, the order of the pieces cannot be used to distinguish the sides of a Bongard problem, and the pieces themselves are otherwise identical.

2C:

This one is the same as 1C - except that its 2D has been replaced with a Square, breaking the rule and preventing a new rule from being possible (as the shapes are otherwise identical or randomized).

2D:

Here, the two sides are almost, but not quite, identical - shades of 2A! There is an apparent rule here, though: Bigger | Smaller.
Unfortunately, much like in 2B, this sort of comparison isn't a valid way to make a rule, and the "small" things are too close in size to the "big" things to just copy-paste the rule for 1D.

2E:

Here, both sides are just a single dot, randomly placed. There's almost a rule here (Centered | Not Centered), but 2F breaks it.

2F:

Here, both sides are just noise. I'm sure a dedicated computer could tease a rule out of this one, but it won't be human readable and will feel very contrived - best not to bother.

So what's the rule for the Meta-Bongard?

I regret to inform you that I cheated - I decoded @athin's rot13 comment under the question. The rule is Valid | Invalid.
That is, the 1 side are all valid Bongard problems, and the 2 side are all invalid Bongard problems. I had an inkling of this, but 2C threw me for a loop (I couldn't see that it was different from 1C until it was too late).

• You may have cheated but the most difficult part was rot13(gb cebir gung gur OC ba gur evtug jrer abg inyvq), so thanks for that detailed answer. Feb 25 '21 at 13:10