This is a generalisation of Bongard Problems that allows them to have any number of sides. There is a sense in which this problem is about valid vs. invalid ways of partitioning a set of examples into equivalence classes.

https://en.wikipedia.org/wiki/Equivalence_class

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BP1148 BP1149 BP1150 BP1151 BP1152  *  BP1154 BP1155 BP1156 BP1157 BP1158

abstract, teach, meta (see left/right), miniproblems, infodense, structure, rules, miniworlds

zoom in left

Leo Crabbe

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BP1146 BP1147 BP1148 BP1149 BP1150  *  BP1152 BP1153 BP1154 BP1155 BP1156

right-null

Leo Crabbe

Left-sorted examples are sometimes called autobiographical or self-descriptive numbers.

https://oeis.org/A349595

https://en.wikipedia.org/wiki/Self-descriptive_number

See BP1147 for a similar idea.

BP1149 was inspired by this.

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nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable

Leo Crabbe

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BP1142 BP1143 BP1144 BP1145 BP1146  *  BP1148 BP1149 BP1150 BP1151 BP1152

nice, precise, notso, handed, leftright, left-narrow, grid, preciseworld, left-listable, right-listable

Leo Crabbe

This is a difficult-to-read attempt at making a Bongard Problem about perfect numbers. Grouping columns together to make rectangular arrays, each maximal (most dots possible) rectangular array of a particular height in any given example has the same number of dots in it (a perfect number, in left-sorted cases), and the dot-width of each array represents a particular divisor of that number.

It is not currently known whether there are a finite amount of examples that would be sorted left.

Every example in this Bongard Problem corresponds to a distinct natural number. There is not a way of representing the number 1 using the rules of construction for examples in this problem (if the problem were simply "Perfect number of dots vs. other number of dots", the example with 1 dot would be sorted right).

https://en.wikipedia.org/wiki/Perfect_number

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overriddensolution, left-listable, right-listable

Leo Crabbe

Although it is tempting at first to make a version of this Bongard Problem with the solution "Shape can be achieved by folding a square a finite amount of times vs. other shapes", this alternate Bongard Problem would just amount to having the solution "Convex shape with straight edges vs. concave shape or convex shape with at least one curved edge."

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precise, notso, stretch, left-narrow, finishedexamples, preciseworld

Leo Crabbe

Left-sorted problems have the keyword "finishedexamples" on the OEBP.

The addition does not have to be slight.

Left-sorted Problems usually have a very specific collection of examples, where the only images sorted all show the same type of object.

Any Bongard Problem where all examples are one shape outline will be sorted left, and (almost) any Bongard Problem where all examples are one fill shape will be sorted right.

See BP1144 for the version about both additions and erasures, and only slight changes are considered.

See BP1167 for a stricter version, the condition that all examples have the same amount of black and white.

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unwordable, notso, meta (see left/right), links, keyword, sideless, problemkiller

Leo Crabbe

This Problem is not to be taken seriously.

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example, overriddensolution, right-full, right-null, invalid, experimental, funny

Leo Crabbe

This classification is specifically concerned with changes to examples that leave them sortable, as there are almost always ways of adding details to a BP's examples that make them unsortable.

Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding either white or black, but not both.

Closely related to gap Problems and stable Problems.

Bongard Problems tagged finishedexamples will fit right.

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meta (see left/right), links, sideless, invariance

Leo Crabbe

This classification is specifically concerned with changes to examples that leave them sortable, as there are almost always ways of adding details to a BP's examples that make them unsortable.

Right-sorted BPs in this Bongard Problem are often Bongard Problems where there is always a way of adding to left-sorted examples to make them right-sorted, but not the other way around, or vice versa.

Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding either white or black, but not both.

Where appropriate, you can assume all images will have some room in a lip of white background around the border (ignoring https://en.wikipedia.org/wiki/Sorites_paradox ).

You can't expand the boundary of an image as you add detail to it. If image boundaries could be expanded, then any shape could be shrunken to a point in relation to the surrounding whiteness, which could then be filled in to make any other shape.

How should this treat cases in which just a few examples can't be added to at all (like an all-black box)? E.g. BP966. Should this be sorted right (should the one special case of a black box spoil it) or should it be sorted left (should examples that can't at all be further added be discounted)? Maybe we should only sort BPs in which all examples can be further added to. (See BP1143^left.) - Aaron David Fairbanks, Nov 12 2021

Is "addition of detail" context-dependent, or does it just mean any addition of blackness to the image? Say you have a points-and-lines Bongard Problem like BP1100, and you're trying to decide whether to sort it left or right here. You would just want to think about adding more points and lines to the picture. You don't want to get bogged down in thinking about whether black could be added to the image in a weird way so that a point gets turned into a line, or something. - Aaron David Fairbanks, Nov 13 2021

See BP1139 for Bongard Problems in which no example can be added to, period.

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meta (see left/right), links, sideless

Leo Crabbe