Left-sorted Bongard Problems have the keyword "left-couldbe" on the OEBP.

Right-sorted Bongard Problems have the keyword "right-couldbe".

In a "couldbe" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "left-couldbe" BPs sound like "Could be a ___ vs. definitely not a ___" (and vice versa for "right-couldbe" BPs.)

To put it in mathematical jargon, there is a "projection" function from objects to pictures, such that objects satisfying property X are mapped to the same picture as objects not satisfying property X. Sorted on the "couldbe" side is the image (under projection) of the collection of objects satisfying property X.

Furthermore, usually X is a relatively narrow criterion, so that most objects do not satisfy it (see keywords left-narrow and right-narrow), and all pictures are in the image (under projection) of the collection of objects not satisfying property X.

Consider BP525, "Cropped image of a circle vs. not so." None of the left-hand examples are definitely an image of a circle, but they fit left because nothing indicates that they are not an image of a circle. A more pedantic solution to this Bongard Problem would be "There is a way of cropping a circle that gives this image vs. there isn't."

See also the keyword seemslike, where neither side can be confirmed.

Either "left-couldbe" or "right-couldbe" implies notso.

Although the descriptions of "left-couldbe" and "right-couldbe" sound similar to left-unknowable and right-unknowable, they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found.

"Left-couldbe" is usually left-narrow and "right-couldbe" usually right-narrow.

Adjacent-numbered pages:
BP1154 BP1155 BP1156 BP1157 BP1158  *  BP1160 BP1161 BP1162 BP1163 BP1164

dual, meta (see left/right), links, keyword, side, viceversa

Leo Crabbe

Operations depicted in right-sorted examples are called "commutative".

"Order matters" here means that if the objects in the top half were to switch places, the output would look different.

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

Adjacent-numbered pages:
BP1152 BP1153 BP1154 BP1155 BP1156  *  BP1158 BP1159 BP1160 BP1161 BP1162

nice, abstract, unwordable, notso, structure, rules, miniworlds

Leo Crabbe

Adjacent-numbered pages:
BP1151 BP1152 BP1153 BP1154 BP1155  *  BP1157 BP1158 BP1159 BP1160 BP1161

precise, minimal, boundingbox, left-finite, left-full, perfect, pixelperfect, finishedexamples, preciseworld, absoluteposition

Leo Crabbe

Adjacent-numbered pages:
BP1150 BP1151 BP1152 BP1153 BP1154  *  BP1156 BP1157 BP1158 BP1159 BP1160

abstract, unwordable, creativeexamples, right-unknowable, traditional, finishedexamples, rules

Leo Crabbe

This Problem is mostly concerned with categorising BPs whose examples aren't necessarily formatted as traditional Bongard Problems.

Adjacent-numbered pages:
BP1149 BP1150 BP1151 BP1152 BP1153  *  BP1155 BP1156 BP1157 BP1158 BP1159

meta (see left/right), links

visualbp [smaller | same | bigger]

Leo Crabbe

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

Adjacent-numbered pages:
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

Adjacent-numbered pages:
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.

Adjacent-numbered pages:
BP1143 BP1144 BP1145 BP1146 BP1147  *  BP1149 BP1150 BP1151 BP1152 BP1153

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

Leo Crabbe

Adjacent-numbered pages:
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

Adjacent-numbered pages:
BP1141 BP1142 BP1143 BP1144 BP1145  *  BP1147 BP1148 BP1149 BP1150 BP1151

overriddensolution, left-listable, right-listable

Leo Crabbe