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BP1153 Valid multi-sided Bongard Problems vs. invalid multi-sided Bongard Problems.
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COMMENTS

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.

CROSSREFS

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

Adjacent-numbered pages:
BP1148 BP1149 BP1150 BP1151 BP1152  *  BP1154 BP1155 BP1156 BP1157 BP1158

KEYWORD

abstract, teach, infodense, structure, rules, miniworlds

WORLD

zoom in left

AUTHOR

Leo Crabbe

BP1151 Section of the image is a Bongard Problem vs. no section of the image is a Bongard Problem.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1146 BP1147 BP1148 BP1149 BP1150  *  BP1152 BP1153 BP1154 BP1155 BP1156

AUTHOR

Leo Crabbe

BP1149 Number in the Nth box (from the left) is how many numbers appear N times vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Inspired by BP1148.

Adjacent-numbered pages:
BP1144 BP1145 BP1146 BP1147 BP1148  *  BP1150 BP1151 BP1152 BP1153 BP1154

KEYWORD

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

CONCEPT self-reference (info | search)

AUTHOR

Aaron David Fairbanks

BP1148 Number of dots in the Nth box (from the left) is how many times the number (N - 1) appears in the whole diagram vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted examples are sometimes called self-descriptive sequences.

CROSSREFS

See BP1147 for a similar idea.

BP1149 was inspired by this.

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

KEYWORD

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

CONCEPT self-reference (info | search)

AUTHOR

Leo Crabbe

BP1147 Columns of the table could be respectively labeled "Number" and "Number of times number appears in this table" vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1142 BP1143 BP1144 BP1145 BP1146  *  BP1148 BP1149 BP1150 BP1151 BP1152

KEYWORD

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

CONCEPT self-reference (info | search)

AUTHOR

Leo Crabbe

BP1146 Same number of dots in top row as in leftmost column vs not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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).

REFERENCE

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

CROSSREFS

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

KEYWORD

overriddensolution, left-listable

AUTHOR

Leo Crabbe

BP1145 Polygon that can be achieved by folding a square once vs. other polygons.
(edit; present; nest [left/right]; search; history)
COMMENTS

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."

CROSSREFS

Adjacent-numbered pages:
BP1140 BP1141 BP1142 BP1143 BP1144  *  BP1146 BP1147 BP1148 BP1149 BP1150

KEYWORD

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

CONCEPT square (info | search)

AUTHOR

Leo Crabbe

BP1141 Object inside of bounding box vs. object outside of bounding box.
(edit; present; nest [left/right]; search; history)
COMMENTS

This Problem is not to be taken seriously.

CROSSREFS

Adjacent-numbered pages:
BP1136 BP1137 BP1138 BP1139 BP1140  *  BP1142 BP1143 BP1144 BP1145 BP1146

KEYWORD

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

AUTHOR

Leo Crabbe

BP1138 Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups
(edit; present; nest [left/right]; search; history)
COMMENTS

Attributes are shading, shape, and number.

There are always three groups.

This problem is related to the card game Set.

CROSSREFS

Adjacent-numbered pages:
BP1133 BP1134 BP1135 BP1136 BP1137  *  BP1139 BP1140 BP1141 BP1142 BP1143

KEYWORD

nice, notso

CONCEPT all (info | search),
number (info | search),
same (info | search),
two (info | search),
three (info | search)

AUTHOR

William B Holland

BP1137 Constructible Polygon vs. Non-constructible Polygon
(edit; present; nest [left/right]; search; history)
REFERENCE

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


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

CROSSREFS

Adjacent-numbered pages:
BP1132 BP1133 BP1134 BP1135 BP1136  *  BP1138 BP1139 BP1140 BP1141 BP1142

KEYWORD

stub, precise, math, hardsort, proofsrequired, preciseworld

AUTHOR

Jago Collins

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