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BP1005 The collection of dot clumps has the same numerical property as each of the dot clumps vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

This is a version of BP999 with only numbers.

Contrast BP1006, which is very similar.

Adjacent-numbered pages:
BP1000 BP1001 BP1002 BP1003 BP1004  *  BP1006 BP1007 BP1008 BP1009 BP1010

KEYWORD

nice, notso, hardsort, left-narrow, rules

CONCEPT recursion (info | search),
self-reference (info | search)

WORLD

[smaller | same | bigger]
zoom in left | zoom in right

AUTHOR

Aaron David Fairbanks

BP1006 The sum of all dot clumps has the same numerical property as each of the dot clumps vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

This is a version of BP1003 with only numbers.

Contrast BP1005, which is very similar.

Adjacent-numbered pages:
BP1001 BP1002 BP1003 BP1004 BP1005  *  BP1007 BP1008 BP1009 BP1010 BP1011

KEYWORD

nice, hardsort, left-narrow, rules

CONCEPT recursion (info | search),
self-reference (info | search)

WORLD

[smaller | same | bigger]
zoom in left | zoom in right

AUTHOR

Leo Crabbe, Aaron David Fairbanks

BP1110 The process that turns one object into the other is the same both ways vs. the process changes depending on which object is chosen as the starting point.
?
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Duality_(mathematics)

https://en.wikipedia.org/wiki/Involution_(mathematics)

CROSSREFS

This is a special case of BP841 and a generalisation of BP822.

Adjacent-numbered pages:
BP1105 BP1106 BP1107 BP1108 BP1109  *  BP1111 BP1112 BP1113 BP1114 BP1115

KEYWORD

nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering

CONCEPT function (info | search)

AUTHOR

Leo Crabbe

BP1127 There is no rule for how the objects in a cluster interrelate vs. there is.
(edit; present; nest [left/right]; search; history)
COMMENTS

Other ways of phrasing this:

"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.

The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.

CROSSREFS

Adjacent-numbered pages:
BP1122 BP1123 BP1124 BP1125 BP1126  *  BP1128 BP1129 BP1130 BP1131 BP1132

KEYWORD

abstract, creativeexamples, left-unknowable, rules, miniworlds

CONCEPT local_global (info | search)

WORLD

[smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1153 Valid multi-sided Bongard Problems vs. invalid multi-sided Bongard Problems.
(edit; present; nest [left/right]; search; history)
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, meta (see left/right), miniproblems, infodense, structure, rules, miniworlds

WORLD

zoom in left

AUTHOR

Leo Crabbe

BP1155 Shapes are sorted according to a simple rule that uniquely determines where everything goes vs. shapes are sorted according to some other rule (or lack thereof).
(edit; present; nest [left/right]; search; history)
CROSSREFS

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

KEYWORD

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

AUTHOR

Leo Crabbe

BP1157 The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

REFERENCE

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

CROSSREFS

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

KEYWORD

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

CONCEPT function (info | search)

AUTHOR

Leo Crabbe

BP1158 Bongard Problems in which each example communicates a rule vs. other Bongard Problems.
BP346
BP349
BP350
BP351
BP352
BP353
BP354
BP355
BP356
BP357
BP361
BP362
BP365
BP372
BP379
BP380
BP393
BP792
BP805
BP839
BP841
BP843
BP845
BP846
BP848
BP849
BP852
BP855
BP870
BP893
BP917
BP951
BP973
BP975
BP979

. . .

?
BP347
(edit; present; nest [left/right]; search; history)
COMMENTS

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


In the typical "rules" Bongard Problem, it is possible to come up with many convoluted rules that fit each example, but the intended interpretation is the only simple and obvious one.


Since it is difficult to communicate a rule with little detail, "rules" Bongard Problems are usually infodense.

Typically, each example is itself a bunch of smaller examples that all obey the rule. It is the same as how a Bongard Problems relies on many examples to communicate rules; likely just one example wouldn't get the answer across.

On the other hand, in BP1157 for example, each intended rule is communicated by just one example; these rules have to be particularly simple and intuitive, and the individual examples have to be complicated enough to communicate them.

Often, each rule is communicated by showing several examples of things satisfying it. (See keywords left-narrow and right-narrow.) Contrast Bongard Problems, which are more communicative, by showing some examples satisfying the rule and some examples NOT satisfying the rule.


A "rules" Bongard Problem is often collective. Some examples may admit multiple equally plausible rules, and the correct interpretation of each example only becomes clear once the solution is known. The group of examples together improve the solver's confidence about having understood each individual one right.

It is common that there will be one or two examples with multiple reasonable interpretations due to oversight of the author.

CROSSREFS

All meta Bongard Problems are "rules" Bongard Problems.

Many other Bongard-Problem-like structures seen on the OEBP are also about recognizing a pattern. (See keyword structure.)


"Rules" Bongard Problems are abstract, although the individual rules in them may not be abstract. "Rules" Bongard Problems also usually have the keyword creativeexamples.

Adjacent-numbered pages:
BP1153 BP1154 BP1155 BP1156 BP1157  *  BP1159 BP1160 BP1161 BP1162 BP1163

KEYWORD

fuzzy, meta (see left/right), links, keyword, left-self, rules

AUTHOR

Aaron David Fairbanks

BP1257 The rule is about squares having a certain relationship with their neighbors vs. it is not.
(edit; present; nest [left/right]; search; history)
COMMENTS

"Local vs. global."


For clarity, rules involving diagonal neighbors or squares more than one step away are never used.


The similar solution "Each square can be deduced from its neighbors vs. not so" does not quite work; for example EX8114 would then not fit left. See also BP1258 ("Each square can be deduced from the rest vs. not so").

CROSSREFS

Adjacent-numbered pages:
BP1252 BP1253 BP1254 BP1255 BP1256  *  BP1258 BP1259 BP1260 BP1261 BP1262

KEYWORD

structure, rules, grid, miniworlds

CONCEPT local_global (info | search)

WORLD

grid_of_images_with_rule [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1258 It is possible to deduce the contents of any square from the rest vs. it is not.
(edit; present; nest [left/right]; search; history)
CROSSREFS

BP979 is very similar: whether a particular square can be deduced from the rest.

Adjacent-numbered pages:
BP1253 BP1254 BP1255 BP1256 BP1257  *  BP1259 BP1260 BP1261 BP1262 BP1263

KEYWORD

notso, rules, grid, miniworlds

CONCEPT convey_enough_information (info | search),
choice (info | search)

WORLD

grid_of_images_with_rule [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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