The On-Line Encyclopedia of Bongard Problems

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Number of dots is n factorial for some n vs. not so.

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	COMMENTS	`Zero is intentionally left out to avoid confusion (although it would fit right).`
	CROSSREFS	`Adjacent-numbered pages: BP984 BP985 BP986 BP987 BP988 * BP990 BP991 BP992 BP993 BP994`
	KEYWORD	`stub, precise, number, math, left-narrow, right-null, help, preciseworld`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP999

The collection of collections obeys the same rule as the individual collections vs. it does not.

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	COMMENTS	`Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)` `See BP793 and BP1004 for similar paradoxes.`
	CROSSREFS	`See BP1005 for the version about only numerical properties; examples in that BP would be sorted the same way here that they are there.` `See BP1003 for a similar idea. Rather than the collection of collections imitating the individual collections, BP1003 is about the total combined collection imitating the individual collections. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.` `Also see BP1004, is likewise about the whole satisfying the same rule as its parts, but there the parts don't themselves have to be collections; there the parts are just plain individual objects. The panels in BP999 (this BP) should be sorted the same way in BP1004.` `See BP1002, which is about only visual self-similarity instead of more general conceptual "self-similarity".` `Adjacent-numbered pages: BP994 BP995 BP996 BP997 BP998 * BP1000 BP1001 BP1002 BP1003 BP1004`
	KEYWORD	`nice, stub, abstract, creativeexamples, left-narrow, rules, miniworlds`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`[smaller \| same \| bigger] zoom in left \| zoom in right`
	AUTHOR	`Aaron David Fairbanks`

BP1004

The whole satisfies the same rule as its parts vs. not so.

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	COMMENTS	`The "whole" is the entire panel including the bounding box. A "part" is some region either stylistically different or amply separated in space from everything else. Smaller parts-within-parts don't count as parts.` `Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)` `See BP793 and BP999 for similar paradoxes.`
	CROSSREFS	`See BP1006 for the version about numerical properties where each part is a cluster of dots; examples in that BP would be sorted the same way here that they are there.` `See BP999 and BP1003 for versions where each object is itself a collection of objects, so that the focus is on rules specifically pertaining to collections (e.g. "all the objects are different").` `See BP1002 for a Bongard Problem about only visual self-similarity instead of conceptual self-similarity.` `The rule shown in each panel is "narrow" (see BP513^left and BP514^left).` `Adjacent-numbered pages: BP999 BP1000 BP1001 BP1002 BP1003 * BP1005 BP1006 BP1007 BP1008 BP1009`
	KEYWORD	`nice, abstract, anticomputer, creativeexamples, left-narrow, rules, miniworlds`
	CONCEPT	`recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1005

The collection of dot clumps has the same numerical property as each of the dot clumps vs. not so.

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	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.

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	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`

BP1011

Polygon can be inscribed in a circle vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1006 BP1007 BP1008 BP1009 BP1010 * BP1012 BP1013 BP1014 BP1015 BP1016`
	KEYWORD	`hard, precise, stretch, challenge, left-narrow, perfect, preciseworld`
	CONCEPT	`circle (info \| search),` `imagined_entity (info \| search)`
	WORLD	`fill_polygon [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1049

3 in a row vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1044 BP1045 BP1046 BP1047 BP1048 * BP1050 BP1051 BP1052 BP1053 BP1054`
	KEYWORD	`teach, creativeexamples, left-narrow, right-narrow, contributepairs, fixedgrid, miniworlds`
	AUTHOR	`Jago Collins`

BP1080

Image of a Bongard Problem vs. other image.

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	COMMENTS	`Various formats of Bongard Problems frequently seen on the OEBP are showcased on the left side here.`
	CROSSREFS	`See BP968, which distinguishes solvable Bongard Problems from other images still formatted like Bongard Problems (as opposed to this page, which distinguishes Bongard Problems from any other images.)` `Adjacent-numbered pages: BP1075 BP1076 BP1077 BP1078 BP1079 * BP1081 BP1082 BP1083 BP1084 BP1085`
	KEYWORD	`notso, teach, left-narrow, right-null`
	CONCEPT	`bongard_problem (info \| search),` `categorization (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1086

Endpoints of curve have the same height vs. not so.

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	REFERENCE	`Solution idea seen here: https://justpuzzles.wordpress.com/2019/07/05/bongard-problem-36-2.`
	CROSSREFS	`Adjacent-numbered pages: BP1081 BP1082 BP1083 BP1084 BP1085 * BP1087 BP1088 BP1089 BP1090 BP1091`
	KEYWORD	`nice, rotate, stretch, left-narrow, traditional`
	CONCEPT	`same (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Teun Spaans`

BP1093

"Inverted symmetry" present vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1088 BP1089 BP1090 BP1091 BP1092 * BP1094 BP1095 BP1096 BP1097 BP1098`
	KEYWORD	`nice, precise, allsorted, boundingbox, left-narrow, right-null, perfect, pixelperfect, preciseworld, bordercontent, blackwhiteinvariant`
	CONCEPT	`black_white_inversion (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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