The On-Line Encyclopedia of Bongard Problems

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Considering only the ways they are connected, anything that can be said about a given edge can be said about every other edge vs. not so.

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

	REFERENCE	`https://mathworld.wolfram.com/Edge-TransitiveGraph.html`
	CROSSREFS	`Adjacent-numbered pages: BP1104 BP1105 BP1106 BP1107 BP1108 * BP1110 BP1111 BP1112 BP1113 BP1114`
	KEYWORD	`precise, allsorted, notso, math, left-narrow, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1113

Bongard Problems relating to the OEBP vs. Bongard Problems unrelated to the OEBP.

BP503	BP504	BP518	BP542	BP546	BP919
BP930	BP943	BP967	BP1113	BP1121	BP1125
BP1150	BP1174

BP1	BP2	BP3	BP4	BP5	BP6
BP7	BP8	BP9	BP10	BP11	BP12
BP13	BP14	BP15	BP16	BP17	BP18
BP19	BP20	BP21	BP22	BP23	BP24
BP25	BP26	BP27	BP28	BP29	BP30
BP31	BP32	BP33	BP34	BP35	. . .

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

	COMMENTS	`Bongard Problems sorted left have the keyword "oebp" on the OEBP.` `Most Bongard Problems relating to the OEBP are meta.`
	CROSSREFS	`Adjacent-numbered pages: BP1108 BP1109 BP1110 BP1111 BP1112 * BP1114 BP1115 BP1116 BP1117 BP1118`
	KEYWORD	`notso, meta (see left/right), links, keyword, oebp, left-self, metameta`
	AUTHOR	`Leo Crabbe`

BP1116

Contains self somewhere within any area around any point within self vs. not so.

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

	COMMENTS	`Very similar to the less clearly-defined solution "tiles itself with infinitely many copies (different sizes allowed) vs. does not".` `The left hand side of this is a weaker condition than the left hand side of BP1241.`
	CROSSREFS	`Adjacent-numbered pages: BP1111 BP1112 BP1113 BP1114 BP1115 * BP1117 BP1118 BP1119 BP1120 BP1121`
	KEYWORD	`notso, perfect, infinitedetail`
	CONCEPT	`topological_density (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`connected_fractal [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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, precise, allsorted, notso, preciseworld`
	CONCEPT	`all (info \| search),` `number (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`William B Holland`

BP1142

Bongard Problems where there is no way to turn an example into any other sorted example by adding black OR white (not both) vs. Bongard Problems where some example can be altered in this way and remain sorted.

BP285	BP304	BP328	BP329	BP342	BP801
BP934	BP1017	BP1056	BP1104	BP1145	BP1155
BP1156	BP1223	BP1269

BP859

BP962

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	COMMENTS	`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.`
	CROSSREFS	`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.` `Adjacent-numbered pages: BP1137 BP1138 BP1139 BP1140 BP1141 * BP1143 BP1144 BP1145 BP1146 BP1147`
	KEYWORD	`unwordable, notso, meta (see left/right), links, keyword, sideless, problemkiller`
	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`

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, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

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 autobiographical or self-descriptive numbers.`
	REFERENCE	`https://oeis.org/A349595` `https://en.wikipedia.org/wiki/Self-descriptive_number`
	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`

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`

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`

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