The On-Line Encyclopedia of Bongard Problems

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Shapes are congruent if (and only if) they are enclosed in the same space vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1077 BP1078 BP1079 BP1080 BP1081 * BP1083 BP1084 BP1085 BP1086 BP1087`
	KEYWORD	`stub, precise, allsorted`
	CONCEPT	`iff (info \| search)`
	AUTHOR	`Leo Crabbe`

More triangles on the right vs. more triangles on the left.

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	CROSSREFS	`Adjacent-numbered pages: BP1080 BP1081 BP1082 BP1083 BP1084 * BP1086 BP1087 BP1088 BP1089 BP1090`
	KEYWORD	`stub, dual, handed, leftright`
	AUTHOR	`Aaron David Fairbanks`

Rubik's Cubes which are solvable vs. not

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	CROSSREFS	`Adjacent-numbered pages: BP1086 BP1087 BP1088 BP1089 BP1090 * BP1092 BP1093 BP1094 BP1095 BP1096`
	EXAMPLE	`A cube which is solved apart from one edge flipped, or one corner twisted, would be unsolveable and so would fit on the right.`
	KEYWORD	`stub`
	AUTHOR	`Jago Collins`

Concave shapes whose cavities are similar to the shape vs. concave shape whose cavities are not similar to the shape.

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	COMMENTS	`"I am agnostic on whether to let this world include examples such as EX8932, where pixelation is used, or examples such as suggested by EX8928 similar to the "Topologist's Comb" (link in references) which are not locally path-connected. These two examples were provided by Aaron David Fairbanks." - Jago Collins 28th January 2021`
	REFERENCE	`https://en.wikipedia.org/wiki/Similarity_(geometry)` `https://en.wikipedia.org/wiki/Self-similarity` `https://en.wikipedia.org/wiki/Comb_space`
	CROSSREFS	`Adjacent-numbered pages: BP1093 BP1094 BP1095 BP1096 BP1097 * BP1099 BP1100 BP1101 BP1102 BP1103`
	EXAMPLE	`A circle with a circle cut out of it does not fit left, because with the circle cut out of it, our shape is no longer a circle.`
	KEYWORD	`stub, precise, allsorted, left-narrow, perfect, infinitedetail`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Jago Collins`

Constructible Polygon vs. Non-constructible Polygon

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	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`

Vertical axis of symmetry vs. no vertical axis of symmetry.

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	COMMENTS	`The solution for this Bongard Problem is also a (less specific) solution for BP500, "vertical axis of symmetry vs. no axis of symmetry".`
	CROSSREFS	`BP1207 is the same solution but using the horizontal axis instead of the vertical axis.` `BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.` `Adjacent-numbered pages: BP1201 BP1202 BP1203 BP1204 BP1205 * BP1207 BP1208 BP1209 BP1210 BP1211`
	KEYWORD	`stub, notso, stretch, left-narrow, traditional`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `vertical (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Horizontal axis of symmetry vs. no horizontal axis of symmetry.

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	CROSSREFS	`BP1206 is the same solution but using the vertical axis instead of the horizontal axis.` `BP1215 is the same solution but with the NW/SE diagonal instead of the vertical axis.` `Adjacent-numbered pages: BP1202 BP1203 BP1204 BP1205 BP1206 * BP1208 BP1209 BP1210 BP1211 BP1212`
	KEYWORD	`stub, notso, stretch, left-narrow, traditional`
	CONCEPT	`horizontal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

More triangles left than right vs. more triangles right than left.

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	COMMENTS	`The triangles vary in size in order to make the solution clearly about quantity, not "total mass".`
	CROSSREFS	`Adjacent-numbered pages: BP1203 BP1204 BP1205 BP1206 BP1207 * BP1209 BP1210 BP1211 BP1212 BP1213`
	KEYWORD	`stub, precise, spectrum, dual, handed, leftright, traditional`
	CONCEPT	`number (info \| search),` `triangle (info \| search),` `quantity_comparison (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Empty square present vs. no square present.

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	CROSSREFS	`Nearly identical to BP1221, which is the same except non-empty squares are allowed.` `See BP24 for "circle present vs. not".` `Adjacent-numbered pages: BP1204 BP1205 BP1206 BP1207 BP1208 * BP1210 BP1211 BP1212 BP1213 BP1214`
	KEYWORD	`stub, left-narrow, traditional`
	CONCEPT	`empty (info \| search),` `existence (info \| search),` `square (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

Vertical, horizontal, and both diagonal axes of symmetry vs. not (more specifically, one or fewer axes of symmetry).

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	CROSSREFS	`Adjacent-numbered pages: BP1205 BP1206 BP1207 BP1208 BP1209 * BP1211 BP1212 BP1213 BP1214 BP1215`
	KEYWORD	`stub, left-narrow, traditional, blackwhiteinvariant`
	CONCEPT	`symmetry_axis (info \| search),` `symmetry (info \| search),` `four (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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